One More Linear Regression Example

As a recap, the assumptions that go into linear regression are:

• Relationship is in fact linear
• Errors should be normally distributed
• Errors should have constant variance
  • Variability of errors (and thus the variability of the predicted $$y$$'s) should not depend on $$x$$
• Errors should not display any obvious pattern

When you have an $$r^2$$ value, you can say that about $$r^2$$ of the variability in $$y$$ can be explained by the linear relationship with $$x$$.

When you get a $$t$$ value and a $$p$$ value from SPSS for linear regression, what you are getting is a $$p$$ value for $$\beta_1 > 0$$. You have to convert the two-tailed $$p$$-value to a one-sided $$p$$-value. If it is greater than 0, divide by two. If this is a less than alternative, subtract 1 and then divide by 2.

You use $$\beta_1$$ for knowing about the population parameter, and you use $$b_1$$ for the sample statistic.

In regression, you can't use the F statistic because you can only use that when you have an alternative of "not equal to".