An online retail store wants to investigate how the number of its website visito
ID: 3296396 • Letter: A
Question
An online retail store wants to investigate how the number of its website visitors (X1), number of members registered in its loyalty program (X2) and average time spent on its website by customers(X3) relate to its revenue. The dependent variable is the revenue. Based on 400 observations, the following regression equation is estimated (=0.05):
Y= 40.99 + 14.66X1 + 6.54 X2 + 8061 X3
S(b0) = 4.58 s(b1)= 2.68 s(b2)= 4.06 s(b3)=723.54
SSR = 312.45 SSE= 67.41
a. Which of the regression coefficient(s) is/are significant?
A. b1 only
B. b2 only
C. b3 only
D. b1 and b3
E. all of them
b. What is the R2 for this model?
c. What is Fcalc for the given regression model?
d. What is the 95% confidence interval for b3?
e. What is the calculated value of the test statistic to test if 1 could be equal to 9.1?
f. What is the critical value of the test of significance of the overall model for this regression model?
Explanation / Answer
a. Which of the regression coefficient(s) is/are significant?
A. b1 only
B. b2 only
C. b3 only
D. b1 and b3
E. all of them
if TS > critical value ,the variable is significant
here b1 and b3 are significant.
b. What is the R2 for this model?
R^2 = SSR/(SSR+SSE) = 0.822539
c. What is Fcalc for the given regression model?
F = 611.8291
d. What is the 95% confidence interval for b3?
95 % confidence interval is
e. What is the calculated value of the test statistic to test if 1 could be equal to 9.1?
TS = (14.66 - 9.1)/2.68 = 2.0746
f. What is the critical value of the test of significance of the overall model for this regression model?
critiical value =
coef se test-statistic b0 40.99 4.58 8.949781659 b1 14.66 2.68 5.470149254 b2 6.54 4.06 1.610837438 b3 8061 723.54 11.14105647 critical value 1.965972608