4.3 Correlation and Regression
We can have different types of correlation and we try to draw a line of best fit, if we can, through the points plotted on the scatter diagram, which will allow us to make point estimates of values of y for any given x.
The line we draw is called the line of regression of y on x. It allows us to predict a value of y for a given value of x, but not the other way round.
We will be looking at linear regression, where the line of best fit is a straight line. But other forms of regression exist, and many scientific calculators with statistical functions can apply more than one form of regression to given data so that you can choose the best one (note – so that you can choose, the calculator won’t make the choice for you!)
| Here we have positive linear correlation.
The line of points is best approximated by a straight line whose form is y = a + bx where b will have a positive value because the line is sloping up from left to right. |
