Regression & Correlation — A-Level Mathematics Revision
Revise Regression & Correlation for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Statistical SamplingWhat is Regression & Correlation?
Regression and correlation at A-Level involve analysing the relationship between two variables. You will learn to calculate and interpret the product moment correlation coefficient to measure the strength of a linear relationship, and to find the equation of a regression line to make predictions.
Board notes: All A-Level Maths boards (AQA, Edexcel, OCR) cover regression and correlation. The calculation of the product moment correlation coefficient and the equation of the regression line are key topics for all boards.
Step-by-step explanationWorked example
A set of data has a product moment correlation coefficient of 0.8. This indicates a strong positive linear relationship between the two variables. The equation of the regression line of y on x is y = 2x + 5. If x = 10, the predicted value of y is 2(10) + 5 = 25.
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Common mistakes
- 1Confusing correlation with causation. A strong correlation between two variables does not necessarily mean that one causes the other; there may be a third variable involved.
- 2Extrapolating beyond the range of the data when using a regression line to make predictions. The regression line is only valid for the range of the data used to create it.
- 3Incorrectly interpreting the product moment correlation coefficient. A value close to 1 or -1 indicates a strong linear relationship, while a value close to 0 indicates a weak linear relationship.
Regression & Correlation exam questions
Exam-style questions for Regression & Correlation with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Regression & Correlation
Core concept
Regression and correlation at A-Level involve analysing the relationship between two variables. You will learn to calculate and interpret the product moment correlation coefficient to measure the stre…
Frequently asked questions
What is the difference between the regression line of y on x and the regression line of x on y?
The regression line of y on x is used to predict y from x, and it minimises the sum of the squared vertical distances from the data points to the line. The regression line of x on y is used to predict x from y, and it minimises the sum of the squared horizontal distances.
What is the product moment correlation coefficient?
The product moment correlation coefficient (PMCC), denoted by r, is a measure of the linear correlation between two variables. It takes a value between -1 and 1, where 1 is total positive linear correlation, -1 is total negative linear correlation, and 0 is no linear correlation.