It is often useful to decision makers at a company to determine what factors ent

Question

It is often useful to decision makers at a company to
determine what factors enter into the size of a customer’s
purchase. Suppose decision makers at Virginia
Semiconductor want to determine from past data what
variables might be predictors of size of purchase and are
able to gather some data on various customer companies.
Assume the following data represent information
gathered for 16 companies on five variables: the total
amount of purchases made during a one-year period
(size of purchase), the size of the purchasing company
(in total sales volume), the percentage of all purchases
made by the customer company that were imports, the
distance of the customer company from Virginia
Semiconductor, and whether the customer company
had a single central purchasing agent. Use these data to
generate a multiple regression model to predict size of
purchase by the other variables. Summarize your findings
in terms of the strength of the model, significant
predictor variables, and any new variables generated by
recoding.

Size of purchase ($1,000) comp. size ($million sales) % of customer imports distance from vsi Central purchases 27.9 25.6 41 18 1 89.6 109.8 16 75 0 12.8 39.4 29 14 0 34.9 16.7 31 117 0 408.6 278.4 14 209 1 173.5 98.4 8 114 1 105.2 101.6 20 75 0 510.6 139.3 17 50 1 382.7 207.4 53 35 1 84.6 26.8 27 15 1 101.4 13.9 31 19 0 27.6 6.8 22 7 0 234.8 84.7 5 89 1 464.3 180.3 27 306 1 309.8 132.6 18 73 1 294.6 118.9 16 11 1

Explanation / Answer

Based on the above figures, it seems only comp. size ($million sales) is a significant predictor variable as it has a p-value less than 0.05.

SUMMARY OUTPUT Regression Statistics Multiple R 0.879085014 R Square 0.772790461 Adjusted R Square 0.690168811 Standard Error 94.43477087 Observations 16 ANOVA df SS MS F Significance F Regression 4 333650.4689 83412.61723 9.353365087 0.001515424 Residual 11 98097.18545 8917.92595 Total 15 431747.6544 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -1.778759417 69.21609014 -0.025698641 0.979957993 -154.1223467 150.5648278 comp. size ($million sales) 1.373539646 0.441244957 3.1128733 0.009874722 0.402366043 2.344713249 % of customer imports -0.320557877 2.064733706 -0.155253859 0.879433437 -4.865006124 4.223890371 distance from vsi 0.111014834 0.378919917 0.292977037 0.774992657 -0.72298228 0.945011948 Central purchases 110.4337388 57.45373817 1.922133221 0.080859506 -16.02108629 236.8885639

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