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.

Question

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.)

Answer 1

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