We want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of sixteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Distance from the beach, x (in miles) Selling price, y (in thousands of dollars) 19.4 223.1 11.7 282.1 8.2 247.8 350- 8.5 292.0 12.5 211.2 300- 7.0 215.9 7.9 270.2 250- 5.7 266.2 12.3 193.9 14.9 258.0 13.0 193.3 150- 9.4 286.8 8.0 238.7 20 12.5 216.3 Figure 1 3.2 316.5 5.2 297.4 Send data to calculator Send data to Excel The least-squares regression line for these data has a slope of approximately –5.48. Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) What is the value of the y-intercept of the least-squares regression line for these data? Round your answer to at least two decimal places. What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.
We want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of sixteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Distance from the beach, x (in miles) Selling price, y (in thousands of dollars) 19.4 223.1 11.7 282.1 8.2 247.8 350- 8.5 292.0 12.5 211.2 300- 7.0 215.9 7.9 270.2 250- 5.7 266.2 12.3 193.9 14.9 258.0 13.0 193.3 150- 9.4 286.8 8.0 238.7 20 12.5 216.3 Figure 1 3.2 316.5 5.2 297.4 Send data to calculator Send data to Excel The least-squares regression line for these data has a slope of approximately –5.48. Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) What is the value of the y-intercept of the least-squares regression line for these data? Round your answer to at least two decimal places. What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Transcribed Image Text:### Predicting House Selling Prices Based on Distance from the Beach
In this study, we aim to predict the selling price of a house in Newburg Park, Florida, based on its distance from the beach. The data is summarized in the table and scatter plot below, featuring sixteen homes sold in Newburg Park over the past year.
#### Data Table
| Distance from the Beach, \( x \) (in miles) | Selling Price, \( y \) (in thousands of dollars) |
|---------------------------------------------|--------------------------------------------------|
| 19.4 | 223.1 |
| 11.7 | 282.1 |
| 8.2 | 247.8 |
| 8.5 | 292.0 |
| 12.5 | 211.2 |
| 7.0 | 215.9 |
| 7.9 | 270.2 |
| 5.7 | 266.2 |
| 12.3 | 193.9 |
| 14.9 | 258.0 |
| 13.0 | 193.3 |
| 9.4 | 286.8 |
| 8.0 | 238.7 |
| 12.5 | 216.3 |
| 3.2 | 316.5 |
| 5.2 | 297.4 |
#### Scatter Plot Explanation (Figure 1)
The scatter plot visually represents the relationship between the "Distance from the Beach" (x-axis) and "Selling Price" (y-axis). Each point corresponds to a house's distance from the beach against its selling price. The data show a visible trend, suggesting that selling prices tend to decrease as the distance from the beach increases.
#### Statistical Analysis
- **Least-Squares Regression Line**: The slope of the regression line is approximately -5.48. This indicates that, on average, the selling price decreases by $5,480 for each additional mile away from the beach.
- **Questions to Consider**:
1. **Y-Intercept**: What is the y-intercept of the least-squares regression line for these data? Round your answer to at least two decimal places.
2. **Sample Correlation Coefficient**: What is
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