1. The slope
represents the the average change in Y associated with a change of one unit on X.
If the relationship between X and Y is causal, then the slope lets you know how much
you can change the average value of Y by increasing X.

2. The standard
error of the estimate reflects the degree to which the points diverge from the
regression line. It reflects the accuracy of the prediction.

3. The standard
deviation of X is related to the variance explained. If a variable has a very
small standard deviation then it will not be able to explain much variance.

4. Pearson's
r is determined by the three independent components: the slope, the standard
error of the estimate, and the standard deviation of X. The same value of r can be
composed of different combinations of these components. The following table shows
three ways to product an r of .707.

Slope |
SE |
sd |
r |

1 |
10 |
10 |
.707 |

.5 |
5 |
10 |
.707 |

1 |
5 |
5 |
.707 |

5. r

The variance explained is equal to (slope

^{2})(sd_{x}^{2}).

The variance unexplained is equal to SE_{est}^{2}.

r^{2 }= explained/(explained + unexplained).

6. The standard deviaiton of Y is simply the square root of the total variance as described above.