Question

SUMMARY OUTPUT Regression Statistics Multiple R 0.789463 R Square 0.623252 Adjusted R Square 0.609468 Standard Error 84181.43 Observations 86 ANOVA df SS MS F Significance F Regression 3 9.61E+11 3.2E+11 45.21736 2.41E-17 Residual 82 5.81E+11 7.09E+09 Total 85 1.54E+12 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 171910.5 37321.6 4.606195 1.48E-05 97666 246155.1 97666 246155.1 Bed 28829.93 5614.291 5.135098 1.87E-06 17661.32 39998.55 17661.32 39998.55 Space 161.2051 22.60143 7.132518 3.55E-10 116.2437 206.1666 116.2437 206.1666 Garage01 2638.712 18970.42 0.139096 0.889715 -35099.5 40376.92 -35099.5 40376.92 a. Write out the regression equation b. Explain the meaning of the coefficient for Garage01. c. For another model Space and Beds, we obtained an R-sq of 62.3% and a standard error of $83,683. What are the R-sq and standard error for this model given here? Are our predictions better?

          SUMMARY OUTPUT
Regression Statistics
Multiple R 0.789463
R Square 0.623252
Adjusted R Square 0.609468
Standard Error 84181.43
Observations 86
ANOVA
df SS MS F Significance F
Regression 3 9.61E+11 3.2E+11 45.21736 2.41E-17
Residual 82 5.81E+11 7.09E+09
Total 85 1.54E+12
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 171910.5 37321.6 4.606195 1.48E-05 97666 246155.1 97666 246155.1
Bed 28829.93 5614.291 5.135098 1.87E-06 17661.32 39998.55 17661.32 39998.55
Space 161.2051 22.60143 7.132518 3.55E-10 116.2437 206.1666 116.2437 206.1666
Garage01 2638.712 18970.42 0.139096 0.889715 -35099.5 40376.92 -35099.5 40376.92

a. Write out the regression equation
b. Explain the meaning of the coefficient for Garage01.
c. For another model Space and Beds, we obtained an R-sq of 62.3% and a standard error of $83,683. What are the R-sq and standard error for this model given here? Are our predictions better?

Added by Ver-Nica V.

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