1. Using the data in Chapter 12, problem 12.11, page 488, do a correlation and regression analysis. 1a. Identify the dependent and independent variables if the data to be used to develop the equation of a regression line to predict the average size of the farm by the number of the farms. Setup and interpret a scatter diagram for this data. Make sure to discuss whether a linear line appears to be adequate for this data and indicate whether the slope is positive or negative. Identify dependent and independent variable in this cell. Interpret the scatter diagram in this cell Discuss whether a linear line appears to be adequate for this data and indicate whether the slope is positive or negative in this cell. 1b. What is the equation of the regression line? Place the equation of the regression line in this cell. 1c. What are the values for coefficient of determination and coefficient of correlation? Discuss what these values mean. Place the values of coefficient of determination and coefficient of correlation this cell. Discuss the interpretation of coefficient of determination and coefficient of correlation in this cell. 1d. Depending on the sign of the slope for the regression line, conduct the appropriate directional test of hypothesis to determine whether there is a significant positive or negative (depending on the sign of the slope) relationship between the two variables. Hint, please read section 12.7 of the course text book. What are the null and alternative hypothesis? Place the null and alternative hypothesis in this cell. What is (are) the critical value(s) for sample test statistics if the test of hypothesis to be evaluated at 5% significance? Place the critical value(s) of the sample test statistics in this cell. What is the value of the sample test statistic? Place the value of the test statistic in this cell. Based on the value of the test statistic and its critical value(s), what statement should be made about the null hypothesis? Place the statement about null hypothesis (reject/don't reject) in this cell. What is the conclusion related to the slope of the regression line based on the statement made about null hypothesis in part d? Place the conclusion in this cell. PLACE THE SCATTER DIAGRAM IN THIS AREA PLACE (COPY/PASTE) YOUR COMPUTER GENERATED OUTPUT SUCH AS EXCEL'S EMBEDDED FUNCTIONS AND EXCELS GENERATED TABULAR DATA IN THIS AREA. 2. Using the data in the sheet "Question 2 Input Data", conduct multiple regression analysis to develop an equation that estimates salary based on age of the person, whether the person is male or female, and whether the person has an MBA degree or not. Show the multiple regression equation in this cell 2b. What is the interpretation of the coefficients of regression equation? Place your answer for question 2b in this cell. 2c. Are the slopes of the regression model statistically significance at 5% significance level? Place your answer for question 2c in this cell. PLACE (COPY/PASTE) YOUR COMPUTER GENERATED OUTPUT SUCH AS EXCEL'S EMBEDDED FUNCTIONS AND EXCELS GENERATED TABULAR DATA IN THIS AREA. Salary $ 65,000.00 $ 85,000.00 $ 74,000.00 $ 83,000.00 $ 110,000.00 $160,000.00 $100,000.00 $122,000.00 $ 85,000.00 $120,000.00 $105,000.00 $ 135,000.00 $125,000.00 $ 175,000.00 $156,000.00 $140,000.00 Male/Female M F F F M F M M M F F M F M M F For variable Male/Female in column C, M means male, and F means Female Age 26 28 36 35 35 40 41 42 45 46 50 51 55 50 61 63 MBA N Y N N Y Y N Y N Y N Y N Y Y N For variable MBA in column E, N means no MBA, Y means the person has MBA degree. 3. The data in the sheet "Question 3 Input Data" shows the sales data in millions for the Ski and Golf Sales Inc. for period of four years between 2005 to 2008. Ski and Golf Sales specializes in sales of golf and ski products exclusively. The data is based on quarterly sales. Compute the seasonal indexes for this data. If Excel is used to carry out the computations, it is acceptable to carry out the computations manually using Excel since Excel does not compute seasonal indexes automatically. You can modify the sheet "Question 3 Input Data" to show the computations using Excel. It is also acceptable to use MINITAB or other statistical software to solve this problem. If other statistical software is used then copy/paste the output in the designated cells below. List the season indexes in this cell. 3b. What is the interpretation of the seasonal indexes. Discuss whether the values computed for seasonal indexes are intuitively logical with respect to the nature of a business that sells ski and golf products exclusively. Place your answer for question 3b in this cell. IF YOU USE ANY OTHER STATISTICAL SOFTWARE OTHER THAN EXCEL TO SOLVE THIS PROBLEM THEN PLACE (COPY/PASTE) YOUR COMPUTER GENERATED OUTPUT HERE. Season Winter Spring Summer Fall Winter Spring Summer Fall Winter Spring Summer Fall Winter Spring Summer Fall Year 2005 2006 2007 2008 Quarter 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Sales 205 96 194 102 230 105 245 120 272 110 255 114 296 130 270 140 4. The data in the sheet "Question 4 Input Data" shows the monthly sales data in ($1000s) for Bolts Inc. Bolts Inc specializes in aircraft fasteners. The data is based on quarterly sales. Develop the fitted fourth-order autoregressive equation for this data. Show the fitted fourth -order autoregressive equation in this cell. Place your statistical software (Excel, MINITAB, ...) output data in the designated area shown below 4b. Is the fourth order parameter (coefficient) statistically significant based on of 5%. Justify your answer based on summary statistics that you have generated and shown below. Place your answer for question 4b in this cell. 4c. What is the most appropriate autoregressive equation based on of 5% if the fourth order parameter is not statistically significant based on of 5%. Place your answer for question 4c in this cell. PLACE YOUR STATISTICAL SOFTWARE OUTPUT THAT WAS GENERATED FOR FOURTH ORDER AUTOREGRESSIVE EQUATION HERE Month 1 2 3 4 5 6 7 8 9 10 11 12 Sales 400 430 420 440 460 440 470 430 440 420 450 435 5. Using the data in Chapter 16, problem #16.8, page 673, do a Chi-square goodness of fit analysis to determine whether Poisson's distribution fit the data. Analyze your results and interpret what they mean in relation to the problem. Use the 5-step hypothesis testing procedure: 5a. What are the null and alternative hypothesis? Place the null and alternative hypothesis in this cell 5b. What is the critical value for sample test statistic if the test of hypothesis to be evaluated at 1% significance? Place the critical value for sample test statistic in this cell 5c. What is the value of the sample test statistic? Place the value of sample test statistic in this cell. 5d. Based on the value test statistic and its critical value, what statement should be made about the null hypothesis? Place the statement about null hypothesis (reject/don't reject) in this cell. 5e. What is the conclusion based on the statement made about null hypothesis in part d? Place the conclusion in this cell. PLACE (COPY/PASTE) YOUR COMPUTER GENERATED OUTPUT SUCH AS EXCEL'S EMBEDDED FUNCTIONS AND EXCELS GENERATED TABULAR DATA IN THIS AREA