30. (continuing to use the information from question 29). What is the coefficient of determination R? [Hint you can compute R? by using the formula, R2=RSS/TSS which the Excel regression output reports.] (a) 0.6207967 (b) 0.6163873 (c) 0.6222574 (d) 0.7821051 SUMMARY OUTPUT Regression Statistics 0.787906548 Multiple R R Square Adjusted R Square 0.616387387 Standard Error 63.61708058 Observations 88 ANOVA df MS F Significance F Regression 1 569801.0753 569801.0753 140.7912919 8.42341E-20 Residual 86 348053.433 4047.132941 Total 87 917854.5083 Standard Error t Stat Upper 95% 60.39081986 Coefficients P-value Lower 95% Intercept 11.20414482 24.74260761 0.452827972 0.651812965 -37.98253022 X Variable 1 (sqrft) 0.140210977 0.011816643 11.86555064 8.42341E-20 0.116720269 0.163701686

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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29. [Simple Regression on House Price] Consider the following model you wish to estimate by using
the OLS,
Price = a + B sqrft + ɛ,
where price is the house price in thousands of dollars and sqrft is size of house in square
feet. The OLS result from Excel is as follows (see below).
Transcribed Image Text:29. [Simple Regression on House Price] Consider the following model you wish to estimate by using the OLS, Price = a + B sqrft + ɛ, where price is the house price in thousands of dollars and sqrft is size of house in square feet. The OLS result from Excel is as follows (see below).
30. (continuing to use the information from question 29). What is the coefficient of determination R??
[Hint you can compute R2 by using the formula, R?-RSS/TSS which the Excel regression output
reports.]
(a) 0.6207967 (b) 0.6163873 (c) 0.6222574
(d) 0.7821051
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
0.787906548
0.616387387
Standard Error
63.61708058
Observations
88
ANOVA
df
MS
Significance F
Regression
1
569801.0753
569801.0753
140.7912919
8.42341E-20
Residual
86
348053.433
4047.132941
Total
87
917854.5083
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
X Variable 1 (sqrft)
11.20414482
24.74260761 0.452827972
0.651812965
-37.98253022
60.39081986
0.140210977
0.011816643
11.86555064
8.42341E-20
0.116720269
0.163701686
Transcribed Image Text:30. (continuing to use the information from question 29). What is the coefficient of determination R?? [Hint you can compute R2 by using the formula, R?-RSS/TSS which the Excel regression output reports.] (a) 0.6207967 (b) 0.6163873 (c) 0.6222574 (d) 0.7821051 SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.787906548 0.616387387 Standard Error 63.61708058 Observations 88 ANOVA df MS Significance F Regression 1 569801.0753 569801.0753 140.7912919 8.42341E-20 Residual 86 348053.433 4047.132941 Total 87 917854.5083 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept X Variable 1 (sqrft) 11.20414482 24.74260761 0.452827972 0.651812965 -37.98253022 60.39081986 0.140210977 0.011816643 11.86555064 8.42341E-20 0.116720269 0.163701686
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