01 Key Concepts
Linear Regression
Models the relationship between an independent variable (x) and dependent variable (y) using a straight line: y = mx + b.
Line of Best Fit
The line that minimizes the overall distance between itself and all the data points, typically found using the least-squares method.
Slope (m)
Represents how much y changes for every one-unit increase in x — the rate of change in the relationship.
Y-Intercept (b)
The predicted value of y when x = 0 — where the line crosses the y-axis.
Using 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.
02 Key Formulas
- y = mx + b
03 Solved Examples
Example 1 A regression line is y = 2x + 5. Predict y when x = 10.
- Substitute x=10 into the equation: y = 2(10) + 5 = 20 + 5.
Answer: y = 25
Example 2 A regression line is y = -3x + 50. Find the slope and y-intercept, and interpret the slope.
- Slope (m) = -3, y-intercept (b) = 50.
- A slope of -3 means y decreases by 3 for every 1-unit increase in x.
Answer: Slope = -3 (y decreases as x increases), y-intercept = 50
Example 3 Given the points (1,3) and (3,9), assuming a line through them, find the slope.
- Slope = (change in y) / (change in x) = (9-3)/(3-1) = 6/2.
Answer: Slope = 3
04 Practice Questions
1A regression line is y = 4x + 2. Predict y when x = 5.
22
2A regression line is y = -2x + 20. Find the y-intercept.
20
3For y = 5x - 1, find the slope.
5
4If the slope of a regression line is negative, how does y behave as x increases?
y decreases as x increases
5What does the y-intercept represent in a regression line?
The predicted value of y when x = 0
📄 Regression — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.