The regression equation is sales = - 19.7 - 0.00063 outlets + 1.74 cars + 0.410
ID: 3313814 • Letter: T
Question
The regression equation is
sales = - 19.7 - 0.00063 outlets + 1.74 cars + 0.410 income + 2.04 age - 0.034 bosses
Predictor Coef SE Coef T P Constant -19.672 5.422 -3.63 0.022 outlets -0.000629 0.002638 -0.24 0.823 cars 1.7399 0.5530 3.15 0.035 income 0.40994 0.04385 9.35 0.001 age 2.0357 0.8779 2.32 0.081 bosses -0.0344 0.1880 -0.18 0.864
S = 1.507 R-Sq = 99.4% R-Sq(adj) = 98.7%
Analysis of Variance
Source DF SS MS F P
Regression 5 1593.81 318.76 140.36 0.000
Residual Error 4 9.08 2.27
Total 9 1602.89
a) What’s the value of the estimated variance of the regression
b) What’s the value of the estimated variance of the b2
c) What’s the value of the standard error of the b2
d) Is the result significant when using F statistic to test the significant of the relationship at a 0.05 level of significance
Explanation / Answer
a) What’s the value of the estimated variance of the regression?
Answer : Here Estimated variance = MSW (regression) = 318.76
b) What’s the value of the estimated variance of the b2?
Estimated variance of b2 = MSE = 2.27
c) What’s the value of the standard error of the b2?
Standard error of b2 = sqrt(MSE) = 1.507
d) Is the result significant when using F statistic to test the significant of the relationship at a 0.05 level of significance?
Here F = SSW/ SSE = 318.76/ 2.27 = 140.36
P- value = 0.00000
so this is less than 0.05 so at the significance levvel 0.05, there is significant linear relationship between both variables.