Question

Management of a soft-drink bottling company wants to develop a method for allocating delivery costs to customers. Although one cost clearly relates to travel times within a particular route, another variable cost reflects the time required to unload the cases of soft drink at the delivery point. A sample of 20 deliveries within a territory was selected. The delivery time and the number of cases delivered were recorded. Develop a regression model to predict delivery time based on the number of cases delivered. a) Use the least-square method to calculate the regression coefficients, b0 and b1. Write your regression equation. b) Interpret the meaning of b0 and b1 in this problem. c) Predict the delivery time for 150 cases of soft drink. d) Would it be appropriate to use to model to predict the delivery time for a customer who is receiving 500 cases of soft drink? Explain why. e) Determine the coefficient of determination, r2, and explain it meaning in this problem. f) Perform a residual analysis. Is there any evidence of patterns in the residuals? Explain. g) At the 0.05 level of significance, is there evidence of a linear relationship between delivery time and the number of cases delivered? Explain. h) Explain how the results in a to g can help allocate delivery costs to customers.

Answer 1

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a) Use the least-square method to calculate the regression coefficients, b0 and b1.

Regression equation : y^ = 24.8345 + 0.1400*x

b) Interpret the meaning of b0 and b1 in this problem.
b1 - Per unit increase in the nUmber of cases, the time of delivery increases by .1400
b0 - if no cases are to be delivered, then it takes 25.8345 minutes to deliver

c) Predict the delivery time for 150 cases of soft drink.
That' = 24.8345 + 0.1400*150 = 45.8345 minutes

d) Would it be appropriate to use to model to predict the delivery time for a customer who is receiving
500 cases of soft drink? Explain why.

No, because 500 is out of the range of x , you can only use values of x within the range of
x in the dataset

e) Determine the coefficient of determination, r2, and explain it meaning in this problem.
r^2 = 0.6330

It means tat 63.3% of variation in delivery time is explained by "Number of cases" variable
It is a moderately high value.

f) Perform a residual analysis. Is there any evidence of patterns in the residuals? Explain.
Can't perform unless data is provided

g) At the 0.05 level of significance, is there evidence of a linear relationship between delivery time and the number of cases delivered? Explain.

Yes, as p-value is less .05, we can say that there is a linear relation between these 2 variables which is statistically significant

h) Explain how the results in a to g can help allocate delivery costs to customers.
We can predict the time required to deliver x cases, and then predict cost based on the time required as costs will be a function of time spent to deliver these cases.