Quantitative Analysis for Management, 13/e

4.5 Testing the Model for Significance

Both the MSE and $r^2$ provide a measure of accuracy in a regression model. However, when the sample size is too small, it is possible to get good values for both of these even if there is no relationship between the variables in the regression model. To determine whether these values are meaningful, it is necessary to test the model for significance.

To see if there is a linear relationship between X and Y, a statistical hypothesis test is performed. The underlying linear model was given in Equation 4-1 as

$$Y={\beta }_0+{\beta }_{1}X+ϵ$$

If ${\beta }_1=0,$ then Y does not depend on X in any way. The null hypothesis says there is no linear relationship between the two variables (i.e., ${\beta }_1=0$). The alternate hypothesis is that there is a linear ...