Question

(b) A simple linear regression model is fitted to the data regarding the weekly advertising expenditures (X) and weekly sales (Y). The excel output is given in the table below. SUMMARY OUTPUT Regression Statistics Multiple R 0.8379 R Square 0.7021 Adjusted R Square 0.6649 Standard Error 6.9724 Observations 10.0000 ANOVA df SS MS F Significance F Regression 1.0000 916.6853 916.6853 18.8563 0.0025 Residual 8.0000 388.9147 48.6143 Total 9.0000 1305.6000 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -40.4232 22.4977 -1.7968 0.1101 -92.3029 11.4565 -92.3029 11.4565 X($) 0.0677 0.0156 4.3424 0.0025 0.0317 0.1036 0.0317 0.1036 (i) Determine the regression equation. (2 marks) (ii) Interpret the meaning of the slope, b1 in this problem. (2 marks) (iii) At the 0.05 level of significance, is there evidence of a linear relationship between advertising expenditures and sales? (8 marks)

          (b) A simple linear regression model is fitted to the data regarding the weekly advertising expenditures (X) and weekly sales (Y). The excel output is given in the table below.

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8379
R Square 0.7021
Adjusted R Square 0.6649
Standard Error 6.9724
Observations 10.0000

ANOVA
df SS MS F Significance F
Regression 1.0000 916.6853 916.6853 18.8563 0.0025
Residual 8.0000 388.9147 48.6143
Total 9.0000 1305.6000

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -40.4232 22.4977 -1.7968 0.1101 -92.3029 11.4565 -92.3029 11.4565
X($) 0.0677 0.0156 4.3424 0.0025 0.0317 0.1036 0.0317 0.1036

(i) Determine the regression equation. (2 marks)
(ii) Interpret the meaning of the slope, b1 in this problem. (2 marks)
(iii) At the 0.05 level of significance, is there evidence of a linear relationship between advertising expenditures and sales? (8 marks)

(b) A simple linear regression model is fitted to the data regarding the weekly advertising expenditures (X) and weekly sales (Y). The excel output is given in the table below.

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8379
R Square 0.7021
Adjusted R Square 0.6649
Standard Error 6.9724
Observations 10.0000

ANOVA
df SS MS F Significance F
Regression 1.0000 916.6853 916.6853 18.8563 0.0025
Residual 8.0000 388.9147 48.6143
Total 9.0000 1305.6000

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -40.4232 22.4977 -1.7968 0.1101 -92.3029 11.4565 -92.3029 11.4565
X() 0.0677 0.0156 4.3424 0.0025 0.0317 0.1036 0.0317 0.1036

(i) Determine the regression equation. (2 marks)
(ii) Interpret the meaning of the slope, b1 in this problem. (2 marks)
(iii) At the 0.05 level of significance, is there evidence of a linear relationship between advertising expenditures and sales? (8 marks)

Added by Samuel L.

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