Correlation and regression · Grade 12

In Grade 12 you get fluent with: the correlation coefficient.

The product moment correlation coefficient r measures how closely points lie to a straight line. It goes from −1 (perfect negative) through 0 (none) to +1 (perfect positive). The least squares regression line y = a + bx is the best straight line for predicting y from x.

Key facts

• Sxx = Σx² − ((Σx)²)/n, Syy = Σy² − ((Σy)²)/n, Sxy = Σxy − ((Σx)(Σy))/n.
• r = Sxy ÷ √(Sxx × Syy). It is always between −1 and 1.
• Regression line of y on x: b = Sxy/Sxx and a = ȳ − bx̄.
• The regression line always passes through the mean point (x̄, ȳ).
• b is the change in y for each extra unit of x. a is the value of y when x = 0.
• Use the line of y on x to predict y from x, and only within the range of the data.
• Changing units (linear coding with positive multipliers) does not change r.

Worked examples

Other years

• Correlation and regression · Grade 9
• Correlation and regression · Grade 10
• Correlation and regression · Grade 11