Given the following data for four houses sold in comparable neighborhoods and their corresponding number of square feet, draw a scatter plot and find a linear regression equation representing a relationship between the number of square feet and the selling price of the house.
Square Feet 1548 2546 3000 3017
Selling Price $94,031 $239,000 $253,000 $272,000
To draw a scatter plot, you will need to plot the number of square feet on the x-axis and the selling price on the y-axis. The scatter plot will show the relationship between these two variables.
Here is the scatter plot:
```
|
280,000 | x
260,000 |
240,000 | x
220,000 |
200,000 |
180,000 |
160,000 | x
140,000 |
120,000 |
40,000 | x
0 |_________________________
1400 2000 3000
Square Feet
```
To find a linear regression equation representing the relationship between the number of square feet and the selling price, you can use the least squares method. This will enable you to find the equation of the line that best fits the data points.
Using the given data, the table below shows the number of square feet (x), the selling price (y), and the product of the number of square feet and the selling price (xy).
```
x | y | xy
1548 | $94,031 | $145,040,388
2546 | $239,000 | $607,694,000
3000 | $253,000 | $759,000,000
3017 | $272,000 | $821,824,000
```
Next, calculate the sum of each column: Σx, Σy, and Σxy.
```
Σx = 10111
Σy = $858,031
Σxy = $2,333,558,388
```
Calculate the mean of the number of square feet (x̄) and the selling price (ȳ).
```
x̄ = Σx/n = 10111/4 = 2527.75
ȳ = Σy/n = $858,031/4 = $214,507.75
```
Now, calculate the sums of squares:
```
Σx^2 = 15236638
Σy^2 = $939,792,266,561
```
Finally, calculate the slope (m) and y-intercept (b) of the regression line:
```
m = (Σxy - n * x̄ * ȳ) / (Σx^2 - n * x̄^2)
= ($2,333,558,388 - 4 * 2527.75 * 214507.75) / (15236638 - 4 * 2527.75^2)
= $0.114267442
b = ȳ - m * x̄
= $214,507.75 - $0.114267442 * 2527.75
= $214,507.75 - $289.16
= $214,218.59
```
Therefore, the linear regression equation representing the relationship between the number of square feet and the selling price is:
Selling Price = $214,218.59 + $0.114267442 * Square Feet