Interpretation of the Regression Equation

Whichever way you calculate the coefficients, you should have a value for:

• Intercept, a 

• Slope (or X coefficient), b

The equation is y = a + bx or, sales = 17.45 +0.62* advertising

The slope (gradient or x coefficient), b , shows the rate of increase of the sales with advertising.  In other words, if b is larger then a small increase in advertising will cause a large increase in sales; but if b is small then a large increase in advertising is needed to obtain a small increase in sales.  So b shows the effectiveness of advertising in changing sales.

The intercept (constant) a is the value of the y when x is zero – what sales would be if there was no advertising.

In using a regression equation, we need to look at three main points.

1. r Squared

The closer this is to 1, the closer the points lie to the straight line, and the better any predictions made using the line will be.

2. Slope

This is the rate of change of y with respect to x.  Even if we had r close to 1, but the slope was flat (close to), then changes in x would not cause much change in y, so would not be very useful or meaningful.

3. Intercept 

This is the fixed value of y when x is zero