Management of a soft-drink company wants to develop a method for allocating deli

Question

Management of a soft-drink company wants to develop a method for allocating delivery costs to customers. Although one cost clearly relates to travel time withing 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 times and the number of cases delivered were recorder and provided:

a) Use the least-squares method to compute the regression coefficients b0 and b1.

b) Interpet the meaning of b0 and b1 in this problem,

c) Predict the delivery time for 150 cases of soft drink.

d) Should you use the model to predict the delivery time for a customer who is receiving 500 cases of soft drink? Why or why not?

e) Determine the coefficient of determination, r2, and explain its imeaning in this problem.

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

h) Cpnstruct a 95% confidence interval estimate of the mean delivery time for 150 caes of soft drink and 95% confidence interval prediction interval of the delivery time for a single delivery of 150 cases of soft drink.

i) Determine residual standard deviation of the model. What does this number tell us?

j) Find the sample correlation coefficient between number of cases delivered and delivery time. Is there statistical evidence that a positive correlation between these variables exists? Test at 0.01 significance.

Customer Number of cases Delivery Time 1 52 32.1 2 64 34.8 3 73 36.2 4 85 37.8 5 95 37.8 6 103 39.7 7 116 38.5 8 121 41.9 9 143 44.2 10 157 47.1 11 161 43 12 184 49.4 13 202 57.2 14 218 56.8 15 243 60.6 16 254 61.2 17 267 58.2 18 275 63.1 19 287 65.6 20 298 67.3

Explanation / Answer

A. Step 1: Find XY and X2 as it was done in the table below.

Step 2: Find the sum of every column:

X=3398 , Y=972.5 , XY=182677.8 , X2=701940

Step 3: Use the following equations to find a and b:

b0=YX2XXY/nX2(X)2=972.57019403398182677.8/207019403398224.835

b1=nXYXY/nX2(X)2=20182677.83398972.5/20701940(3398)20.14

b. b1 - This is the SLOPE of the regression line. Thus this is the amount that the Y variable (dependent) will change for each 1 unit change in the X variable. b0 - This is the intercept of the regression line with the y-axis.

c.Substitute a and b in regression equation formula

y = a + bx= 24.835 + 0.14x

For x=150, y=45.835

d. For x=500, y=94.835 this is very high

X Y XY XX 52 32.1 1669.2 2704 64 34.8 2227.2 4096 73 36.2 2642.6 5329 85 37.8 3213 7225 95 37.8 3591 9025 103 39.7 4089.1 10609 116 38.5 4466 13456 121 41.9 5069.9 14641 143 44.2 6320.6 20449 157 47.1 7394.7 24649 161 43 6923 25921 184 49.4 9089.6 33856 202 57.2 11554.4 40804 218 56.8 12382.4 47524 243 60.6 14725.8 59049 254 61.2 15544.8 64516 267 58.2 15539.4 71289 275 63.1 17352.5 75625 287 65.6 18827.2 82369 298 67.3 20055.4 88804

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