The answers are in red, but I would like to know how he got the answer An online

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The answers are in red, but I would like to know how he got the answer

An online retail store wants to investigate how the number of its website visitors (X_1), number of members registered in its loyalty program (X_2) and average time spent on its website by customers(X_3) relate to its revenue. The dependent variable is the revenue. Based on 400 observations, the following regression equation is estimated (alpha = 0.05): Y = 40.99 + 14.66 X_1 + 6.54 X_2 + 8061 X_3 S(b_0) = 4.58 s(b_1) = 2.68 s(b_2) = 4.06 s(b_3) = 723.54 SSR = 312.45 SSE = 67.41 Which of the regression coefficient(s) is/are significant? a. b_1 only b. b_2 only c. b_3 only d. b_1 and b_3 e. all of them What is the R^2 for this model? a. 80.99% b. 82.25% c. 85.33% d. 21.57% e. 17.74% What is F_calc for the given regression model? a. 920.06 b. 450.65 c. 302.10 d. 611.83 e. 1011.82

Explanation / Answer

n = 400

b0 = 40.99 , b1 = 14.66 , b2 = 6.54 , b3 = 8061

5) We have to check the which regression coefficient is significant.

For checking significancy we have to find value of test statistic and critical value.

First check for b1

Test statistic is

t = b1 / s(b1) = 14.66 / 2.68 = 5.47

degrees of freedom = n - 1 = 399

So critical value = 1.96                ( Using excel function =TINV(0.05,399) )

So t statistic > critical value then b1 is significant,

First check for b2

Test statistic is

t = b2 / s(b2) = 6.54 / 4.06 = 1.61

degrees of freedom = n - 1 = 399

So critical value = 1.96                ( Using excel function =TINV(0.05,399) )

So t statistic < critical value then b1 is not significant,

First check for b3

Test statistic is

t = b3 / s(b3) = 8061 / 723.54 = 11.14

degrees of freedom = n - 1 = 399

So critical value = 1.96                ( Using excel function =TINV(0.05,399) )

So t statistic > critical value then b3 is significant,

So the correct option is d. b1 and b3

6 . SSR = 312.45   , SSE = 67.41 , SST = SSR + SSE = 312.45 + 67.41 = 379.86

R^2 = SSR / SST = 312.45 / 379.86 = 0.8225

So the correct option is d. 82.25%

7. Fcal = MSR / MSE

MSR = SSR / df = 312.45 / 2 = 104.45

MSE = SSE / df = 67.41 / 395 = 0.170227

Fcal = 104.45 / 0.170227 = 611.83

So correct option is d. 611.83

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