A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in meter square and income is measured in IDR millions. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below: Regression Statistics Multiple R 0.8479 R Square 0.7189 Adjusted R Square 0.7069 Standard Error 17.5571 Observations 50   ANOVA   df SS MS F Significance   F Regression   370443.3236 18521.662   0.0000 Residual   14487.7627 308.2503     Total 49 51531.0863           Coefficients Standard Error t Stat P-value Intercept -5.5146 7.2273 -0.763 0.4493 Income 0.4262 0.0392 10.8668 0.0000 Size 5.5437 1.6949 3.2708 0.00020   a. What is the population model of this regression problem? b. What is the sample estimates of the regression problem? c. Which of the independent variables in the model are significant at the 5% level? Formulate the hypothesis and explain the answer. d. How far can you rely upon this model? Or, what is the percentage variation in House explained by the model? e. What is the predicted house size (in hundreds of square feet) for an individual earning an annual income of IDR 400 million and having a family size of 4?

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in meter square and income is measured in IDR millions. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:

Regression Statistics
Multiple R 0.8479
R Square 0.7189
Adjusted R Square 0.7069
Standard Error 17.5571
Observations 50

 

ANOVA

  df SS MS F Significance   F
Regression   370443.3236 18521.662   0.0000
Residual   14487.7627 308.2503    
Total 49 51531.0863      

 

  Coefficients Standard Error t Stat P-value
Intercept -5.5146 7.2273 -0.763 0.4493
Income 0.4262 0.0392 10.8668 0.0000
Size 5.5437 1.6949 3.2708 0.00020

 

a. What is the population model of this regression problem?
b. What is the sample estimates of the regression problem?
c. Which of the independent variables in the model are significant at the 5% level? Formulate the hypothesis and explain the answer.
d. How far can you rely upon this model? Or, what is the percentage variation in House explained by the model?
e. What is the predicted house size (in hundreds of square feet) for an individual earning an annual income of IDR 400 million and having a family size of 4?

Regression Statistics
Multiple R
0.8479
R Square
0.7189
Adjusted R Square
0.7069
Standard Error
17.5571
Observations
50
ANOVA
df
S
MS
Significance F
Regression
37043.3236
18521.6618
0.0000
Residual
14487.7627
308.2503
Total
49
51531.0863
Coefficients
Standard Error
t Stat
P-value
Intercept
-5.5146
7.2273
-0.7630
0.4493
Income
0.4262
0.0392
10.8668
0.0000
Size
5.5437
1.6949
3.2708
0.0020
Transcribed Image Text:Regression Statistics Multiple R 0.8479 R Square 0.7189 Adjusted R Square 0.7069 Standard Error 17.5571 Observations 50 ANOVA df S MS Significance F Regression 37043.3236 18521.6618 0.0000 Residual 14487.7627 308.2503 Total 49 51531.0863 Coefficients Standard Error t Stat P-value Intercept -5.5146 7.2273 -0.7630 0.4493 Income 0.4262 0.0392 10.8668 0.0000 Size 5.5437 1.6949 3.2708 0.0020
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