Question

QUESTION 3

The managing director of a real estate company investigated how advertising budget (in $000s) and number of agents affected annual sales ($ million). He used data from 15 offices, and obtained the following regression output:

SUMMARY OUTPUT
Regression Statistics
Multiple R		0.72
R Square		0.52
Adjusted R Square		0.44
Standard Error		7.36
Observations		15
ANOVA
		df	SS	MS	F	Significance
Regression		2	716.58	358.29	6.61	0.01
Residual		12	650.35	54.20
Total		14	1366.93
		Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept		-19.47	15.84	-1.23	0.24	-53.98	15.05
Advertising		0.16	0.06	2.82	0.02	0.04	0.28
Agents		0.96	0.78	1.24	0.24	-0.73	2.66

                                                                                                                                              

1. What is the fitted regression model?

2. Assess the fit of the model and justify this assessment                                             

3. Is there any evidence that all the regression coefficients are simultaneously zero? Justify your answer.                                                                                                                
4. Is this the best model for the data? Fully justify

Answer 1

1. The fitted regression model is:

y = -19.47 + 0.16*x1 + 0.96*x2

2. 52% of the variation in the model is explained. This is not a well-fitted model.

3. The hypothesis being tested is:

H0: β1 = 0

H1: β1 ≠ 0

The p-value is 0.02.

Since the p-value (0.) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the slope is significant.

The hypothesis being tested is:

H0: β2 = 0

H1: β2 ≠ 0

The p-value is 0.24.

Since the p-value (0.24) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the slope is significant.

4. This is not the best model because one of the variables is insignificant and the explained variation is not good enough.

Please give me a thumbs-up if this helps you out. Thank you!