Linear Regression Calculator

About Linear Regression Calculator

Linear regression finds the best-fit line through data points by minimizing the sum of squared residuals (least squares method).

How to use this calculator

1. Enter your paired data values as \(x\) and \(y\) points.
2. Run the calculation to find the slope \(m\) and intercept \(b\).
3. Read the equation of the best fit line, \(y = mx + b\).
4. Use the line to estimate \(y\) for a chosen \(x\) value.

The formula explained

The formula \(y = mx + b\) computes the line of best fit. Here, \(m\) tells the rate of change, and \(b\) tells where the line crosses the \(y\)-axis.

• x = the input or independent variable
• y = the predicted or dependent variable
• m = the slope of the best fit line
• b = the y-intercept, where the line crosses the y-axis

Step by step method

1. Choose two points on the trend line, or use the calculator to process all data points.
2. Find the slope with \(m = \frac{y_2 - y_1}{x_2 - x_1}\) if you are working by hand.
3. Use one point and the slope to solve for \(b\) in \(y = mx + b\).

Worked example

Problem. Find the line of best fit for the data points \((1, 2)\), \((2, 3)\), \((3, 5)\), and \((4, 4)\).

1. The calculator identifies a best fit line with slope about \(m = 0.8\).
2. Using the data, it finds the intercept is about \(b = 1.4\).
3. So the regression line is \(y = 0.8x + 1.4\).

Tips and common mistakes

• Linear regression gives a best fit, not a perfect fit, so the line may not pass through every point.
• Make sure your \(x\) and \(y\) values are paired correctly, because switching them changes the result.

Frequently asked questions