Correlation and regression · Year 12
In Year 12 you learn: correlation.
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.
- 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.