Statistics · Quick Reference

Regression Cheat Sheet

Statistics · Lesson 9/11

In one line: regression finds the best-fitting line through a set of data points, letting us model the relationship between two variables and make predictions.

Key Ideas

1Linear Regression. Models the relationship between an independent variable (x) and dependent variable (y) using a straight line: y = mx + b.

2Line of Best Fit. The line that minimizes the overall distance between itself and all the data points, typically found using the least-squares method.

3Slope (m). Represents how much y changes for every one-unit increase in x — the rate of change in the relationship.

4Y-Intercept (b). The predicted value of y when x = 0 — where the line crosses the y-axis.

5Using Regression to Predict. Once the line's equation is known, substitute any x-value to predict the corresponding y-value, though predictions become less reliable far outside the range of the original data.

Worked Examples

A regression line is y = 2x + 5. Predict y when x = 10.

y = 25

A regression line is y = -3x + 50. Find the slope and y-intercept, and interpret the slope.

Slope = -3 (y decreases as x increases), y-intercept = 50

Given the points (1,3) and (3,9), assuming a line through them, find the slope.

Slope = 3

Formulas

y = mx + b

Practice Yourself

A regression line is y = 4x + 2. Predict y when x = 5.

A regression line is y = -2x + 20. Find the y-intercept.

For y = 5x - 1, find the slope.