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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
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,
Where,
a denotes the intercept,
b1, b2 and b3 denote the slope of variables X1, X2 and X3.
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