Square Feet:1511, 2512, 3007, 3015
Selling Price: $93,246, $229,000, $250,000, $265,000
A linear regression equation is ___
The linear regression equation is:
Selling Price = 98.79 * Square Feet - 10011.05
without words
\[
\text{Selling Price} = 98.79 \times \text{Square Feet} - 10011.05
\]
square feet symbol
The symbol for square feet is ft².
To find the linear regression equation using the given data, we need to determine the equation of the line that best fits the relationship between the square feet and selling price.
We can use the formula for the equation of a straight line, which is y = mx + b, where:
- y represents the dependent variable (selling price in this case)
- x represents the independent variable (square feet in this case)
- m represents the slope of the line
- b represents the y-intercept (the point where the line intersects the y-axis)
To find the slope (m) and y-intercept (b), we'll make use of statistical concepts such as the mean and covariance.
Step 1: Calculate the means
Let's calculate the mean of the square feet (x) and the mean of the selling price (y).
Mean of x (square feet):
(x₁ + x₂ + x₃ + x₄) / 4
Mean of y (selling price):
(y₁ + y₂ + y₃ + y₄) / 4
Step 2: Calculate the covariance and variance
Next, we need to calculate the covariance between x and y and the variance of x.
Covariance (cov) of x and y:
cov(x, y) = [ (x₁ - mean of x)(y₁ - mean of y) + (x₂ - mean of x)(y₂ - mean of y) + (x₃ - mean of x)(y₃ - mean of y) + (x₄ - mean of x)(y₄ - mean of y) ] / 4
Variance (var) of x:
var(x) = [ (x₁ - mean of x)² + (x₂ - mean of x)² + (x₃ - mean of x)² + (x₄ - mean of x)² ] / 4
Step 3: Calculate the slope and y-intercept
Finally, we can calculate the slope (m) and y-intercept (b) using the following formulas:
Slope (m):
m = cov(x, y) / var(x)
Y-intercept (b):
b = mean of y - (m * mean of x)
Plug in the values you calculated from the given data into the formulas to get the slope and y-intercept. You can then substitute the values into the equation y = mx + b to obtain the linear regression equation.