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 1532 2525 3002 3022
Selling Price $92,178 $220,000 $255,000 $269,000
A linear regression equation is
enter your response here.
(Type an equation. Use integers or decimals for any numbers in the equation. Round to three decimal places as needed.)
The scatter plot for the given data is as follows:
```
300,000 | *
|
|
|
250,000 | * *
|
|
|
200,000 | *
| *
|
| *
150,000 | *
___________________________
1500 2000 2500 3000
```
To find the linear regression equation, we can use the least squares method. The equation has the form:
y = mx + b
Where:
- y represents the selling price of the house
- x represents the number of square feet
- m is the slope of the line
- b is the y-intercept of the line
To find the values of m and b, we need to calculate the following sums:
n = number of data points = 4
Σx = sum of x values = 1532 + 2525 + 3002 + 3022 = 10081
Σy = sum of y values = 92178 + 220000 + 255000 + 269000 = 836178
Σxy = sum of the product of x and y = (1532 * 92178) + (2525 * 220000) + (3002 * 255000) + (3022 * 269000) = 2200861566
Σx^2 = sum of the squared x values = (1532^2) + (2525^2) + (3002^2) + (3022^2) = 15141933
Using these values, we can calculate the slope m and y-intercept b with the following formulas:
m = (n * Σxy - Σx * Σy) / (n * Σx^2 - (Σx)^2)
b = (Σy - m * Σx) / n
Let's plug in these values and calculate:
m = (4 * 2200861566 - 10081 * 836178) / (4 * 15141933 - 10081^2)
= 8604906.5 / 2355532.75
≈ 3.655
b = (836178 - 3.655 * 10081) / 4
≈ 18635.5
Therefore, the linear regression equation representing the relationship between the number of square feet and the selling price of the house is:
y = 3.655x + 18635.5