A realtor has examined the impact of lot size on housing prices for homes in a lakeside resort. The output appears on the next page. One of his colleagues believes that the realtor should also have included whether the house was lakeside as another independent variable. The realtor added this dummy variable to the regression (1=house is lakeside; 0=not). The new regression is also presented on the next page. a) (3 points) What is the regression equation? (I want the specific estimates for the coefficients for the regression including the lakeside variable.) b) (3 points) What is your interpretation of the slope coefficient on lakeside? c) (8 points) Explain the interpretation of the “significance F” value in the regression output. Specifically, what are the hypotheses being tested? What is the purpose of the test? What can you conclude about the result of the test given the estimate of the “significance F” output? d) (6 points) Should the lakeside variable be included in the regression? Why or why not? Be sure to comment on the significance of the lakeside dummy variable and the improvement of the regression fit.
Multiple R
0.303524708
R Square
0.092127248
Adjusted R Square
0.07647427
Standard Error
43290.16017
Observations
60
df
SS
MS
F
Significance F
Regressions
1
11029847233
11029847233
5.885605
0.018396055
Residual
58
1.09E+11
1874037967
Total
59
1.20E+11
Coefficients
Standard Error
t stat
P-Value
Lower 95%
Intercept
37645.54569
20983.51574
1.794053301
0.078017
-4357.52465
Lot Size
1362.741742
561.7175628
2.426026587
0.018396
238.3418752
New Regression Output
Multiple R
0.304263563
R Square
0.092576315
Adjusted R Square
0.060736888
Standard Error
43657.44605
Observations
60
df
SS
MS
F
Significance F
Regressions
2
11083611361
5541805681
2.9076
0.032746304
Residual
57
1.09E+11
1905972596
Total
59
1.20E+11
Coefficients
Standard Error
t stat
P-Value
Lower 95%
Intercept
37081.45017
21426.42167
1.730641296
0.088927
-5824.219139
Lot Size
1386.834292
567.6436065
2.411432589
0.019135
232.1475765
Lake
2954.769374
17592.82614
0.167953082
0.867215
-32274.25731
In: Economics
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