Problem Definition/ Research Objective: Management of a sports drink bottling company has the business objective of developing a method for allocating delivery costs to customers. Although one cost clearly relates to travel time within a particular route, another variable cost reflects the time required to unload the cases of sports drinks at the delivery point. To begin, management decides to develop a regression model to predict the delivery time based on the number of cases delivered. A sample of 26 deliveries within the delivery a territory was selected. The delivery times and the number of cases delivered were organized in the following table. Set alpha at .01.

Order sizes and shipping costs for last twelve months

Customer	Number of Cases=X	Delivery Time Minutes =Y
1	55	32.10
2	57	33.00
3	64	34.80
4	73	35.35
5	85	36.15
6	95	37.80
7	97	38.50
8	103	39.70
9	116	40.25
10	121	41.90
11	143	44.20
12	157	47.10
13	161	48.50
14	184	52.50
15	202	54.25
16	218	56.75
17	243	60.60
18	254	61.20
19	267	62.50
20	275	63.25
21	287	65.60
22	298	67.30
23	300	69.25
24	305	69.50
25	307	69.75
26	309	70.00

Overall Problem Definition/Research Objective for the entire project: Briefly explain (why are you doing this analysis?

Scatterplot

Use Minitab Scatterplot with description of relationship between x and y. Describe scatterplot to determine whether positive or negative and explain how you made this determination in your graph description? Neither?

Correlation Coefficient

Hypothesis test of correlation coefficient to determine if a linear relationship exists between Size or delivery time and number of cases - Use six step process

Use OLS (ordinary least squares as demonstrated during lecture and as shown in this handout. Be sure to select expanded tables under the Results dialog box.

Regression Equation (show only the equation not the entire table or output)

Use Minitab to develop the regression equation-In your report, paste the Minitab output of regression equation and define regression coefficients b₀ and b₁ as learned during lecture. You must use numbers in your definitions. Example b1 is the represents the average change in delivery time per x number of cases of sports drinks delivered. Each additional case of sports drink order increases delivery time by xx minutes on average. Numbers are examples only.

bo = and is defined as...

b1= and is defined as....

Be able to discuss the quantitative assessment of each in terms of average delivery time.

Significance Testing (ANOVA) What percentage of error or variation is ...

F Test to test R-sqd - Use six step process and in interpretation step discusses percentage of variability in y explained by x. Use six step process

Significance Testing (Regression Coefficient) Is x a significant predictor of y?

T test for significance of regression coefficient Use six step process in interpretation step discuss average amount of change in y for one unit change in x.

Satisfying Regression Assumptions (Normality and Homoscedasticity)

Minitab plots to include in report: Size graphs to fit neatly within report and place each description with the graph you are discussing. Graphical analyses are used to evaluate residuals plotted on graphs. Each graph speaks to one or more of the regression assumptions that are used to determine if the model is valid and may be used for prediction and/or net regression analysis

Regression Plots and associated assumptions

-NP Plot for residuals -Minitab graph with description addressing to assumption(s)

-Residuals vs. Fits-Minitab graph with description addressing to assumption(s)

-Residuals and x variable-Minitab graph with description addressing to assumption(s)

Confidence Interval for Regression Coefficient

Develop confidence interval for regression coefficient and interpret regarding hypothesis testing and regarding the change in delivery time per additional case of sports drink delivered- Minitab 19 of calculates confidence intervals about the regression coefficient b_k are computed when the expanded table selection is chosen under the Results command box.

Prediction and Confidence Interval for Fit value of Y

Use Minitab to develop prediction interval and confidence interval for y for a value of x you select and enter into Minitab - Be able to interpret both intervals as they relate to y for given values of x

Simple Regression Problem Format

Students are required to demonstrate the ability to utilize a software program (Minitab) to analyze a business problem and present the results to an unsophisticated user of statistics. Students may use either p-values or the critical value/critical ratio technique to test hypotheses and all significance testing must be presented using the six-step process.

Important: Format report as follows and label each section as instructed below.

Label: Problem Definition or Research Objective for the entire report.

Begin with Problem Definition

Label: Scatterplot

Use Minitab Scatterplot with description of relationship between x and y positive or negative? Neither? Refer to the graph in your explanation. For example; "As we move along the x axis we see y increases as values of x increase.

Label: Correlation Coefficient

Hypothesis six step test of correlation coefficient to determine if a linear relationship exists between y and x. Use six step process

Note: To produce the required output, in Minitab use Results>Expanded Tables.

Label: Regression Equation (show only the equation not the entire table or output)

Use Minitab to develop the regression equation-In your report, paste the Minitab output of regression equation and define regression coefficients b₀ and b₁ as learned during lecture.

Label: Significance Testing (ANOVA) Be sure to paste the ANOVA table from Minitab in the Test step. Use F Test to determine if a significant amount of variability is being explained by the independent variables and address R-sqd in your Interpretation by discussing the percentage of variability in y explained by x. - Use six the step process.

Label: Significance Testing (Regression Coefficient) Be sure to paste the Regression table in the

Test step. T test for significance of regression coefficient Use six step process in the interpretation step discuss whether x is a contributing to the model Is x a significant predictor of y?

Label: Confidence Interval for Regression Coefficient

Paste confidence interval for regression coefficient and interpret. Discuss whether 0 lies in interval and interpret interval using partial regression terminology. Example: We are 95% confident an increasing x by one unit will cause an average change in y between...Use the variable names from the study.

Label: Satisfying Regression Assumptions

Minitab plots to include in report: Size graphs to fit neatly within report and place each description with the graph you are discussing. Place descriptions below each plot. Plots not sized properly will result in point deductions.

NP Plot for residuals -Minitab graph with description addressing to assumption(s)

Residuals vs. Fits-Minitab graph with description addressing to assumption(s)

Residuals and x variable-Minitab graph with description addressing to assumption(s)

Label: Prediction and Confidence Interval for Fit value of Y

Use Minitab to develop prediction interval and confidence interval for y for a value of x you select and enter into Minitab - Interpret both intervals as they relate to y and use variable names from problem