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Listed in the table below are the selling prices, number of bedrooms, number of full baths, and above-ground square footage for 15 single-family residential homes that sold in Boulder, CO in January of 2011. Above-Ground Sq.Ft. Sale Price # Bedrooms# Full baths $479,500 3 1 $394,100 3 1 $638,000 3 2 $745,900 4 2 4521 $300,000 3 1 950 $1,366,600 5 3 3536 $587,500 5 2 1204 $399,000 3 1 1070 $1,450,000 5 2 5308 $275,200 2 1 745 $298,500 3 1 1026 $1,269,000 3 3 2598 $490,000 3 2 1026 $1,700,000 5 4 3774 $310,000 2 2 1760 Assuming the regression assumptions are met, perform the multiple regression of y = sale price on the set of predictor variables x₁ = number of bedrooms, x2 = number of full bath and x3 = above-ground square footage. Conduct the F test for the significance of overall regression and state your conclusion. Use a significance level of a = 0.05. 1222 1128 1204 Select one: O a. Since the p-value is approximately 0, there is evidence that a linear relationship exists between sale price and each of the predictor variables. O b. Since the p-value is approximately 0, there is evidence that a linear relationship exists between sale price and at least one of the predictor variables. O c. Since the p-value is greater than 0.05, there is evidence that a linear relationship does not exist between sale price and the set of predictor variables. O d. Since the p-value is greater than 0.05, this multiple regression is not significant. Individual t tests must be performed to determine whether a linear relationship exists between sale price and the individual predictors.

Listed in the table below are the selling prices, number of bedrooms, number of full baths, and above-ground square footage for 15 single-family residential homes that sold in Boulder, CO in January of 2011. Above-Ground Sq.Ft. Sale Price # Bedrooms# Full baths $479,500 3 1 $394,100 3 1 $638,000 3 2 $745,900 4 2 4521 $300,000 3 1 950 $1,366,600 5 3 3536 $587,500 5 2 1204 $399,000 3 1 1070 $1,450,000 5 2 5308 $275,200 2 1 745 $298,500 3 1 1026 $1,269,000 3 3 2598 $490,000 3 2 1026 $1,700,000 5 4 3774 $310,000 2 2 1760 Assuming the regression assumptions are met, perform the multiple regression of y = sale price on the set of predictor variables x₁ = number of bedrooms, x2 = number of full bath and x3 = above-ground square footage. Conduct the F test for the significance of overall regression and state your conclusion. Use a significance level of a = 0.05. 1222 1128 1204 Select one: O a. Since the p-value is approximately 0, there is evidence that a linear relationship exists between sale price and each of the predictor variables. O b. Since the p-value is approximately 0, there is evidence that a linear relationship exists between sale price and at least one of the predictor variables. O c. Since the p-value is greater than 0.05, there is evidence that a linear relationship does not exist between sale price and the set of predictor variables. O d. Since the p-value is greater than 0.05, this multiple regression is not significant. Individual t tests must be performed to determine whether a linear relationship exists between sale price and the individual predictors.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**Home Sale Data Analysis** Below is a table listing the selling prices, number of bedrooms, number of full baths, and above-ground square footage for 15 single-family homes sold in Boulder, CO, in January 2011. | Sale Price | # Bedrooms | # Full Baths | Above-Ground Sq. Ft. | |------------|------------|--------------|----------------------| | $479,500 | 3 | 1 | 1222 | | $394,100 | 3 | 1 | 1128 | | $638,000 | 3 | 2 | 1204 | | $745,900 | 4 | 2 | 4521 | | $300,000 | 3 | 1 | 950 | | $1,366,600 | 5 | 3 | 3536 | | $587,500 | 5 | 2 | 1204 | | $399,000 | 3 | 1 | 1070 | | $1,450,000 | 5 | 2 | 5308 | | $275,200 | 2 | 1 | 745 | | $298,500 | 3 | 1 | 1026 | | $1,269,000 | 3 | 3 | 2598 | | $490,000 | 3 | 2 | 1026 | | $1,700,000 | 5 | 4 | 3774 | | $310,000 | 2 | 2 | 1760 | **Analysis Task:** Using the data provided, perform a multiple regression analysis where: - \( y \) = Sale price - \( x_1 \) = Number of bedrooms - \( x_2 \) = Number of full baths - \( x_3 \) = Above-ground square footage Conduct an \( F \) test for the significance of the overall regression and state your conclusion. Use a significance level of \( \alpha = 0.05 \). **Options for Conclusion:** - a. Since the \( p \)-value is approximately 0, there is evidence
Transcribed Image Text:**Home Sale Data Analysis** Below is a table listing the selling prices, number of bedrooms, number of full baths, and above-ground square footage for 15 single-family homes sold in Boulder, CO, in January 2011. | Sale Price | # Bedrooms | # Full Baths | Above-Ground Sq. Ft. | |------------|------------|--------------|----------------------| | $479,500 | 3 | 1 | 1222 | | $394,100 | 3 | 1 | 1128 | | $638,000 | 3 | 2 | 1204 | | $745,900 | 4 | 2 | 4521 | | $300,000 | 3 | 1 | 950 | | $1,366,600 | 5 | 3 | 3536 | | $587,500 | 5 | 2 | 1204 | | $399,000 | 3 | 1 | 1070 | | $1,450,000 | 5 | 2 | 5308 | | $275,200 | 2 | 1 | 745 | | $298,500 | 3 | 1 | 1026 | | $1,269,000 | 3 | 3 | 2598 | | $490,000 | 3 | 2 | 1026 | | $1,700,000 | 5 | 4 | 3774 | | $310,000 | 2 | 2 | 1760 | **Analysis Task:** Using the data provided, perform a multiple regression analysis where: - \( y \) = Sale price - \( x_1 \) = Number of bedrooms - \( x_2 \) = Number of full baths - \( x_3 \) = Above-ground square footage Conduct an \( F \) test for the significance of the overall regression and state your conclusion. Use a significance level of \( \alpha = 0.05 \). **Options for Conclusion:** - a. Since the \( p \)-value is approximately 0, there is evidence
Expert Solution
Step 1: Define the given data

From the information, given that

 

Let Y denotes the sale price

Let X1 denotes the number of bedrooms

Let X2 denotes the number of full baths

Let X3 denotes the above-ground square footage

 

The multiple regression equation is given by,

Statistics homework question answer, step 1, image 1

 Where,

a denotes the intercept,

b1, b2 and b3 denote the slope of variables X1, X2 and X3.

 

 

steps

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