Question

Number 3 (10 pts) You collect data on house sale prices (in thousands of dollars), along with the number of bedrooms of the house, and the size of the house measured in square feet. Running a regression in Excel with the sale price as the response variable gives the following output:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.724573411
R Square 0.525006628
Adjusted R Square 0.419452545
Standard Error 193.4364724
Observations 12
ANOVA
df SS MS F Significance F
Regression=Model 2 372217.2302 186108.6 4.973816 0.035083
Residual=Error 9 336759.0198 37417.67
Total 11 708976.25
Coefficients Standard Error t Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0%
Intercept 28.58688504 197.6129556 0.144661 0.888166 -418.445 475.6184 -418.44468 475.618448
Bedrooms 54.90997005 61.30590451 0.895672 0.393753 -83.7736 193.5936 -83.773621 193.5935611
Square Feet 0.228708602 0.117629013 1.944321 0.083727 -0.03739 0.494804 -0.0373867 0.494803918

(a) (2 pts) Is the regression significant at a 5% level of significance?
(b) (2 pts) What is the interpretation of the coefficient of the “Bedrooms” variable?
(c) (4 pts) What would you expect the price of a house with 3 bedrooms and 1500 square feet to be?
(d) (2 pts) Would you expect the two explanatory variables “Bedrooms” and “Square Feet” to be correlated? If so, would you expect them to be positively or negatively correlated?

Answer 1

(a) From ANOVA table, p-value for F-statistic=0.035083<0.05 so the regression is significant at a 5% level of significance.

(b) If number of bedrooms of the house is increased by 1 and the size of the house is kept fix then expected house sale prices is increased by 54.90997005*1000=$54909.97.

(c) When no. of bedrooms of the house=3, size of the house=1500 square feet then

expected the price of a house=(28.58688504+54.90997005*3+0.228708602*1500)*1000=$536379.70.

(d) Yes, we expect that the two explanatory variables “Bedrooms” and “Square Feet” are correlated and it is positively correlated.