Question

eBook Video In a regression analysis involving 30 observations, the following estimated regression equation was obtained. 17.6+3.8z-2.3z +7.6z, +2.7z For this estimated regression equation SST- 1805 and SSR- 1,764. a. At a 0.05, test the significance of the relashionship among the variables. SSE (to 1 decimal, if necessary) MSR (to 1 decimal, if necessary) MSE (to 2 decimal if necessary) What is the value of the F test statistic (to 1 decimal)? Use Table 4 in Appendix B. What is the p-value? - Select youur answer- Using a.05, what is your condlusion? Select your answer- b. Suppose variables z1 and z4 are dropped from the model and the following estimated regression equation is obtained. =11.1-3.6z2 +8.1z For this model SST= 1805 and SSR =1,705. Compute SSE(1, 2 , 3 , 4 ) . (to 1 decimal, if necessary) Compute SSE(, ). (to 1 decimal, if necessary) C. Use an F test and am.05 to determine whether 1 and 4 contribute significantly to the model. What is the value of the F test statistic (to 2 decimals)? Use Table 4 in Appendix B What is the p-value? Select your answer what is your conclusion about the two variables z1 and z4? Select your answer

Answer 1

a) SSE =SST - SSR = 1805 - 1764 = 41

MSR = SSR/p

= 1764/4 = 441

MSE = SSE/(n-p-1) = 41/25 = 1.64

F = MSR/MSE = 441/1.64 = 268.9

We find that for (4,25) degrees of freedom the area in the upper tail of the F distribution corresponding to the test statistic F = 268.9 must be less 0.01

Excel shows the p value = 0.000

Because the p-value is less than 0.05,we ewject the null hypothesis that the relationship among the variables y and x1,x2,x3,x4 is not significant

So we conclude that the relationship among y and x1,x2,x3 and x4 is significant

b)

SSE(1, 2, 3,X4) SST(, 2, 3, T4)- SSR(x1, 2, T3, T4) 1805 1764 41

SSE(T2, 3) SST(x2, 3) SSR(x2,3)= 1805 1705 100

c)

SE()SS(ful) number of extra terms F SSE (full) n-p-

100-41 29.5 F = 2 41 30-4-1 17.98 1.64

We find that for (2,25) degrees of freedom the area in the upper tail of the F distribution corresponding to the test statistic F = 17.98 must be less 0.01

Excel shows the p value = 0.000

Because the p-value is less than 0.05,we ewject the null hypothesis that x1 and x4 are not statistically significant

So we conclude that adding x1 and x4 are significant