Question

# QUESTION 3 The managing director of a real estate company investigated how advertising budget (in \$000s)...

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?

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

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

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.

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