Question 1 Use the data from Question 1 of Homework 6, with the variables delive

Question

Question 1 Use the data from Question 1 of Homework 6, with the variables delivery time (), the number of cases of product stocked (X) and the distance walked by the route driver (X2), with 24 observations on the delivery times. Number Delivery of Cases, Distance, X, (t) Time, X 16,68 560 10.75 150 a) Calculate SSR(X,| X2). b) Calculate SSR(XX,1x,x) c Tes to see if the interaction term is useful in the model d) Calculate SSR(XX, , ?,2.x2l X,, X.) and MSR(XX, , Perform a nested models test to test Ho: ß,-,-n-0 in the model: e) Which model would you use when trying to predict the delivery time?

Explanation / Answer

a) SSR(X1/X2)=SSE(X2)-SSE(X1, X2)

                        = 905.25-124.00=781.25

b) SSR(X1X2/X1, X2)=SSE(X1, X2)-SSE(X1, X2, X1X2)

                                 =124.00-120.29=3.71

c)

ANOVA

By Obseverving above ANOVA P-value for interaction term X1X2 is 0.441 is not significant at 5% level of significance.

Therefore, interaction term is not useful in model.

d) SSR(X1X2, X12, X22 /X1, X2)=SSE(X1, X2)- SSE(X1, X2, X1X2, X12, X22 )

                                                   =124- 119.01=4.99

and MSR(X1X2, X12, X22 /X1, X2)=SSR(X1X2, X12, X22 /X1, X2)/df=1

                                                        =4.99

e) Nested Model for testing above hypothesis we use following test statistics

F=[(SSER   - SSEc)/3]/(SSEc/17)

   =[(124-119.01)/3]/(119.01/17)

   =(1.66/7.00)

=0.237

At 5% level significant, we compare the F?statistic to an F3, 17= 3.197 from table,

• If F < F3, 17= 3.197, we fail to reject H0.

Acceept Hypothsis

H0= B3=B4=B5=0

f) Only Reduced model is used to predict delivery time include X1 variable and X2 variable and not interaction and square term.

i.e. Y=Bo+B1X1+B2x2+e is only used to predict delivery time.

Source DF Adj SS Adj MS F-value P-value Regression 3 2296.95 765.651 127.3 0 X1 1 92.43 92.426 15.37 0.001 X2 1 23.27 23.271 3.87 0.063 X1X2 1 3.71 3.709 0.62 0.441 Error 20 120.29 6.015 Total 23 2417.25

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