Data Table Square Footage, x 2306 3154 1093 1926 3157 2654 4288 2145 2608 1774 1808 3668 Selling Price ($000s), y 396 370.6 184.4 330.3 627.7 352.3 654.8 366.7 424.8 308.6 274.6 666.8

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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(e)

### Data Table

This table presents data on the relationship between the square footage of a property and its selling price, measured in thousands of dollars. 

| **Square Footage, x** | **Selling Price ($000s), y** |
|-----------------------|-----------------------------|
| 2306                  | 396                         |
| 3154                  | 370.6                       |
| 1093                  | 184.4                       |
| 1926                  | 330.3                       |
| 3157                  | 627.7                       |
| 2654                  | 352.3                       |
| 4288                  | 654.8                       |
| 2145                  | 366.7                       |
| 2608                  | 424.8                       |
| 1774                  | 308.6                       |
| 1808                  | 274.6                       |
| 3668                  | 666.8                       |

### Explanation:

- **Square Footage, x**: This column lists the size of each property in square feet.
- **Selling Price ($000s), y**: This column lists the selling price of each property in thousands of dollars.

This data can be used to analyze trends and relationships between the size of a property and its market value, potentially assisting in real estate evaluations and investment decisions.
Transcribed Image Text:### Data Table This table presents data on the relationship between the square footage of a property and its selling price, measured in thousands of dollars. | **Square Footage, x** | **Selling Price ($000s), y** | |-----------------------|-----------------------------| | 2306 | 396 | | 3154 | 370.6 | | 1093 | 184.4 | | 1926 | 330.3 | | 3157 | 627.7 | | 2654 | 352.3 | | 4288 | 654.8 | | 2145 | 366.7 | | 2608 | 424.8 | | 1774 | 308.6 | | 1808 | 274.6 | | 3668 | 666.8 | ### Explanation: - **Square Footage, x**: This column lists the size of each property in square feet. - **Selling Price ($000s), y**: This column lists the selling price of each property in thousands of dollars. This data can be used to analyze trends and relationships between the size of a property and its market value, potentially assisting in real estate evaluations and investment decisions.
**Understanding the Relationship Between Square Footage and Home Value**

One of the significant factors affecting the value of a home is its square footage. The accompanying data illustrate the square footage and selling prices (in thousands of dollars) for a random sample of homes for sale in a particular region. The task is to complete parts (a) through (h) as outlined below.

**Data Overview:**

- The data are divided into two variables: 
  - **Square Footage**: Represented on various axes from 1000 to 4500.
  - **Price in Thousands**: Represented on various axes from 150 to 700.

**Statistical Analysis:**

(c) **Linear Correlation Coefficient Calculation**

- The calculated linear correlation coefficient \( r = 0.906 \).
- This metric is crucial as it quantifies the strength and direction of the linear relationship between square footage and asking price.
  
  *Note*: Results are rounded to three decimal places where necessary.

(d) **Linear Relationship Determination**

- Is there a linear relationship between square footage and asking price?

  - **Yes**

(e) **Least-Squares Regression Line**

- To express the linear relationship, the least-squares regression line is used, treating square footage as the explanatory variable. The equation is represented as:

  \[
  y = \_ \times (\text{{Square Footage}}) + (\_)
  \]

  - Here, rounding the slope to three decimal places and the intercept to one decimal place is necessary for precision.

**Important Note**: Understanding the correlation and the least-squares regression line helps in predicting home values based on square footage, thus aiding buyers, sellers, and real estate professionals in making data-driven decisions.

**Graphs/Diagrams**: The scatter plots are not detailed in this transcript, but they represent the correlation visually with one axis for square footage and another for price, highlighting data distribution and potential trends.
Transcribed Image Text:**Understanding the Relationship Between Square Footage and Home Value** One of the significant factors affecting the value of a home is its square footage. The accompanying data illustrate the square footage and selling prices (in thousands of dollars) for a random sample of homes for sale in a particular region. The task is to complete parts (a) through (h) as outlined below. **Data Overview:** - The data are divided into two variables: - **Square Footage**: Represented on various axes from 1000 to 4500. - **Price in Thousands**: Represented on various axes from 150 to 700. **Statistical Analysis:** (c) **Linear Correlation Coefficient Calculation** - The calculated linear correlation coefficient \( r = 0.906 \). - This metric is crucial as it quantifies the strength and direction of the linear relationship between square footage and asking price. *Note*: Results are rounded to three decimal places where necessary. (d) **Linear Relationship Determination** - Is there a linear relationship between square footage and asking price? - **Yes** (e) **Least-Squares Regression Line** - To express the linear relationship, the least-squares regression line is used, treating square footage as the explanatory variable. The equation is represented as: \[ y = \_ \times (\text{{Square Footage}}) + (\_) \] - Here, rounding the slope to three decimal places and the intercept to one decimal place is necessary for precision. **Important Note**: Understanding the correlation and the least-squares regression line helps in predicting home values based on square footage, thus aiding buyers, sellers, and real estate professionals in making data-driven decisions. **Graphs/Diagrams**: The scatter plots are not detailed in this transcript, but they represent the correlation visually with one axis for square footage and another for price, highlighting data distribution and potential trends.
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