ABSTRACT
In Chapter 20 an example was given of attempts to predict mathematical ability from ability at English. It was pointed out that the equation for linear regression is the equation for the straight line that could be drawn through the data points on a scattergram such that the distance between the line and the points was at a minimum. This line is called the best-fit line and for simple linear regression (where there is one IV and one DV) is always of the form:
DV = a + (b × IV)
or rather, when the prediction is not perfect:
predicted DV = a + (b × IV)
(a and b are described as regression coefficients. If we were drawing the bestfit line on a graph, a would be the point where the line crosses the vertical
axis. It is called the intercept and is the value the predicted DV would have if the IV were 0. The slope of the line would be b; that is, the amount by which the DV would change for every change of one unit in the IV.)
To find b, we use the following equation:
b
n n
[ ( )] ( )
[ ( )] ( ) =
× × − ×
× −
total of IV DV total for IV total for DV total of IV total for IV2 2
where n is the sample size and total of (IV × DV) means multiply each person’s score on the IV by the same person’s score on the DV and add the results for each person together.
