The data below shows the square feet of living space and the selling price of 12 residential properties. Residence 1 2 3 4 5 6 7 8 9 10 11 12 x (sq. ft.) y (in thousands) 1,360 1,940 1,750 1,550 1,790 1,750 2,230 1,600 1,450 1,870 2,210 1,480 $662.1 $788.4 $741.4 $728.7 $684.3 $703.4 $898.7 $696.8 $675.2 $775.4 $852.9 $649.4
The data below shows the square feet of living space and the selling price of 12 residential properties. Residence 1 2 3 4 5 6 7 8 9 10 11 12 x (sq. ft.) y (in thousands) 1,360 1,940 1,750 1,550 1,790 1,750 2,230 1,600 1,450 1,870 2,210 1,480 $662.1 $788.4 $741.4 $728.7 $684.3 $703.4 $898.7 $696.8 $675.2 $775.4 $852.9 $649.4
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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Transcribed Image Text:The data below shows the square feet of living space and the selling price of 12 residential properties.
| Residence | x (sq. ft.) | y (in thousands) |
|-----------|-------------|------------------|
| 1 | 1,360 | $662.1 |
| 2 | 1,940 | $788.4 |
| 3 | 1,750 | $741.4 |
| 4 | 1,550 | $728.7 |
| 5 | 1,790 | $684.3 |
| 6 | 1,750 | $703.4 |
| 7 | 2,230 | $898.7 |
| 8 | 1,600 | $696.8 |
| 9 | 1,450 | $675.2 |
| 10 | 1,870 | $775.4 |
| 11 | 2,210 | $852.9 |
| 12 | 1,480 | $649.4 |
This data table lists 12 residences, detailing the relationship between their living space in square feet (x) and their selling price in thousands of dollars (y). The data suggests that larger living spaces generally correspond to higher selling prices, with some variations.
![**Educational Content: Linear Regression Analysis**
**Instruction:**
(a) **Find the best-fitting line** that describes these data. (Round your numeric values to three decimal places.)
\[ y = \text{______} \]
Plot the line and the data points on the same graph.
**Graph Analysis:**
1. **Top Left Graph:** The scatter plot shows data points with a fitted line that slopes upward, suggesting a positive linear relationship between the variables \( x \) and \( y \). The line closely follows the trend of the data points.
2. **Top Middle Graph:** The scatter plot displays data points with a fitted line that has a slight positive slope. The line does not closely match the data points, indicating a weaker linear relationship.
3. **Top Right Graph:** This scatter plot consists of data points with a fitted line that is nearly horizontal. This suggests little to no linear relationship between \( x \) and \( y \).
4. **Bottom Graph:** The scatter plot shows data points with a fitted line that slopes downward, suggesting a negative linear relationship between the variables. The line aligns with the trend of the data points.
**Question (b):**
How well does the fitted line describe the selling price of a residential property as a linear function of the square feet of living area?
- ○ The selling price of homes decreases as square feet of living space increases. The relationship is approximately linear and the fitted line describes the relationship between the two variables reasonably well.
- ○ The selling price of homes increases and then decreases as square feet of living space increases. The relationship is not linear and the fitted line does not describe the relationship between the two variables well.
- ○ The selling price of homes decreases and then increases as square feet of living space increases. The relationship is not linear and the fitted line does not describe the relationship between the two variables well.
- ○ **The selling price of homes increases as square feet of living space increases. The relationship is approximately linear and the fitted line describes the relationship between the two variables reasonably well.**
**Conclusion:**
The most suitable graph indicates a positive linear relationship where the selling price increases with the increase in square feet of living space. Selecting the appropriate fitted line helps in understanding and predicting trends in real estate pricing based on living area.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb365fa56-db01-4f82-bc2c-5bb5151e447e%2F28cece08-867c-41db-8062-123e804579ba%2Fenh705f_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Linear Regression Analysis**
**Instruction:**
(a) **Find the best-fitting line** that describes these data. (Round your numeric values to three decimal places.)
\[ y = \text{______} \]
Plot the line and the data points on the same graph.
**Graph Analysis:**
1. **Top Left Graph:** The scatter plot shows data points with a fitted line that slopes upward, suggesting a positive linear relationship between the variables \( x \) and \( y \). The line closely follows the trend of the data points.
2. **Top Middle Graph:** The scatter plot displays data points with a fitted line that has a slight positive slope. The line does not closely match the data points, indicating a weaker linear relationship.
3. **Top Right Graph:** This scatter plot consists of data points with a fitted line that is nearly horizontal. This suggests little to no linear relationship between \( x \) and \( y \).
4. **Bottom Graph:** The scatter plot shows data points with a fitted line that slopes downward, suggesting a negative linear relationship between the variables. The line aligns with the trend of the data points.
**Question (b):**
How well does the fitted line describe the selling price of a residential property as a linear function of the square feet of living area?
- ○ The selling price of homes decreases as square feet of living space increases. The relationship is approximately linear and the fitted line describes the relationship between the two variables reasonably well.
- ○ The selling price of homes increases and then decreases as square feet of living space increases. The relationship is not linear and the fitted line does not describe the relationship between the two variables well.
- ○ The selling price of homes decreases and then increases as square feet of living space increases. The relationship is not linear and the fitted line does not describe the relationship between the two variables well.
- ○ **The selling price of homes increases as square feet of living space increases. The relationship is approximately linear and the fitted line describes the relationship between the two variables reasonably well.**
**Conclusion:**
The most suitable graph indicates a positive linear relationship where the selling price increases with the increase in square feet of living space. Selecting the appropriate fitted line helps in understanding and predicting trends in real estate pricing based on living area.
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