Least squares regression line

Definition

The least squares regression line ŷ = a + bx minimises the total squared vertical distance between the data points and the line. It is used to predict one variable from another.

Worked example

If ŷ = 12 + 3,5x, a learner studying 6 hours is predicted to score 12 + 3,5(6) = 33 marks.

Where it appears in the exam

Paper 2 asks you to find the least squares regression line with a calculator, draw it on a scatter plot and use it to predict values.

Step-by-step method

1. Enter the paired data in regression mode.
2. Read off a and b and write ŷ = a + bx.
3. Substitute the given x-value to predict y.
4. Comment on how reliable the prediction is, using r.

Common mistake

Swapping a and b, because calculators label them differently.

Related statistics terms

• Standard deviation
• Correlation coefficient
• Outlier

Frequently asked questions

What does least squares regression line mean in Grade 12 Maths?

The least squares regression line ŷ = a + bx minimises the total squared vertical distance between the data points and the line. It is used to predict one variable from another.

Which NSC paper tests least squares regression line?

Least squares regression line belongs to the Statistics section of CAPS Grade 12 Mathematics, which is examined in Paper 2.

How do I practise questions involving least squares regression line?

Snap a question that uses least squares regression line into the Snap&Learn AI solver, or work through the statistics topic guide and NSC past papers.