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d. The p-value to test the null hypothesis that the slope on sqft is 0 (Ho : B₁ = 0), is approximately 0. What can you say about sqft being a significant explanatory variable or covariate when explaining price? e. State the coefficient of determination value R2 and interpret it in context of the study. f. What is the estimate of the correlation coefficient, R?

d. The p-value to test the null hypothesis that the slope on sqft is 0 (Ho : B₁ = 0), is approximately 0. What can you say about sqft being a significant explanatory variable or covariate when explaining price? e. State the coefficient of determination value R2 and interpret it in context of the study. f. What is the estimate of the correlation coefficient, R?

Linear Algebra: A Modern Introduction
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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d. The p-value to test the null hypothesis that the slope on sqft is 0 (Ho : B₁ = 0), is approximately 0. What can you say about sqft being a significant explanatory variable or covariate when explaining price? e. State the coefficient of determination value R² and interpret it in context of the study. f. What is the estimate of the correlation coefficient, R?
Transcribed Image Text:d. The p-value to test the null hypothesis that the slope on sqft is 0 (Ho : B₁ = 0), is approximately 0. What can you say about sqft being a significant explanatory variable or covariate when explaining price? e. State the coefficient of determination value R² and interpret it in context of the study. f. What is the estimate of the correlation coefficient, R?
4. A study was conducted to investigate the relationship between the size of a house (in square feet) and the selling price of a house (in dollars). The response variable is price in dollars, and we want to study if the covariate of the square footage helps explain the response. A random sample of 522 houses was used, and the linear regression output from R is below. 1m (formula price sqft, data Coefficients: = house) Estimate Std. Error t value Pr(>|t|) (Intercept) -81432.946 11551.846 -7.049 5.74e-12 *** sqft 158.950 4.875 32.605 <2e-16 *** Residual standard error: 79120 on 520 degrees of freedom Multiple R-squared: 0.6715, Adjusted R-squared: 0.6709
Transcribed Image Text:4. A study was conducted to investigate the relationship between the size of a house (in square feet) and the selling price of a house (in dollars). The response variable is price in dollars, and we want to study if the covariate of the square footage helps explain the response. A random sample of 522 houses was used, and the linear regression output from R is below. 1m (formula price sqft, data Coefficients: = house) Estimate Std. Error t value Pr(>|t|) (Intercept) -81432.946 11551.846 -7.049 5.74e-12 *** sqft 158.950 4.875 32.605 <2e-16 *** Residual standard error: 79120 on 520 degrees of freedom Multiple R-squared: 0.6715, Adjusted R-squared: 0.6709
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