Correlation and regression · Grade 10
In Grade 10 you learn: regression lines.
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.
- 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
Example 1
Find the regression line of y on x for x: 1, 2, 3, 4, 5 and y: 3, 5, 4, 7, 8.
Answer: y = 1.8 + 1.2x