Statistical significance is often confused with the size of the observed effect. Statistical significance tells you, or should tell you, how likely you are to observe a given relationship by mere chance - if, in fact, no such relationship actually exists.

In a linear regression analysis, it is assumed that - if no relationship exists - the fitted line would be horizontal (on average at least). The reasoning underlying statistical tests in general, and regression analyses in particular are explored in Units 5 and 12.