Question1 Management of a soft-drink bottling company has the business objective

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Question1 Management of a soft-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. To begin, management decided to develop a regression model to predict delivery time based on the number of cases delivered. A sample of 20 deliveries within a territory was selected. The delivery times and the number of cases delivered were organized in the following table. Number of Cases Delivery Time (minutes Customers 32 52 64 73 85 36 38 38 40 39 42 5 95 103 116 121 143 157 161 184 202 218 243 254 267 7 47 43 49 57 57 61 61 58 63 10 12 13 14 15 16 17 275 19 20 287 298 67 a) What is the dependent variable? Why? Label it as Y and find its mean value b) What is the independent variable? Why? c) Construct a scatter plot. Hint: see page 430 d) For these data, bo 124.84 and bi 0.14. Interpret the meaning of bo and bi in this problem. e) What is the predicted line in this problem? Hint: See page 43 or 432 f) Predict the mean delivery time for 150cases of soft drink? Question 2 If SSR = 66 and SST 88: a. Determine the coefficient of determination, r2, and interpret its meaning. b. Determine the standard error of estimate, if the sample size 50 c. How useful do you think this regression model is for predicting sales?Explain

Explanation / Answer

SolutionA:

given to predict delivery times based on number of cases

to predict y based on x

dependent variable=y=delivery times

average of y=sum/total

=973/20

average of   =48.65

SolutonB:

independent variable=x

x=number of cases

given to predict delivery times based on number of cases

to predict y based on x

so x= number of cases

Solutiond:

y intercept=b0=124.84

For x=0,that is for no cases ,predicted delivery times is 124.84 units,practically has no meaning

slope=m=0.14

For unit increase in number of cases predicted delivery time increases by 0.14 units

Solutione

predicted line is

yhat=b0+b1x

predicted delivery time=124.84+0.14*number of cases

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