Create charts to better understand data sets. For cross-sectional data, use a scatter chart. For time series data, use a line chart. Linear y = a + bx Logarithmic y = ln(x) Polynomial (2nd order) y = ax2 + bx + c Polynomial (3rd order) y = ax3 + bx2 + dx + e Power y = axb Exponential y = abx (the base of natural logarithms, e = 2.71828...is often used for the constant b) Right click on data series and choose Add trendline from pop-up menu Check the boxes Display Equation on chart and Display R-squared value on chart R2 (R-squared) is a measure of the \"fit\" of the line to the data. The value of R2 will be between 0 and 1. A value of 1.0 indicates a perfect fit and all data points would lie on the line; the larger the value of R2 the better the fit. Linear demand function: Sales = 20,512 - 9.5116(price) Line chart of historical crude oil prices Excel's Trendline tool is used to fit various functions to the data. Exponential Logarithmic Polynomial 2 Polynomial 3 Power y = 50.49e0.021x y = 13.02ln(x) + 39.60 y = 0.13x2 2.399x + 68.01 y = 0.005x3 0.111x2 + 0.648x + 59.497 y = 45.96x0.0169 R2 = 0.664 R2 = 0.382 R2 = 0.905 R2 = 0.928 * R2 = 0.397 Third order polynomial trendline fit to the data Figure 8.11 The R2 value will continue to increase as the order of the polynomial increases; that is, a 4th order polynomial will provide a better fit than a 3rd order, and so on. Higher order polynomials will generally not be very smooth and will be difficult to interpret visually. Thus, we don't recommend going beyond a third-order polynomial when fitting data. Use your eye to make a good judgment! Regression analysis is a tool for building mathematical and statistical models that characterize relationships between a dependent (ratio) variable and one or more independent, or explanatory variables (ratio or categorical), all of which are numerical. Simple linear regression involves a single independent variable. Multiple regression involves two or more independent variables. Finds a linear relationship between: - one independent variable X and - one dependent variable Y First, prepare a scatter plot to verify the data has a linear trend. Use alternative approaches if the data is not linear. Size of a house is typically related to its market value. X = square footage Y = market value ($) The scatter plot of the full data set (42 homes) indicates a linear trend. Market value = a + b square feet Two possible lines are shown below. Line A is clearly a better fit to the data. We want to determine the best regression line. Market value = 32,673 + $35.036 square feet The estimated market value of a home with 2,200 square feet would be: market value = $32,673 + $35.036 2,200 = $109,752 The regression model explains variation in market value due to size of the home. It provides better estimates of market value than simply using the average. Simple linear regression model: We estimate the parameters from the sample data: Let Xi be the value of the independent variable of the ith observation. When the value of the independent variable is Xi, then Yi = b0 + b1Xi is the estimated value of Y for Xi. Residuals are the observed errors associated with estimating the value of the dependent variable using the regression line: The best-fitting line minimizes the sum of squares of the residuals. Excel functions: =INTERCEPT(known_y's, known_x's) =SLOPE(known_y's, known_x's) Slope = b1 = 35.036 =SLOPE(C4:C45, B4:B45) Intercept = b0 = 32,673 =INTERCEPT(C4:C45, B4:B45) Estimate Y when X = 1750 square feet ^ Y = 32,673 + 35.036(1750) = $93,986 =TREND(C4:C45, B4:B45, 1750) Data > Data Analysis > Regression Input Y Range (with header) Input X Range (with header) Check Labels Excel outputs a table with many useful regression statistics. Multiple R -- | r |, where r is the sample correlation coefficient. The value of r varies from 1 to +1 (r is negative if slope is negative) R Square -- coefficient of determination, R2, which varies from 0 (no fit) to 1 (perfect fit) Adjusted R Square - adjusts R2 for sample size and number of X variables Standard Error - variability between observed and predicted Y values. This is formally called the standard error of the estimate, SYX. 53% of the variation in home market values can be explained by home size. The standard error of $7287 is less than standard deviation (not shown) of $10,553. ANOVA conducts an F-test to determine whether variation in Y is due to varying levels of X. ANOVA is used to test for significance of regression: H0: population slope coefficient = 0 H1: population slope coefficient 0 Excel reports the p-value (Significance F). Rejecting H0 indicates that X explains variation in Y. Home size is not a significant variable Home size is a significant variable p-value = 3.798 x 10-8 Reject H0: The slope is not equal to zero. Using a linear relationship, home size is a significant variable in explaining variation in market value. An alternate method for testing whether a slope or intercept is zero is to use a t-test: Excel provides the p-values for tests on the slope and intercept. Use p-values to draw conclusion Neither coefficient is statistically equal to zero. Confidence intervals (Lower 95% and Upper 95% values in the output) provide information about the unknown values of the true regression coefficients, accounting for sampling error. We may also use confidence intervals to test hypotheses about the regression coefficients. To test the hypotheses check whether B1 falls within the confidence interval for the slope. If it does, reject the null hypothesis. For the Home Market Value data, a 95% confidence interval for the intercept is [14,823, 50,523], and for the slope, [24.59, 45.48]. Although we estimated that a house with 1,750 square feet has a market value of 32,673 + 35.036(1,750) =$93,986, if the true population parameters are at the extremes of the confidence intervals, the estimate might be as low as 14,823 + 24.59(1,750) = $57,855 or as high as 50,523 + 45.48(1,750) = $130,113. Residual = Actual Y value Predicted Y value Standard residual = residual / standard deviation Rule of thumb: Standard residuals outside of 2 or 3 are potential outliers. Excel provides a table and a plot of residuals. This point has a standard residual of 4.53 Linearity examine scatter diagram (should appear linear) examine residual plot (should appear random) Normality of Errors view a histogram of standard residuals regression is robust to departures from normality Homoscedasticity: variation about the regression line is constant examine the residual plot Independence of Errors: successive observations should not be related. This is important when the independent variable is time. Linearity - linear trend in scatterplot - no pattern in residual plot Normality of Errors - residual histogram appears slightly skewed but is not a serious departure Homoscedasticity - residual plot shows no serious difference in the spread of the data for different X values. Independence of Errors - Because the data is cross-sectional, we can assume this assumption holds. A linear regression model with more than one independent variable is called a multiple linear regression model. We estimate the regression coefficientscalled partial regression coefficients b0, b1, b2,... bk, then use the model: The partial regression coefficients represent the expected change in the dependent variable when the associated independent variable is increased by one unit while the values of all other independent variables are held constant. The independent variables in the spreadsheet must be in contiguous columns. So, you may have to manually move the columns of data around before applying the tool. Key differences: Multiple R and R Square are called the multiple correlation coefficient and the coefficient of multiple determination, respectively, in the context of multiple regression. ANOVA tests for significance of the entire model. That is, it computes an F-statistic for testing the hypotheses: ANOVA tests for significance of the entire model. That is, it computes an F-statistic for testing the hypotheses: The multiple linear regression output also provides information to test hypotheses about each of the individual regression coefficients. If we reject the null hypothesis that the slope associated with independent variable i is 0, then the independent variable i is significant and improves the ability of the model to better predict the dependent variable. If we cannot reject H0, then that independent variable is not significant and probably should not be included in the model. Predict student graduation rates using several indicators: Regression model The value of R2 indicates that 53% of the variation in the dependent variable is explained by these independent variables. All coefficients are statistically significant. A good regression model should include only significant independent variables. However, it is not always clear exactly what will happen when we add or remove variables from a model; variables that are (or are not) significant in one model may (or may not) be significant in another. Therefore, you should not consider dropping all insignificant variables at one time, but rather take a more structured approach. Adding an independent variable to a regression model will always result in R2 equal to or greater than the R2 of the original model. Adjusted R2 reflects both the number of independent variables and the sample size and may either increase or decrease when an independent variable is added or dropped. An increase in adjusted R2 indicates that the model has improved. 1. 2. 3. Construct a model with all available independent variables. Check for significance of the independent variables by examining the p-values. Identify the independent variable having the largest pvalue that exceeds the chosen level of significance. Remove the variable identified in step 2 from the model and evaluate adjusted R2. (Don't remove all variables with p-values that exceed a at the same time, but remove only one at a time.) 4. Continue until all variables are significant. Banking Data Home value has the largest p-value; drop and re-run the regression. Bank regression after removing Home Value Adjusted R2 improves slightly. All X variables are significant. Use the t-statistic. If | t | < 1, then the standard error will decrease and adjusted R2 will increase if the variable is removed. If | t | > 1, then the opposite will occur. You can follow the same systematic approach, except using t-values instead of p-values. Multicollinearity occurs when there are strong correlations among the independent variables, and they can predict each other better than the dependent variable. When significant multicollinearity is present, it becomes difficult to isolate the effect of one independent variable on the dependent variable, the signs of coefficients may be the opposite of what they should be, making it difficult to interpret regression coefficients, and p-values can be inflated. Correlations exceeding 0.7 may indicate multicollinearity The variance inflation factor is a better indicator, but not computed in Excel. Colleges and Universities correlation matrix; none exceed the recommend threshold of 0.7 Banking Data correlation matrix; large correlations exist If we remove Wealth from the model, the adjusted R2 drops to 0.9201, but we discover that Education is no longer significant. Dropping Education and leaving only Age and Income in the model results in an adjusted R2 of 0.9202. However, if we remove Income from the model instead of Wealth, the Adjusted R2 drops to only 0.9345, and all remaining variables (Age, Education, and Wealth) are significant. Identifying the best regression model often requires experimentation and trial and error. The independent variables selected should make sense in attempting to explain the dependent variable Logic should guide your model development. In many applications, behavioral, economic, or physical theory might suggest that certain variables should belong in a model. Additional variables increase R2 and, therefore, help to explain a larger proportion of the variation. Even though a variable with a large p-value is not statistically significant, it could simply be the result of sampling error and a modeler might wish to keep it. Good models are as simple as possible (the principle of parsimony). Overfitting means fitting a model too closely to the sample data at the risk of not fitting it well to the population in which we are interested. In fitting the crude oil prices in Example 8.2, we noted that the R2value will increase if we fit higher-order polynomial functions to the data. While this might provide a better mathematical fit to the sample data, doing so can make it difficult to explain the phenomena rationally. In multiple regression, if we add too many terms to the model, then the model may not adequately predict other values from the population. Overfitting can be mitigated by using good logic, intuition, theory, and parsimony. Regression analysis requires numerical data. Categorical data can be included as independent variables, but must be coded numeric using dummy variables. For variables with 2 categories, code as 0 and 1. Employee Salaries provides data for 35 employees Predict Salary using Age and MBA (code as yes=1, no=0) Salary = 893.59 + 1044.15 Age + 14767.23 MBA If MBA = 0, salary = 893.59 + 1044 Age If MBA = 1, salary =15,660.82 + 1044 Age An interaction occurs when the effect of one variable is dependent on another variable. We can test for interactions by defining a new variable as the product of the two variables, X3 = X1 X2 , and testing whether this variable is significant, leading to an alternative model. Define an interaction between Age and MBA and re-run the regression. The MBA indicator is not significant; drop and re-run. Adjusted R2 increased slightly, and both age and the interaction term are significant. The final model is salary = 3,323.11 + 984.25 age + 425.58 MBA age When a categorical variable has k > 2 levels, we need to add k - 1 additional variables to the model. The Excel file Surface Finish provides measurements of the surface finish of 35 parts produced on a lathe, along with the revolutions per minute (RPM) of the spindle and one of four types of cutting tools used. Because we have k = 4 levels of tool type, we will define a regression model of the form Add 3 columns to the data, one for each of the tool type variables Regression results Surface finish = 24.49 + 0.098 RPM - 13.31 type B - 20.49 type C - 26.04 type D Curvilinear models may be appropriate when scatter charts or residual plots show nonlinear relationships. A second order polynomial might be used Here 1 represents the linear effect of X on Y and 2 represents the curvilinear effect. This model is linear in the parameters so we can use linear regression methods. The U-shape of the residual plot (a second-order polynomial trendline was fit to the residual data) suggests that a linear relationship is not appropriate. Add a variable for temperature squared. The model is: sales = 142,850 - 3,643.17 temperature + 23.3 temperature2 The regression analysis tool in XLMiner has some advanced options not available in Excel's Descriptive Statistics tool. Best-subsets regression evaluates either all possible regression models for a set of independent variables or the best subsets of models for a fixed number of independent variables. Best subsets evaluates models using a statistic called Cp, (the Bonferroni criterion). Cp estimates the bias introduced in the estimates of the responses by having an underspecified model (a model with important predictors missing). If Cp is much greater than the number of independent variables plus 1, there is substantial bias. The full model always has Cp = k + 1. If all models except the full model have large Cps, it suggests that important predictor variables are missing. Models with a minimum value or having Cp less than or at least close to are good models to consider. Backward Elimination begins with all independent variables in the model and deletes one at a time until the best model is identified. Forward Selection begins with a model having no independent variables and successively adds one at a time until no additional variable makes a significant contribution. Stepwise Selection is similar to Forward Selection except that at each step, the procedure considers dropping variables that are not statistically significant. Sequential Replacement replaces variables sequentially, retaining those that improve performance. These options might terminate with a different model. Exhaustive Search looks at all combinations of variables to find the one with the best fit, but it can be time consuming for large numbers of variables. 9-68 Click the Predict button in the Data Mining group and choose Multiple Linear Regression. 9-69 Enter the range of the data (including headers) Move the appropriate variables to the boxes on the right. Add independent variables to the Selected Variables box Add the dependent variable (Balance) to the Output Variable box Click Next Screenshot of finished step 1 1) Select the output options: check Fitted Values and ANOVA table 2) Check the Summary Report box. 3) Before clicking Finish, click on the Variable Selection button. Check Perform variable selection Select Backward Elimination procedure Click OK 4) Click Finish XLMiner will generate analysis results in three worksheets Screenshot of the top part of the MLR_Output table Click the links in Output Navigator table to view results Regression output (all variables) and ANOVA table Variable Selection If you click \"Choose Subset,\" XLMiner will create a new worksheet with the results for this model. If select Best Subsets as the selection procedure for Variable Selection (see slide 72) then the variable selection output will be similar to that shown in figure 8.43 Typically choose the model with the highest adjusted R2. Models with a minimum value of Cp or having Cp less than or at least close to k + 1 are good models to consider. Probability is a quasi-hypothesis test that a given subset is acceptable; if this is less than 0.05, you can rule out that subset. Dealer Satisfaction Survey Scale: North America 2010 2011 2012 2013 2014 0 1 2 3 4 1 0 1 1 2 0 0 1 2 3 2 2 1 6 5 14 14 8 12 15 22 20 34 34 44 5 Sample Size 11 50 14 50 15 60 45 100 56 125 0 0 0 0 1 0 0 0 1 1 0 0 1 1 2 2 2 4 3 4 6 6 11 12 22 2 2 14 33 60 10 10 30 50 90 2010 2011 2012 2013 2014 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 3 2 2 2 4 7 8 15 21 17 4 4 7 6 8 15 15 25 30 30 2010 2011 2012 2013 2014 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 2 1 1 2 2 2 3 3 5 7 0 0 1 3 2 5 5 6 10 12 2012 2013 2014 0 0 0 0 0 0 0 1 1 1 4 5 0 2 8 0 0 2 1 7 16 South America 2010 2011 2012 2013 2014 Europe Pacific Rim China End-User Satisfaction North America 2010 2011 2012 2013 2014 0 1 1 1 0 0 1 3 2 2 2 2 2 6 4 5 4 3 3 15 18 17 15 15 4 37 35 34 33 31 Sample 5 Size 38 100 40 100 41 100 46 100 49 100 South America 2010 2011 2012 2013 2014 1 1 0 0 0 2 3 2 2 2 5 6 6 5 5 18 17 19 20 19 36 36 37 37 37 38 37 36 36 37 100 100 100 100 100 2010 2011 2012 2013 2014 1 1 1 1 0 2 2 1 1 1 4 5 4 3 2 21 21 26 17 19 36 34 37 41 45 36 37 31 37 33 100 100 100 100 100 2010 2011 2012 2013 2014 2 1 1 0 0 3 2 2 2 1 5 7 5 4 3 15 15 16 17 19 41 41 40 40 42 34 34 36 37 35 100 100 100 100 100 2012 2013 2014 0 1 0 3 2 1 3 2 1 6 4 3 28 30 31 10 11 14 50 50 50 Europe Pacific Rim China 2014 Customer Survey Region NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA Quality Ease of Use Price Service 4 1 3 4 4 4 4 5 4 5 4 3 5 4 4 4 5 4 5 4 5 5 3 5 5 4 4 2 5 5 4 5 4 4 4 5 4 5 4 5 4 5 1 4 5 5 4 4 5 4 3 3 4 5 4 4 5 4 3 5 5 5 2 5 5 4 2 5 5 4 2 5 4 5 4 4 4 4 5 4 4 4 2 4 4 3 3 4 5 5 2 5 5 3 4 3 5 4 4 5 5 5 2 5 5 5 5 3 4 4 5 4 5 4 4 4 5 1 5 5 5 4 3 5 4 5 1 4 4 4 3 5 5 3 4 4 5 5 2 4 5 4 4 4 5 5 4 4 5 5 4 5 4 3 3 5 5 4 4 3 5 4 3 4 5 5 1 5 5 4 5 4 3 4 3 4 5 4 2 4 5 5 4 5 5 5 3 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 5 5 5 5 5 5 4 5 5 5 4 5 4 5 5 5 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Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Pac Pac Pac Pac Pac Pac Pac Pac Pac Pac China China China China China China China 3 4 4 4 4 3 3 4 5 5 4 3 3 4 5 5 5 3 4 4 5 4 3 4 5 5 4 4 5 2 5 4 5 5 5 4 4 5 4 5 4 3 5 5 5 4 4 4 4 4 4 4 3 5 4 4 4 4 5 5 5 4 5 4 4 3 5 4 5 5 4 5 5 4 5 3 5 3 4 4 4 5 4 4 5 4 3 4 4 5 2 4 4 5 5 4 4 4 4 4 3 1 4 5 4 5 1 5 5 5 5 4 3 5 5 4 4 4 4 4 4 4 3 4 3 4 2 4 3 4 5 4 1 4 5 4 4 5 4 4 3 4 4 4 4 3 3 3 3 3 4 4 3 3 2 4 3 5 5 1 4 4 3 4 5 4 5 4 5 4 5 4 4 2 4 5 4 4 3 4 4 3 5 5 5 4 4 4 4 5 3 4 5 4 3 3 3 2 3 2 China China China 3 3 2 4 4 3 3 2 2 3 2 1 Complaints Month World NA SA Eur Pac Jan-10 169 102 12 52 Feb-10 187 115 13 55 Mar-10 210 128 15 61 Apr-10 226 136 16 67 May-10 232 137 17 73 Jun-10 261 151 19 82 Jul-10 245 140 18 80 Aug-10 223 128 16 76 Sep-10 195 103 15 73 Oct-10 174 96 14 62 Nov-10 154 84 11 59 Dec-10 163 99 9 54 Jan-11 195 123 10 59 Feb-11 221 141 13 62 Mar-11 240 152 16 66 Apr-11 264 163 20 70 May-11 283 178 22 75 Jun-11 296 170 28 86 Jul-11 269 153 25 81 Aug-11 256 146 23 79 Sep-11 231 131 20 73 Oct-11 214 125 16 68 Nov-11 201 118 13 66 Dec-11 171 96 11 61 Jan-12 200 112 15 66 Feb-12 216 117 18 71 Mar-12 234 126 20 76 Apr-12 253 138 23 79 May-12 282 152 26 85 Jun-12 305 163 30 91 Jul-12 296 156 28 89 Aug-12 279 148 26 86 Sep-12 266 143 24 82 Oct-12 243 131 21 76 Nov-12 232 128 18 73 Dec-12 203 107 15 70 Jan-13 216 110 19 74 Feb-13 239 123 23 79 Mar-13 266 138 26 83 Apr-13 284 150 30 88 May-13 315 169 33 91 Jun-13 340 181 37 95 Jul-13 319 169 34 92 Aug-13 304 160 32 90 Sep-13 277 141 29 87 Oct-13 250 123 26 83 Nov-13 228 112 24 77 Dec-13 213 105 23 74 Jan-14 240 121 26 80 Feb-14 251 126 28 82 Mar-14 281 148 31 85 Apr-14 298 155 35 89 May-14 322 168 39 95 Jun-14 350 183 43 98 Jul-14 330 170 41 95 Aug-14 311 158 38 93 Sep-14 289 149 33 89 Oct-14 265 136 30 85 Nov-14 239 121 26 80 Dec-14 219 108 23 76 China 3 4 6 7 5 9 7 3 4 2 0 1 3 5 6 11 8 12 10 8 7 5 4 3 4 6 9 11 14 15 18 15 13 12 10 7 8 10 13 11 15 19 17 15 14 12 10 7 8 10 12 13 12 15 14 13 11 8 7 7 3 4 3 2 5 6 5 4 4 3 3 4 5 4 6 5 7 8 7 7 6 6 5 4 5 5 5 6 8 11 10 9 7 6 5 5 A B C D E F G 1 Mower Unit Sales 2 3 Month NA SA Europe Pacific China World 4 Jan-10 6000 200 720 100 0 7020 Feb-10 7950 220 990 120 0 9280 5 Mar-10 8100 250 1320 110 0 9780 6 Apr-10 9050 280 1650 120 0 11100 7 May-10 9900 310 1590 130 0 11930 8 Jun-10 10200 300 1620 120 0 12240 9 Jul-10 8730 280 1590 140 0 10740 10 Aug-10 8140 250 1560 130 0 10080 11 Sep-10 6480 230 1590 130 0 8430 12 Oct-10 5990 220 1320 120 0 7650 13 Nov-10 5320 210 990 130 0 6650 14 Dec-10 4640 180 660 140 0 5620 15 Jan-11 5980 210 690 140 0 7020 16 Feb-11 7620 240 1020 150 0 9030 17 Mar-11 8370 250 1290 140 0 10050 18 Apr-11 8830 290 1620 150 0 10890 19 May-11 9310 330 1650 130 0 11420 20 Jun-11 10230 310 1590 140 0 12270 21 Jul-11 8720 290 1560 150 0 10720 22 Aug-11 7710 270 1530 140 0 9650 23 Sep-11 6320 250 1590 150 0 8310 24 Oct-11 5840 250 1260 160 0 7510 25 Nov-11 4960 240 900 150 0 6250 26 Dec-11 4350 210 660 150 0 5370 27 Jan-12 6020 220 570 160 0 6970 28 Feb-12 7920 250 840 150 0 9160 29 Mar-12 8430 270 1110 160 0 9970 30 Apr-12 9040 310 1500 170 0 11020 31 May-12 9820 360 1440 160 0 11780 32 Jun-12 10370 330 1410 170 0 12280 33 Jul-12 9050 310 1440 160 0 10960 34 Aug-12 7620 300 1410 170 0 9500 35 Sep-12 6420 280 1350 180 0 8230 36 Oct-12 5890 270 1080 180 0 7420 37 Nov-12 5340 260 840 190 0 6630 38 Dec-12 4430 230 510 180 0 5350 39 Jan-13 6100 250 480 200 0 7030 40 Feb-13 8010 270 750 190 0 9220 41 Mar-13 8430 280 1140 200 0 10050 42 Apr-13 9110 320 1410 210 0 11050 43 May-13 9730 380 1340 190 0 11640 44 Jun-13 10120 360 1360 200 0 12040 45 Jul-13 9080 320 1410 200 0 11010 46 Aug-13 7820 310 1490 210 0 9830 47 Sep-13 6540 300 1310 220 0 8370 48 Oct-13 6010 290 980 210 0 7490 49 Nov-13 5270 270 770 220 0 6530 50 Dec-13 5380 260 430 230 0 6300 51 Jan-14 6210 270 400 200 0 7080 52 Feb-14 8030 280 750 190 0 9250 53 Mar-14 8540 300 970 210 0 10020 54 Apr-14 9120 340 1310 220 5 10995 55 May-14 9570 390 1260 200 16 11436 56 Jun-14 10230 380 1240 210 22 12082 57 Jul-14 9580 350 1300 230 26 11486 58 Aug-14 7680 340 1250 220 14 9504 59 Sep-14 6870 320 1210 220 15 8635 60 Oct-14 5930 310 970 230 11 7451 61 Nov-14 5260 300 650 240 3 6453 62 Dec-14 4830 290 300 230 1 5651 63 Tractor Unit Sales Month NA Jan-10 Feb-10 Mar-10 Apr-10 May-10 Jun-10 Jul-10 Aug-10 Sep-10 Oct-10 Nov-10 Dec-10 Jan-11 Feb-11 Mar-11 Apr-11 May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11 Dec-11 Jan-12 Feb-12 Mar-12 Apr-12 May-12 Jun-12 Jul-12 Aug-12 Sep-12 Oct-12 Nov-12 Dec-12 Jan-13 Feb-13 Mar-13 Apr-13 May-13 Jun-13 Jul-13 Aug-13 Sep-13 Oct-13 Nov-13 Dec-13 Jan-14 Feb-14 Mar-14 Apr-14 May-14 Jun-14 Jul-14 Aug-14 Sep-14 Oct-14 Nov-14 Dec-14 SA 570 611 630 684 650 600 512 500 478 455 407 360 571 650 740 840 830 760 681 670 640 620 570 533 620 792 890 960 1040 1032 1006 910 803 730 699 647 730 930 1160 1510 1650 1490 1460 1390 1360 1340 1240 1103 1250 1550 1820 2010 2230 2490 2440 2334 2190 2080 2050 2004 Eur 250 270 260 270 280 270 264 280 290 280 290 280 320 350 390 440 470 490 481 460 460 440 436 420 510 590 610 600 620 640 590 600 670 630 710 570 650 680 724 730 760 800 840 830 820 810 827 750 780 805 830 890 930 980 1002 970 960 930 920 902 Pac 560 600 680 650 580 590 760 645 650 670 888 850 620 760 742 780 690 721 680 711 695 650 680 657 610 680 730 820 810 807 760 720 660 630 603 570 500 590 620 730 740 720 670 610 599 560 550 520 480 523 560 570 590 600 580 570 550 530 517 490 China 212 230 240 263 269 280 290 270 263 258 240 230 250 275 270 280 290 300 312 305 290 260 250 240 250 250 260 270 290 310 340 320 313 290 280 260 287 290 300 310 330 340 350 341 330 320 300 290 200 210 220 230 253 270 280 250 230 220 190 190 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 12 20 22 20 24 20 31 30 37 32 33 35 50 63 68 70 82 80 90 100 102 110 114 111 121 123 120 130 136 134 132 137 130 139 131 World 1592 1711 1810 1867 1779 1740 1826 1695 1681 1663 1825 1720 1761 2035 2142 2340 2280 2271 2154 2146 2085 1970 1936 1850 2000 2324 2510 2672 2780 2813 2716 2581 2476 2317 2324 2080 2202 2540 2867 3348 3550 3432 3400 3261 3209 3132 3027 2777 2821 3209 3553 3820 4133 4476 4436 4256 4067 3890 3816 3717 Industry Mower Total Sales Month NA SA Eur Pac Jan-10 60000 571 13091 Feb-10 77184 611 17679 Mar-10 77885 658 22759 Apr-10 86190 778 27966 May-10 96117 886 27895 Jun-10 97143 882 30566 Jul-10 84757 848 29444 Aug-10 79804 735 28364 Sep-10 64800 657 28393 Oct-10 59307 595 24444 Nov-10 52157 553 18000 Dec-10 45049 462 12453 Jan-11 58627 553 12778 Feb-11 76200 615 18214 Mar-11 82871 658 23889 Apr-11 84904 784 29455 May-11 93100 846 29464 Jun-11 93000 838 27414 Jul-11 83048 763 27368 Aug-11 74854 694 27321 Sep-11 60769 625 29444 Oct-11 55619 610 23774 Nov-11 48155 571 17308 Dec-11 42647 512 12941 Jan-12 57885 537 10962 Feb-12 77647 595 15273 Mar-12 81845 659 20556 Apr-12 86095 756 26786 May-12 91776 878 24828 Jun-12 100680 825 24737 Jul-12 86190 756 24828 Aug-12 71887 714 25179 Sep-12 60000 651 24545 Oct-12 55566 643 19286 Nov-12 50857 619 15273 Dec-12 42596 548 9107 Jan-13 58095 581 8571 Feb-13 75566 614 13158 Mar-13 80286 622 19655 Apr-13 85140 727 25179 May-13 90093 826 23103 Jun-13 95472 783 24286 Jul-13 87308 681 24737 Aug-13 74476 646 26607 Sep-13 61698 625 22982 Oct-13 57238 617 16897 Nov-13 50673 587 13750 Dec-13 51238 591 7818 Jan-14 59712 563 7547 Feb-14 77961 571 13889 Mar-14 83725 625 18302 Apr-14 90297 723 25192 May-14 91143 848 24706 Jun-14 99320 792 25306 Jul-14 93922 745 27083 Aug-14 73143 739 26042 Sep-14 66699 667 26304 Oct-14 56476 660 22558 Nov-14 51068 625 14773 Dec-14 46893 608 6977 1045 1111 1068 1237 1313 1176 1359 1238 1215 1154 1262 1386 1443 1515 1373 1442 1215 1333 1415 1296 1402 1468 1351 1389 1509 1402 1524 1574 1468 1560 1441 1545 1667 1698 1810 1731 1887 1845 1923 1981 1810 1942 1961 2000 2075 2019 2095 2150 1852 1743 1892 2037 1887 1944 2170 2037 2018 2072 2182 2035 World 74662 96585 102369 116171 126210 129768 116409 110141 95065 85500 71972 59349 73401 96545 108791 116584 124625 122585 112594 104164 92241 81470 67386 57489 70892 94917 104583 115211 118949 127801 113216 99325 86863 77193 68558 53982 69135 91182 102486 113027 115832 122482 114686 103729 87381 76771 67105 61797 69673 94165 104544 118250 118583 127363 123919 101961 95688 81766 68648 56510 Industry Tractor Total Sales Month NA Jan-10 Feb-10 Mar-10 Apr-10 May-10 Jun-10 Jul-10 Aug-10 Sep-10 Oct-10 Nov-10 Dec-10 Jan-11 Feb-11 Mar-11 Apr-11 May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11 Dec-11 Jan-12 Feb-12 Mar-12 Apr-12 May-12 Jun-12 Jul-12 Aug-12 Sep-12 Oct-12 Nov-12 Dec-12 Jan-13 Feb-13 Mar-13 Apr-13 May-13 Jun-13 Jul-13 Aug-13 Sep-13 Oct-13 Nov-13 Dec-13 Jan-14 Feb-14 Mar-14 Apr-14 May-14 Jun-14 Jul-14 Aug-14 Sep-14 Oct-14 Nov-14 Dec-14 SA 8143 8592 8630 8947 8442 7500 6145 5882 5595 5233 4494 3913 5938 6633 7327 8077 7830 7103 6239 6036 5664 5345 4831 4454 5299 6529 7120 7619 8387 8110 7752 6894 6015 5368 4964 4444 5000 6284 7785 9934 10645 9491 9182 8528 8293 8221 7470 6509 7267 8807 10168 11044 12120 13459 13048 12275 11347 10667 10459 10082 Eur 984 1051 1016 1027 1057 1019 977 1057 1086 1045 1078 1029 1172 1273 1423 1612 1728 1815 1776 1685 1679 1618 1564 1522 1835 2115 2202 2151 2214 2278 2100 2128 2367 2211 2483 1986 2257 2353 2457 2517 2612 2749 2887 2833 2789 2765 2746 2534 2635 2703 2795 2997 3131 3311 3390 3277 3232 3131 3087 3030 Pac 5091 5310 6071 5856 5273 5315 7170 5926 6075 6321 8381 7944 5688 7037 6981 7500 6571 6990 6667 6762 6635 6311 6476 6250 5922 6667 7228 8200 7941 7921 7677 7200 6735 6495 6061 5816 5051 6082 6327 7604 7789 7347 6979 6489 6316 5833 5789 5591 5106 5474 6022 6064 6344 6593 6304 6064 5789 5699 5604 5444 China 987 1090 1127 1209 1221 1327 1324 1268 1209 1168 1127 1085 1185 1286 1286 1346 1388 1449 1490 1449 1394 1256 1214 1171 1208 1214 1256 1311 1415 1520 1675 1584 1527 1422 1366 1262 1373 1436 1478 1512 1642 1667 1733 1700 1642 1576 1493 1450 1010 1045 1106 1150 1244 1357 1421 1263 1173 1128 974 979 278 283 285 288 286 287 289 290 293 295 298 301 306 302 303 307 309 312 315 318 321 315 318 320 333 313 606 571 556 526 513 769 750 732 714 698 714 1063 1264 1333 1556 1739 1702 1915 2083 2128 2292 2245 2292 2449 2400 2353 2600 2653 2600 2549 2453 2517 2541 2453 World 15483 16325 17129 17327 16278 15448 15905 14422 14258 14061 15378 14272 14289 16530 17320 18842 17826 17669 16487 16250 15692 14844 14402 13716 14597 16836 18412 19852 20513 20355 19716 18575 17394 16226 15587 14207 14394 17218 19310 22901 24244 22993 22483 21465 21123 20523 19789 18329 18311 20477 22489 23607 25439 27374 26764 25428 23995 23142 22666 21989 Unit Production Costs Month Tractor Mower Jan-10 $1,750 $50 Feb-10 $1,755 $50 Mar-10 $1,763 $51 Apr-10 $1,770 $51 May-10 $1,778 $51 Jun-10 $1,785 $51 Jul-10 $1,792 $51 Aug-10 $1,795 $51 Sep-10 $1,801 $52 Oct-10 $1,804 $52 Nov-10 $1,810 $52 Dec-10 $1,813 $52 Jan-11 $1,835 $55 Feb-11 $1,841 $55 Mar-11 $1,848 $55 Apr-11 $1,854 $55 May-11 $1,860 $56 Jun-11 $1,866 $56 Jul-11 $1,872 $56 Aug-11 $1,878 $56 Sep-11 $1,885 $56 Oct-11 $1,892 $57 Nov-11 $1,897 $57 Dec-11 $1,903 $57 Jan-12 $1,925 $59 Feb-12 $1,931 $59 Mar-12 $1,938 $59 Apr-12 $1,944 $59 May-12 $1,950 $59 Jun-12 $1,956 $60 Jul-12 $1,963 $60 Aug-12 $1,969 $60 Sep-12 $1,976 $60 Oct-12 $1,983 $60 Nov-12 $1,990 $61 Dec-12 $1,996 $61 Jan-13 $1,940 $59 Feb-13 $1,946 $59 Mar-13 $1,952 $59 Apr-13 $1,958 $59 May-13 $1,964 $60 Jun-13 $1,970 $60 Jul-13 $1,976 $60 Aug-13 $1,983 $60 Sep-13 $1,990 $60 Oct-13 $1,996 $60 Nov-13 $2,012 $61 Dec-13 Jan-14 Feb-14 Mar-14 Apr-14 May-14 Jun-14 Jul-14 Aug-14 Sep-14 Oct-14 Nov-14 Dec-14 $2,008 $2,073 $2,077 $2,081 $2,086 $2,092 $2,098 $2,104 $2,110 $2,116 $2,122 $2,129 $2,135 $61 $63 $63 $63 $63 $63 $63 $64 $64 $64 $64 $64 $64 Operating and Interest Expenses Month Administrative Depreciation Interest Jan-10 $633,073 $140,467 $7,244 Feb-10 $607,904 $165,636 $7,679 Mar-10 $630,687 $142,853 $6,887 Apr-10 $613,401 $160,139 $6,917 May-10 $607,664 $165,876 $8,316 Jun-10 $632,967 $140,573 $7,428 Jul-10 $609,604 $163,936 $8,737 Aug-10 $607,749 $165,791 $7,054 Sep-10 $603,367 $170,173 $8,862 Oct-10 $629,083 $144,457 $8,488 Nov-10 $611,995 $161,545 $7,049 Dec-10 $625,712 $147,828 $8,807 Jan-11 $656,123 $175,447 $7,430 Feb-11 $652,679 $178,891 $6,791 Mar-11 $655,521 $176,049 $8,013 Apr-11 $676,581 $154,989 $8,979 May-11 $676,581 $154,989 $7,484 Jun-11 $656,440 $175,130 $7,858 Jul-11 $661,969 $169,601 $7,424 Aug-11 $677,212 $154,358 $6,848 Sep-11 $653,545 $178,025 $6,751 Oct-11 $657,388 $174,182 $8,160 Nov-11 $672,475 $159,095 $7,898 Dec-11 $656,325 $175,245 $8,953 Jan-12 $723,594 $226,526 $9,443 Feb-12 $759,042 $191,078 $8,464 Mar-12 $749,187 $200,933 $10,264 Apr-12 $751,499 $198,621 $8,547 May-12 $741,452 $208,668 $8,578 Jun-12 $729,122 $220,998 $9,519 Jul-12 $734,783 $215,337 $9,343 Aug-12 $748,208 $201,912 $8,448 Sep-12 $738,186 $211,934 $9,957 Oct-12 $759,403 $190,717 $9,738 Nov-12 $726,183 $223,937 $9,785 Dec-12 $757,037 $193,083 $8,191 Jan-13 $672,232 $179,138 $9,914 Feb-13 $665,023 $186,347 $9,954 Mar-13 $667,657 $183,713 $10,859 Apr-13 $654,198 $197,172 $9,730 May-13 $659,435 $191,935 $10,430 Jun-13 $661,190 $190,180 $10,222 Jul-13 $647,321 $204,049 $10,102 Aug-13 $666,743 $184,627 $10,610 Sep-13 $678,705 $172,665 $9,374 Oct-13 $658,990 $192,380 $10,830 Nov-13 $656,221 $195,149 $9,017 Dec-13 Jan-14 Feb-14 Mar-14 Apr-14 May-14 Jun-14 Jul-14 Aug-14 Sep-14 Oct-14 Nov-14 Dec-14 $676,934 $641,571 $634,973 $662,054 $654,962 $645,579 $658,112 $637,711 $638,317 $651,996 $630,766 $645,095 $637,807 $174,436 $210,589 $217,187 $190,106 $197,198 $206,581 $194,048 $214,449 $213,843 $200,164 $221,394 $207,065 $214,353 $10,423 $9,985 $9,766 $11,148 $9,339 $9,468 $10,324 $9,737 $9,290 $9,213 $10,143 $10,383 $9,059 On-Time Delivery Month Number of deliveries Number On Time Percent Jan-10 1086 1069 98.4% Feb-10 1101 1080 98.1% Mar-10 1116 1089 97.6% Apr-10 1216 1199 98.6% May-10 1183 1168 98.7% Jun-10 1176 1160 98.6% Jul-10 1198 1181 98.6% Aug-10 1205 1189 98.7% Sep-10 1223 1210 98.9% Oct-10 1209 1194 98.8% Nov-10 1198 1180 98.5% Dec-10 1243 1223 98.4% Jan-11 1220 1201 98.4% Feb-11 1241 1224 98.6% Mar-11 1237 1217 98.4% Apr-11 1258 1242 98.7% May-11 1262 1246 98.7% Jun-11 1227 1212 98.8% Jul-11 1243 1227 98.7% Aug-11 1281 1264 98.7% Sep-11 1272 1254 98.6% Oct-11 1295 1278 98.7% Nov-11 1298 1281 98.7% Dec-11 1318 1296 98.3% Jan-12 1281 1264 98.7% Feb-12 1320 1304 98.8% Mar-12 1352 1334 98.7% Apr-12 1336 1320 98.8% May-12 1291 1276 98.8% Jun-12 1342 1326 98.8% Jul-12 1352 1337 98.9% Aug-12 1377 1360 98.8% Sep-12 1385 1368 98.8% Oct-12 1356 1338 98.7% Nov-12 1362 1346 98.8% Dec-12 1349 1333 98.8% Jan-13 1386 1371 98.9% Feb-13 1358 1342 98.8% Mar-13 1371 1356 98.9% Apr-13 1362 1348 99.0% May-13 1350 1338 99.1% Jun-13 1381 1366 98.9% Jul-13 1392 1378 99.0% Aug-13 1371 1359 99.1% Sep-13 1402 1387 98.9% Oct-13 1384 1370 99.0% Nov-13 1399 1377 98.4% Dec-13 1369 1357 99.1% Jan-14 1401 1390 99.2% Feb-14 1388 1376 99.1% Mar-14 1395 1385 99.3% Apr-14 1412 1401 99.2% May-14 1403 1392 99.2% Jun-14 1415 1402 99.1% Jul-14 1426 1415 99.2% Aug-14 1431 1420 99.2% Sep-14 1445 1426 98.7% Oct-14 1425 1414 99.2% Nov-14 1413 1403 99.3% Dec-14 1456 1427 98.0% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 A B Defects After Delivery C D E Defects per million items received from suppliers Month 2010 2011 2012 2013 January 812 828 824 682 February 810 832 836 695 March 813 847 818 692 April 823 839 825 686 May 832 832 804 673 June 848 840 812 681 July 837 849 806 696 August 831 857 798 688 September 827 839 804 671 October 838 842 713 645 November 826 828 705 617 December 819 816 686 603 F 2014 571 575 547 542 532 496 472 460 441 445 438 436 Time to Pay Suppliers Month Working Days Jan-10 8.32 Feb-10 8.28 Mar-10 8.29 Apr-10 8.32 May-10 8.36 Jun-10 8.35 Jul-10 8.34 Aug-10 8.32 Sep-10 8.36 Oct-10 8.33 Nov-10 8.32 Dec-10 8.29 Jan-11 7.89 Feb-11 7.65 Mar-11 7.58 Apr-11 7.53 May-11 7.48 Jun-11 7.45 Jul-11 7.36 Aug-11 7.35 Sep-11 7.32 Oct-11 7.3 Nov-11 7.27 Dec-11 7.25 Jan-12 7.22 Feb-12 7.21 Mar-12 7.22 Apr-12 7.29 May-12 7.25 Jun-12 7.23 Jul-12 7.28 Aug-12 7.25 Sep-12 7.24 Oct-12 7.26 Nov-12 7.21 Dec-12 7.23 Jan-13 7.24 Feb-13 7.19 Mar-13 7.21 Apr-13 7.23 May-13 7.22 Jun-13 7.19 Jul-13 7.17 Aug-13 7.15 Sep-13 7.16 Oct-13 7.16 Nov-13 7.15 Dec-13 7.14 Jan-14 7.12 Feb-14 7.11 Mar-14 7.11 Apr-14 7.11 May-14 7.11 Jun-14 7.12 Jul-14 7.08 Aug-14 7.09 Sep-14 7.09 Oct-14 7.04 Nov-14 7.06 Dec-14 7.08 Response times to customer service calls Q1 2013 Q2 2013 Q3 2013 Q4 2013 Q1 2014 Q2 2014 Q3 2014 Q4 2014 4.36 4.33 3.71 4.44 2.75 3.45 1.67 2.55 5.42 4.73 2.52 4.07 3.24 1.95 2.58 2.30 5.50 1.63 2.69 5.11 4.35 2.77 3.47 1.04 2.79 4.21 3.47 3.49 5.58 1.83 3.12 1.59 5.55 6.89 5.12 4.69 2.89 3.72 1.00 3.11 3.65 0.92 1.00 6.36 5.09 4.59 5.40 4.05 8.02 5.27 3.44 8.26 2.33 1.17 3.90 3.38 4.00 0.90 6.04 1.91 1.69 1.46 4.49 1.26 3.34 3.85 2.53 8.93 3.88 1.90 2.06 0.90 4.92 5.00 2.39 6.85 3.39 2.95 4.49 2.31 3.55 3.52 3.26 5.69 5.14 4.69 3.57 2.71 3.52 5.20 4.68 3.05 0.98 3.34 3.41 1.65 1.25 5.13 3.59 5.91 2.34 3.59 3.31 3.58 2.18 5.29 1.07 1.00 2.80 4.03 2.79 2.96 4.35 1.00 2.86 1.82 3.06 2.39 2.09 3.78 2.46 2.18 4.44 3.74 2.40 1.63 4.28 2.87 2.07 4.55 4.87 6.11 1.59 2.40 4.47 0.90 2.90 2.13 6.76 4.78 3.05 4.44 1.94 4.87 2.58 5.24 2.84 4.13 1.50 4.96 3.90 3.11 5.50 4.08 1.25 7.17 5.58 4.41 3.32 0.90 2.47 4.04 3.43 5.70 3.11 3.40 2.20 3.52 4.24 5.09 2.98 1.00 1.08 3.15 3.52 3.18 1.88 7.66 4.65 3.40 3.63 4.87 2.31 0.90 4.25 4.65 2.66 2.04 1.86 3.97 1.00 1.35 5.08 0.90 4.99 4.37 1.90 3.85 5.90 1.62 4.40 2.01 3.76 2.47 6.07 2.81 1.09 1.87 1.64 1.34 3.12 3.20 1.00 1.76 4.60 1.03 6.40 8.05 2.12 5.83 1.00 5.58 3.52 2.31 3.68 4.91 4.32 3.94 1.19 4.92 4.14 1.99 3.92 5.06 3.61 2.47 3.79 2.63 4.13 3.97 4.13 3.26 4.02 3.89 5.86 3.27 2.43 1.00 3.34 4.26 2.63 6.88 0.90 2.86 2.34 3.51 3.28 1.70 4.47 1.71 2.24 3.83 2.53 2.41 3.24 2.30 4.18 6.39 0.90 1.79 4.14 2.47 3.25 5.35 4.73 6.57 3.87 2.70 2.65 4.02 5.20 2.33 2.65 4.18 2.46 3.61 3.21 2.03 5.28 3.67 2.36 8.82 3.84 0.90 3.85 3.62 4.33 4.73 3.64 3.35 2.43 3.38 2.20 4.12 4.64 1.05 5.62 5.50 1.54 4.38 4.57 1.40 2.65 2.67 0.90 6.51 0.90 2.87 2.99 2.49 3.42 4.16 6.40 0.90 3.69 2.11 4.19 2.67 3.97 0.90 3.21 2.87 1.73 2.86 3.03 4.33 1.26 3.51 3.55 7.45 3.52 3.12 1.90 1.95 6.16 5.95 5.93 3.49 2.23 1.86 2.09 2.70 6.40 2.05 5.52 3.03 5.35 2.41 1.03 1.76 1.00 8.21 4.96 7.46 5.11 2.98 2.95 2.64 3.63 2.52 4.85 4.84 6.46 0.90 7.42 4.49 5.34 3.99 5.57 2.88 5.61 1.01 3.79 1.62 3.74 2.59 4.82 0.95 3.63 4.56 2.48 1.10 5.63 1.34 3.18 3.05 3.87 5.67 2.71 4.50 Employee Satisfaction Results Averages using a 5 point scale Design & Sales & Quarter Production Sample size Manager Sample size Administration Sample size Total 1st Q-11 2.86 100 3.81 10 3.51 30 2nd Q-11 2.91 100 3.76 10 3.38 30 3rd Q-11 2.84 100 3.86 10 3.45 30 4th Q-11 2.83 100 3.48 10 3.61 30 1st Q-12 2.91 100 3.75 20 3.37 30 2nd Q-12 2.94 100 3.92 20 3.53 30 3rd Q-12 2.86 100 3.89 20 3.47 30 4th Q-12 2.83 100 3.58 20 3.66 30 1st Q-13 2.95 100 3.82 20 3.71 40 2nd Q-13 3.01 100 4.01 20 3.53 40 3rd Q-13 3.03 100 3.92 20 3.62 40 4th Q-13 2.96 100 3.84 20 3.48 40 1st Q-14 3.05 100 3.92 20 3.52 40 2nd Q-14 3.12 100 4.00 20 3.37 40 3rd Q-14 3.06 100 3.93 20 3.46 40 4th Q-14 3.02 100 3.70 20 3.59 40 3.07 3.07 3.04 3.04 3.11 3.19 3.12 3.10 3.25 3.27 3.29 3.20 3.28 3.29 3.27 3.25 Sample size 140 140 140 140 150 150 150 150 160 160 160 160 160 160 160 160 Engine Production Time Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Production Time (min) 65.1 62.3 60.4 58.7 58.1 56.9 57.0 56.5 55.1 54.3 53.7 53.2 52.8 52.5 52.1 51.8 51.5 51.3 50.9 50.5 50.2 50.0 49.7 49.5 49.3 49.4 49.1 49.0 48.8 48.5 48.3 48.2 48.1 47.9 47.7 47.6 47.4 47.1 46.9 46.8 46.7 46.6 46.5 46.5 46.2 46.3 46.0 45.8 45.7 45.6 Unit Tractor Transmission Costs Current Process A Process B $242.00 $242.00 $292.00 $176.00 $275.00 $321.00 $286.00 $199.00 $314.00 $269.00 $219.00 $242.00 $327.00 $273.00 $278.00 $264.00 $265.00 $300.00 $296.00 $435.00 $301.00 $333.00 $285.00 $286.00 $242.00 $384.00 $315.00 $288.00 $387.00 $300.00 $314.00 $299.00 $304.00 $302.00 $145.00 $300.00 $335.00 $266.00 $351.00 $242.00 $216.00 $277.00 $281.00 $331.00 $284.00 $289.00 $247.00 $276.00 $259.00 $280.00 $312.00 $322.00 $267.00 $273.00 $209.00 $210.00 $281.00 $282.00 $391.00 $303.00 $304.00 $297.00 $306.00 $391.00 $346.00 $312.00 $236.00 $230.00 $287.00 $383.00 $332.00 $306.00 $299.00 $301.00 $312.00 $300.00 $277.00 $295.00 $278.00 $336.00 $288.00 $303.00 $217.00 $313.00 $315.00 $274.00 $286.00 $321.00 $339.00 $338.00 Blade Weight Sample Weight 1 4.88 2 4.92 3 5.02 4 4.97 5 5.00 6 4.99 7 4.86 8 5.07 9 5.04 10 4.87 11 4.77 12 5.14 13 5.04 14 5.00 15 4.88 16 4.91 17 5.09 18 4.97 19 4.98 20 5.07 21 5.03 22 5.12 23 5.08 24 4.86 25 5.11 26 4.92 27 5.18 28 4.93 29 5.12 30 5.08 31 4.75 32 4.99 33 5.00 34 4.91 35 5.18 36 4.95 37 4.63 38 4.89 39 5.11 40 5.05 41 5.03 42 5.02 43 4.96 44 5.04 45 4.93 46 5.06 47 5.07 48 5.00 49 5.03 50 5.00 51 4.95 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 4.99 5.02 4.90 5.10 5.01 4.84 5.01 4.88 4.97 4.97 5.06 5.06 5.04 4.87 5.00 5.03 5.02 5.02 5.06 5.21 5.09 4.97 5.01 4.90 4.89 4.93 5.16 5.02 5.01 5.10 5.03 5.07 4.92 5.08 4.96 4.74 4.91 5.12 5.00 4.93 4.88 4.88 4.81 5.16 5.03 4.87 5.09 4.94 5.08 4.97 5.23 5.12 5.09 5.12 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 4.93 4.79 5.10 5.12 4.86 5.00 4.94 4.95 4.95 4.87 5.09 4.94 5.01 5.04 5.05 5.05 4.97 4.96 4.96 4.99 5.04 4.91 5.19 5.03 4.99 5.12 4.97 4.88 5.07 5.01 4.89 4.95 5.09 5.09 4.89 4.93 4.85 5.03 4.92 5.09 4.99 4.92 4.87 4.90 5.02 5.21 5.02 4.9 5 5.16 5.03 4.96 5.04 4.98 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 5.07 5.02 5.08 4.85 4.9 4.97 5.09 4.89 4.87 5.01 4.97 5.87 5.33 5.11 5.07 4.93 4.99 5.04 5.14 5.09 5.06 4.85 4.93 5.04 5.09 5.07 4.99 5.01 4.88 4.93 5.1 4.94 4.88 4.89 4.89 4.85 4.82 5.02 4.9 4.73 5.04 5.07 4.81 5.04 5.03 5.01 5.14 5.12 4.89 4.91 4.97 4.98 5.01 5.01 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 5.09 4.93 5.04 5.11 5.07 4.95 4.86 5.13 4.95 5.22 4.81 4.91 4.95 4.94 4.81 5.11 4.81 4.97 5.07 5.03 4.81 4.95 4.89 5.08 4.93 4.99 4.94 5.13 5.02 5.07 4.82 5.03 4.85 4.89 4.82 5.18 5.02 5.05 4.88 5.08 4.98 5.02 4.99 5.02 5.03 5.02 5.07 4.95 4.95 4.94 5.12 5.08 4.91 4.96 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 4.96 4.94 5.19 4.91 5.01 4.93 5.05 4.96 4.92 4.95 5.08 4.97 5.04 4.94 4.98 5.03 5.05 4.91 5.09 5.21 4.87 5.02 4.81 4.96 5.06 4.86 4.96 4.99 4.94 5.06 4.95 5.02 5.01 5.04 5.01 5.02 5.03 5.18 5.08 5.14 4.92 4.97 4.92 5.14 4.92 5.03 4.98 4.76 4.94 4.92 4.91 4.96 5.02 5.13 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 5.13 4.92 4.98 4.89 4.88 5.11 5.11 5.08 5.03 4.94 4.88 4.91 4.86 4.89 4.91 4.87 4.93 5.14 4.87 4.98 4.88 4.88 5.01 4.93 4.93 4.99 4.91 4.96 4.78 Mower Test Functional Performance Sample Observation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass 2 Fail Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 3 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 4 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 5 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 6 Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 7 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 8 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 9 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 10 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 11 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 12 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 13 Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 14 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 15 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 16 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 17 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 18 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 19 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass 20 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Fail Pass Pass Pass Pass Pass 21 Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 22 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 23 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 24 Pass Pass Fail Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 25 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 26 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 27 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 28 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 29 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 30 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Employee Retention YearsPLE YrsEducation College GPA 10 18 3.01 10 16 2.78 10 18 3.15 10 18 3.86 9.6 16 2.58 8.5 16 2.96 8.4 17 3.56 8.4 16 2.64 8.2 18 3.43 7.9 15 2.75 7.6 13 2.95 7.5 13 2.50 7.5 16 2.86 7.2 15 2.38 6.8 16 3.47 6.5 16 3.10 6.3 13 2.98 6.2 16 2.71 5.9 13 2.95 5.8 18 3.36 5.4 16 2.75 5.1 17 2.48 4.8 14 2.76 4.7 16 3.12 4.5 13 2.96 4.3 16 2.80 4 17 3.57 3.9 16 3.00 3.7 16 2.86 3.7 15 3.19 3.7 16 3.50 3.5 14 2.84 3.4 16 3.13 2.5 13 1.75 1.8 16 2.98 1.5 15 2.13 0.9 16 2.79 0.8 18 3.15 0.7 13 1.84 0.3 18 3.79 Age Gender College Grad Local 33 F Y Y 25 M Y Y 26 M Y N 24 F Y Y 25 F Y Y 23 M Y Y 35 M Y Y 23 M Y Y 32 F Y Y 34 M N Y 28 M N Y 23 M N Y 24 M Y Y 23 F N Y 27 F Y Y 26 M Y Y 21 M N Y 23 M Y N 20 F N Y 25 M Y Y 24 M Y N 32 M Y N 28 M N Y 25 F Y N 23 M N Y 25 M Y N 24 M Y Y 26 F Y N 23 M Y N 24 M N N 23 F Y N 21 M N Y 24 M Y N 22 M N N 25 M Y N 22 M N N 23 F Y Y 26 M Y N 22 F N N 24 F Y N Unit Shipping Cost Plant Singapore Birmingham Frankfurt Mumbai Kansas City Auckland Santiago Singapore Birmingham Frankfurt Mumbai Kansas City Auckland Santiago Singapore Birmingham Frankfurt Mumbai Kansas City Auckland Santiago Singapore Birmingham Frankfurt Mumbai Kansas City Auckland Santiago Singapore Birmingham Frankfurt Mumbai Kansas City Auckland Santiago Singapore Birmingham Frankfurt Mumbai Kansas City Auckland Santiago Singapore Birmingham Frankfurt Mumbai Kansas City Customer Mowers Tractors Toronto $1.71 $2.03 Toronto $1.34 $1.78 Toronto $1.52 $1.87 Toronto $1.67 $2.14 Toronto $1.36 $1.79 Toronto $1.86 $2.19 Toronto $1.49 $2.13 Shanghai $1.44 $1.78 Shanghai $1.60 $2.15 Shanghai $1.65 $2.32 Shanghai $1.21 $1.47 Shanghai $1.58 $2.13 Shanghai $1.18 $1.63 Shanghai $1.47 $2.03 Mexico City $1.72 $2.09 Mexico City $1.29 $1.79 Mexico City $1.54 $2.04 Mexico City $1.56 $2.22 Mexico City $1.32 $1.76 Mexico City $1.50 $2.07 Mexico City $1.22 $1.58 Melbourne $1.43 $1.70 Melbourne $1.52 $2.06 Melbourne $1.73 $2.28 Melbourne $1.38 $1.63 Melbourne $1.72 $2.34 Melbourne $0.91 $1.17 Melbourne $1.49 $1.80 London $1.88 $2.68 London $1.47 $1.77 London $1.37 $1.64 London $1.44 $1.82 London $1.49 $1.86 London $1.98 $2.60 London $1.58 $2.14 Caracas $1.50 $2.01 Caracas $1.37 $1.86 Caracas $1.59 $1.88 Caracas $1.61 $2.08 Caracas $1.54 $1.90 Caracas $1.54 $1.98 Caracas $1.00 $1.26 Atlanta $1.73 $2.35 Atlanta $1.02 $1.25 Atlanta $1.42 $1.70 Atlanta $1.57 $2.23 Atlanta $1.31 $1.82 Auckland Santiago Atlanta Atlanta $1.74 $1.31 $2.26 $1.76 Fixed Costs of Capacity Increase or New Construction Current Plants Kansas City Kansas City Santiago Santiago Additional Capacity 10000 20000 5000 10000 Cost $605,000.00 $985,000.00 $381,000.00 $680,000.00 Proposed Locations Auckland Auckland Birmingham Birmingham Frankfurt Frankfurt Mumbai Mumbai Singapore Singapore Maximum capacity 15,000 20,000 15,000 20,000 15,000 20,000 15,000 25,000 15,000 20,000 Cost $917,000.00 $1,136,000.00 $962,000.00 $1,180,000.00 $874,000.00 $1,093,000.00 $750,000.00 $959,000.00 $839,000.00 $1,058,000.00 Purchasing Survey Delivery speed Price level Price flexibility Manufacturing image Overall service 4.1 0.6 6.9 4.7 2.4 1.8 3 6.3 6.6 2.5 3.4 5.2 5.7 6 4.3 2.7 1 7.1 5.9 1.8 6 0.9 9.6 7.8 3.4 1.9 3.3 7.9 4.8 2.6 4.6 2.4 9.5 6.6 3.5 1.3 4.2 6.2 5.1 2.8 5.5 1.6 9.4 4.7 3.5 4 3.5 6.5 6 3.7 2.4 1.6 8.8 4.8 2 3.9 2.2 9.1 4.6 3 2.8 1.4 8.1 3.8 2.1 3.7 1.5 8.6 5.7 2.7 4.7 1.3 9.9 6.7 3 3.4 2 9.7 4.7 2.7 3.2 4.1 5.7 5.1 3.6 4.9 1.8 7.7 4.3 3.4 5.3 1.4 9.7 6.1 3.3 4.7 1.3 9.9 6.7 3 3.3 0.9 8.6 4 2.1 3.4 0.4 8.3 2.5 1.2 3 4 9.1 7.1 3.5 2.4 1.5 6.7 4.8 1.9 5.1 1.4 8.7 4.8 3.3 4.6 2.1 7.9 5.8 3.4 2.4 1.5 6.6 4.8 1.9 5.2 1.3 9.7 6.1 3.2 3.5 2.8 9.9 3.5 3.1 4.1 3.7 5.9 5.5 3.9 3 3.2 6 5.3 3.1 2.8 3.8 8.9 6.9 3.3 5.2 2 9.3 5.9 3.7 3.4 3.7 6.4 5.7 3.5 2.4 1 7.7 3.4 1.7 1.8 3.3 7.5 4.5 2.5 3.6 4 5.8 5.8 3.7 4 0.9 9.1 5.4 2.4 0 2.1 6.9 5.4 1.1 2.4 2 6.4 4.5 2.1 1.9 3.4 7.6 4.6 2.6 5.9 0.9 9.6 7.8 3.4 4.9 2.3 9.3 4.5 3.6 5 1.3 8.6 4.7 3.1 2 2.6 6.5 3.7 2.4 5 2.5 9.4 4.6 3.7 3.1 1.9 10 4.5 2.6 3.4 3.9 5.6 5.6 3.6 5.8 0.2 8.8 4.5 3 5.4 2.1 8 3 3.8 3.7 0.7 8.2 6 2.1 2.6 4.5 2.8 3.8 2.9 4.9 5.4 4.3 2.3 3.1 5.1 4.1 3 1.1 3.7 4.2 1.6 5.3 2.3 3.6 5.6 3.6 5.2 3 4.2 3.8 3.3 1 4.5 5.5 3.4 1.6 2.3 2.6 2.5 2.4 2.1 2.9 4.3 3 4.8 3.1 1.9 4 0.6 6.1 2 3.1 2.5 4.8 4.1 2.4 0.8 2.6 4.4 2.5 1.8 4.5 1.9 1.9 1.1 3.8 2 1.4 2.5 4.5 1.7 3.7 5.4 2.2 2.2 1.3 2 2.4 0.8 2.6 1.9 1.6 1.8 4.6 2.8 3.7 3 3.1 2.9 3.5 1.2 2.5 2.8 1.7 4.2 2.7 0.5 1.6 0.5 2.8 2.2 1.8 8.2 6.3 6.7 8.7 7.7 7.4 9.6 7.6 8 9.9 9.2 9.3 5.5 7.2 9 9.2 6.4 8.5 8.3 5.9 8.2 9.9 9.1 6.6 9.4 8.3 9.7 7.1 8.7 8.7 5.5 6.1 7.6 8.5 7 8.4 7.4 7.3 9.3 7.8 7.6 5.1 5 6.7 6.4 9.2 5.2 6.7 9 5 5.9 4.9 2.9 7 6.9 5.5 5.4 4.7 4.5 5.8 5.5 4.9 4.7 4.5 6.2 5.3 3.7 5.2 6.2 3.1 4.8 4.5 6.6 4.9 6.1 3.3 4.5 4.6 3.8 8.2 6.4 5 6 4.2 5.9 4.8 6.1 6.3 7.1 4.2 7.8 4.9 4.5 5 4.8 5 6.8 5 3.6 4.3 2.5 1.6 2.8 4.6 4 3.1 3.3 2.6 3.6 2.5 3.4 1.6 2.6 3.3 3 3.5 3 4.5 4 2.9 3.3 2.4 3.2 2.2 2.9 1.5 3.1 3.6 4 2.3 3 2.8 2.8 2.7 2.8 2 3.4 3 3.3 3.6 2.2 2.2 0.7 3.3 2.4 2.6 2.2 Salesforce image Product quality Usage Level Satisfaction Level Size of firm 2.3 5.2 3