Management of a soft-drink bottling company wants to develop a method for alloca

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 time within a particular route, another cost variable 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 (in minutes) and the number of cases delivered were recorded in the file WK3_X2.xls. An analyst computes the delivery time per case delivered and averages these to get 0.33 minutes. Using this he gives an estimated delivery time of 50 minutes for 150 cases to be delivered. Is this a reasonable delivery time? Explain why or why not. Looking at the data in the file, can you give a better estimate? Make sure that you justify your estimate.

If you answer this, can you please show your work so I can follow the logic. Thank you!

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

y^ = 24.83453095 + 0.140026304*x^

where x - number of cases

and y - delevery time

x =150

y^ = 24.83453095 + 0.140026304*150 = 45.83847

t-critical = 2.101

hence it should be 45.83847min

95 % confidence interval for y^ when x = 150 is

(45.83847 - 2.101 *   1.98565 ,   45.83847 + 2.101 *   1.98565)

=(41.666619, 50.0103)

since 50 is in this confidence interval , this a reasonable delivery time

as predicted from model ,which is significant

see significance F = 2.15*10^(-15) << 0.05

hence    better estimate is 45.83847 ,

SUMMARY OUTPUT Regression Statistics Multiple R 0.985774425 R Square 0.971751217 Adjusted R Square 0.97018184 Standard Error 1.986502982 Observations 20 ANOVA df SS MS F Significance F Regression 1 2443.466006 2443.466 619.1956 2.15E-15 Residual 18 71.03149378 3.946194 Total 19 2514.4975 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 24.83453095 1.054218648 23.55729 5.61E-15 22.6197 27.04936 22.6197 27.04936 X Variable 1 0.140026304 0.005627243 24.88364 2.15E-15 0.128204 0.151849 0.128204 0.151849

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