A national homebuilder builds single-family homes and condominium-style townhouses. The accompanying dataset provides information on the selling price, lot cost, and type of home for closings during one month. Complete parts a through c. E Click the icon to view the house sales data. a. Develop a multiple regression model for sales price as a function of lot cost and type of home without any interaction term. Create a dummy variable named "Townhouse", where it is equal to 1 when Type = "Townhouse" and 0 otherwise. Determine the coefficients of the regression equation. Sales Price = 108726 + (3.68 )• Lot Cost + ( - 75063 )• Townhouse (Round the constant and coefficient of Townhouse to the nearest integer as needed. Round all other values to two decimal places as needed.) b. Determine if an interaction exists between lot cost and type of home and find the best model. Use a = 0.1 as the level of significance. First determine whether an interaction exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. An interaction exists because the p-value of the variable Lot Cost • Townhouse is. which is less than a. (Type an integer or a decimal rounded to three decimal places as needed.) O B. An interaction exists because the p-value of the variable Townhouse is (Type an integer or a decimal rounded to three decimal places as needed.) which is greater than a. O C. An interaction exists because the p-value of the variable Lot Cost is, which is greater than a. (Type an integer or a decimal rounded to three decimal places as needed.) O D. No interaction exists because the p-value is less than a for all of the independent variables.
A national homebuilder builds single-family homes and condominium-style townhouses. The accompanying dataset provides information on the selling price, lot cost, and type of home for closings during one month. Complete parts a through c. E Click the icon to view the house sales data. a. Develop a multiple regression model for sales price as a function of lot cost and type of home without any interaction term. Create a dummy variable named "Townhouse", where it is equal to 1 when Type = "Townhouse" and 0 otherwise. Determine the coefficients of the regression equation. Sales Price = 108726 + (3.68 )• Lot Cost + ( - 75063 )• Townhouse (Round the constant and coefficient of Townhouse to the nearest integer as needed. Round all other values to two decimal places as needed.) b. Determine if an interaction exists between lot cost and type of home and find the best model. Use a = 0.1 as the level of significance. First determine whether an interaction exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. An interaction exists because the p-value of the variable Lot Cost • Townhouse is. which is less than a. (Type an integer or a decimal rounded to three decimal places as needed.) O B. An interaction exists because the p-value of the variable Townhouse is (Type an integer or a decimal rounded to three decimal places as needed.) which is greater than a. O C. An interaction exists because the p-value of the variable Lot Cost is, which is greater than a. (Type an integer or a decimal rounded to three decimal places as needed.) O D. No interaction exists because the p-value is less than a for all of the independent variables.
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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![**Title: Analyzing Home Sales Data for Regression Modeling**
**Introduction to Dataset:**
A national homebuilder constructs single-family homes and condominium-style townhouses. This dataset provides information on the selling price, lot cost, and type of home for recent closings. The task is to analyze the data to build a regression model that predicts sales prices based on these variables.
**Developing a Multiple Regression Model:**
- **Objective:** Create a regression model to predict sales price using lot cost and type of home.
- **Dummy Variable:** Create a dummy variable named "Townhouse" which equals 1 for Townhouse and 0 for otherwise.
- **Regression Equation:**
\[
\text{Sales Price} = 108726 + (3.68 \times \text{Lot Cost}) + (-75063 \times \text{Townhouse})
\]
- Note: Round the constant and Townhouse coefficient to the nearest integer. Other values are rounded to two decimal places.
**Interaction Term Analysis:**
- **Objective:** Determine if there is an interaction effect between lot cost and home type.
- **Level of Significance (\(\alpha = 0.1\)):**
- Check if the p-value of each variable within the interaction term (Lot Cost, Townhouse, Lot Cost * Townhouse) indicates an interaction effect.
**Choices for Interaction Effect:**
- **A.** An interaction exists if the p-value of Lot Cost * Townhouse is **less** than \(\alpha\).
- **B.** An interaction exists if the p-value of Townhouse is **greater** than \(\alpha\).
- **C.** An interaction exists if the p-value of Lot Cost is **greater** than \(\alpha\).
- **D.** No interaction exists if p-values are all **greater** than \(\alpha\).
**Dataset Overview:**
Below is a sample of the house sales data. It includes columns for the home type, sales price, and lot cost.
| Type | Sales Price | Lot Cost |
|-------------|-------------|----------|
| Townhouse | $114,740 | $21,700 |
| Single Family | $138,530 | $26,550 |
| Townhouse | $149,905 | $25,550 |
| Single Family | $172,000 | $26,200 |
| ...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e048f0b-5f9a-4230-bf35-655b1c461c20%2Fdbbb78cd-928f-4a1f-8502-dbb1d28b2cf8%2Fqujk1b_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Analyzing Home Sales Data for Regression Modeling**
**Introduction to Dataset:**
A national homebuilder constructs single-family homes and condominium-style townhouses. This dataset provides information on the selling price, lot cost, and type of home for recent closings. The task is to analyze the data to build a regression model that predicts sales prices based on these variables.
**Developing a Multiple Regression Model:**
- **Objective:** Create a regression model to predict sales price using lot cost and type of home.
- **Dummy Variable:** Create a dummy variable named "Townhouse" which equals 1 for Townhouse and 0 for otherwise.
- **Regression Equation:**
\[
\text{Sales Price} = 108726 + (3.68 \times \text{Lot Cost}) + (-75063 \times \text{Townhouse})
\]
- Note: Round the constant and Townhouse coefficient to the nearest integer. Other values are rounded to two decimal places.
**Interaction Term Analysis:**
- **Objective:** Determine if there is an interaction effect between lot cost and home type.
- **Level of Significance (\(\alpha = 0.1\)):**
- Check if the p-value of each variable within the interaction term (Lot Cost, Townhouse, Lot Cost * Townhouse) indicates an interaction effect.
**Choices for Interaction Effect:**
- **A.** An interaction exists if the p-value of Lot Cost * Townhouse is **less** than \(\alpha\).
- **B.** An interaction exists if the p-value of Townhouse is **greater** than \(\alpha\).
- **C.** An interaction exists if the p-value of Lot Cost is **greater** than \(\alpha\).
- **D.** No interaction exists if p-values are all **greater** than \(\alpha\).
**Dataset Overview:**
Below is a sample of the house sales data. It includes columns for the home type, sales price, and lot cost.
| Type | Sales Price | Lot Cost |
|-------------|-------------|----------|
| Townhouse | $114,740 | $21,700 |
| Single Family | $138,530 | $26,550 |
| Townhouse | $149,905 | $25,550 |
| Single Family | $172,000 | $26,200 |
| ...
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