A linear regression calculator is used to analyze the relationship between two variables. It helps determine how one variable (the independent variable) influences another (the dependent variable).
Linear regression assumes a linear relationship between the variables, represented by a straight line on a scatter plot. The calculator determines the best-fitting line through the data points, minimizing the overall distance between the line and the actual data points.
Linear Regression Example Chart
| X (Independent) | Y (Dependent) |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 5 |
| 4 | 4 |
| 5 | 6 |
Linear Regression Formula
The linear regression formula is:
Y = mx + bWhere:
- Y is the dependent variable
- m is the slope of the line
- x is the independent variable
- b is the y-intercept
We can calculate the slope (m) and y-intercept (b) using the following formulas:
m = (n∑xy - ∑x∑y) / (n∑x² - (∑x)²)
b = (∑y - m∑x) / nWhere n is the number of data points.
How do you calculate the linear regression equation?
To calculate the linear regression equation:
Sum up all x values, y values, xy products, and x² values.
Use these sums to calculate the slope (m) using the formula above.
Calculate the y-intercept (b) using the slope and the sums of x and y.
Plug the calculated m and b values into the equation Y = mx + b.
For our example data, after calculations, we might end up with an equation like:
Y = 0.8x + 1.6This equation can be used to predict Y values for any given X value within the range of our data.