In a study of housing demand, the county assessor develops the following regression model to estimate the market value (i.e., selling price) of residential property within his jurisdiction. The assessor suspects that important variables affecting selling price (Y, measured in thousands of dollars) are the size of a house (X₁, measured in hundreds of square feet), the total number of rooms (X₂), age (X3), and whether or not the house has an attached garage (X4, No = 0, Yes = 1). Y = a + B₁X₁+B₂X2 + B3X3 + B4X4+ ε Now suppose that the estimate of the model produces following results: a = 182.550, b₁ = 4.067, b₂ = 3.422, b3 = 0.019, b4= -8.962, Sb1 = 0.571, sb2= 3.225, sh=0.432, sb4=7.302, R² = 0.946, F-statistic = 43.61, and se = 7.923. Note that the sample consists of 15 randomly selected observations. According to the estimated model, holding all else constant, an additional room means the market value by approximately
In a study of housing demand, the county assessor develops the following regression model to estimate the market value (i.e., selling price) of residential property within his jurisdiction. The assessor suspects that important variables affecting selling price (Y, measured in thousands of dollars) are the size of a house (X₁, measured in hundreds of square feet), the total number of rooms (X₂), age (X3), and whether or not the house has an attached garage (X4, No = 0, Yes = 1). Y = a + B₁X₁+B₂X2 + B3X3 + B4X4+ ε Now suppose that the estimate of the model produces following results: a = 182.550, b₁ = 4.067, b₂ = 3.422, b3 = 0.019, b4= -8.962, Sb1 = 0.571, sb2= 3.225, sh=0.432, sb4=7.302, R² = 0.946, F-statistic = 43.61, and se = 7.923. Note that the sample consists of 15 randomly selected observations. According to the estimated model, holding all else constant, an additional room means the market value by approximately
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![In a study of housing demand, the county assessor develops the following regression model to estimate the market value (i.e., selling price) of residential property within his jurisdiction. The assessor suspects that important variables affecting selling price (\(Y\), measured in thousands of dollars) are the size of a house (\(X_1\), measured in hundreds of square feet), the total number of rooms (\(X_2\)), age (\(X_3\)), and whether or not the house has an attached garage (\(X_4\), \(No = 0\), \(Yes = 1\)).
\[ Y = a + \beta_1X_1 + \beta_2X_2 + \beta_3X_3 + \beta_4X_4 + \epsilon \]
Now suppose that the estimate of the model produces the following results:
\[ a = 182.550, \, \beta_1 = 4.067, \, \beta_2 = 3.422, \, \beta_3 = 0.019, \, \beta_4 = -8.962, \]
\[ s_{\beta_1} = 0.571, \, s_{\beta_2} = 3.225, \, s_{\beta_3} = 0.432, \, s_{\beta_4} = 7.302, \, R^2 = 0.946, \, F\text{-statistic} = 43.61, \, s_e = 7.923. \]
Note that the sample consists of 15 randomly selected observations.
According to the estimated model, holding all else constant, an additional room means the market value __________ by approximately __________.
Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining the market value of residential property? Check all that apply.
- [ ] Size of the house (\(X_1\))
- [ ] Total number of rooms (\(X_2\))
- [ ] Age (\(X_3\))
- [ ] Having an attached garage (\(X_4\))
What proportion of the total variation in sales is explained by the regression equation?
- [ ] 0.436
- [ ] 0.432
- [ ] 0.946
The given F-value](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94a8cceb-0882-4bfc-b07b-9c756050dcc4%2F6c05607e-651d-4086-9a3f-2d29bda96446%2Fl5zegv_processed.png&w=3840&q=75)
Transcribed Image Text:In a study of housing demand, the county assessor develops the following regression model to estimate the market value (i.e., selling price) of residential property within his jurisdiction. The assessor suspects that important variables affecting selling price (\(Y\), measured in thousands of dollars) are the size of a house (\(X_1\), measured in hundreds of square feet), the total number of rooms (\(X_2\)), age (\(X_3\)), and whether or not the house has an attached garage (\(X_4\), \(No = 0\), \(Yes = 1\)).
\[ Y = a + \beta_1X_1 + \beta_2X_2 + \beta_3X_3 + \beta_4X_4 + \epsilon \]
Now suppose that the estimate of the model produces the following results:
\[ a = 182.550, \, \beta_1 = 4.067, \, \beta_2 = 3.422, \, \beta_3 = 0.019, \, \beta_4 = -8.962, \]
\[ s_{\beta_1} = 0.571, \, s_{\beta_2} = 3.225, \, s_{\beta_3} = 0.432, \, s_{\beta_4} = 7.302, \, R^2 = 0.946, \, F\text{-statistic} = 43.61, \, s_e = 7.923. \]
Note that the sample consists of 15 randomly selected observations.
According to the estimated model, holding all else constant, an additional room means the market value __________ by approximately __________.
Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining the market value of residential property? Check all that apply.
- [ ] Size of the house (\(X_1\))
- [ ] Total number of rooms (\(X_2\))
- [ ] Age (\(X_3\))
- [ ] Having an attached garage (\(X_4\))
What proportion of the total variation in sales is explained by the regression equation?
- [ ] 0.436
- [ ] 0.432
- [ ] 0.946
The given F-value
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