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Regression Analysis - Statistics and Minitab

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Management of a soft-drink bottling company wishes to develop a method for allocating delivery costs to customers. Although part of total cost clearly relates to travel time within a particular outlet, another variable reflects the time required to unload the cases of soft drink at the delivery point. A sample of 20 customers was selected from routes within a particular sales territory and the delivery time (in minutes) and the number of cases delivered were measured and recorded in the data set. Develop a regression model to help allocate delivery costs by predicting unloading time based on the number of cases delivered.

1) Begin with a brief description of the problem in your own words. Prepare a report using headings that reflect the tasks you are asked to complete in (4). You are expected to follow the report format guidelines document provided in D2L. You should cut-and-paste al Minitab output--tabular and/or graphical--that is relevant to your analysis,from Minitab into your document.

4) Use your Minitab software to generate the numerical and graphical output
used in your analysis. The file containing the problem data, <DELIVERY.MTW>, is available to you from the D2L announcement for this assignment. Complete the following tasks and discuss each, excluding (b) which does not require discussion:
-1-
Computer Project #3
a) Set up a scatter diagram.
b) Use Minitab's least squares method to obtain the regression output. Show the entire tabluar output for this problem here (you may wish to copy and paste pieces of it into other sections of your report for discussion) .
c) State the regression equation and interpret (justify if necessary) the values for b0 and b1 as applicable for this problem.

d) State the coefficient of determination r2 and interpret its meaning for this problem.

e) Predict the delivery time with both confidence and prediction intervals for a customer that is receiving 20 cases of soft drink.

f) Would it be apropriate to use this model to predict delivery time for a customer who is receiving 50 cases of soft drink? Explain.

g) Discus evidence of a linearelationship betwen the model variables using both the F-test and t-test statistics. Discus the t-test for the y-intercept. Asume an α = .05
level of significance for al tests.

h) Perform a residual analysis. Using the standardized residuals, generate a histogram, normal probabilty plot, and residuals vs. fits. Discus each in terms of the apropriate asumptions of linear egresion.

i) Summarize your findings above in determining the adequacy of the fit of the model and your confidence in its abilty to alocate delivery costs to customers.

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The solution provides a step by step method for the calculation of regression analysis. The formula for the calculation and interpretations of the results are also included.

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Statistics: Regression models; elasticities

See attached data file.

G = Total U.S. gasoline consumption, computed as total expenditure divided by price index.
Pop = U.S. total population in millions
GasP = Price index for gasoline,
Income = Per capita disposable income,
Pnc = Price index for new cars,
Puc = Price index for used cars,
Ppt = Price index for public transportation,
Pd = Aggregate price index for consumer durables,
Pn = Aggregate price index for consumer nondurables,
Ps = Aggregate price index for consumer services,

Use Minitab

I. Create regression models (four of them) to predict the consumption of gasoline using the following independent variables. Create a table with the coefficients and their related statistics:
a. Price index for gasoline and the per capita disposable income
b. Price index for gasoline, per capita disposable income, and the price index for new cars
c. Price index for gasoline, per capita disposable income, the price index for new cars, and the price index for used cars.
d. Price index for gasoline, per capita disposable income, the price index for new cars, the price index for used cars, and the price index for public transportation

II. Calculate the following elasticities, using the means of the variables, obtaining separate estimates from each of the above 4 regressions.
a. Own price elasticity of gasoline
b. Income elasticity
c. Cross price elasticity with new cars
d. Cross price elasticity with used cars
e. Cross price elasticity with public transportation

III. a. Compare the regression models from question I. What are the strengths and weaknesses of each model?
b. Consider the model in part c - what may this model, reasonably, be used for, and what does it leave out?
c. If you were going to do a retail level demand study for one particular company's gasoline products (for example, GP), what would you do differently from the above?

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