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?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 37E

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Question

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

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