## Regression Line

The coefficients and of the linear regression model

The data set consists of

- explanatory variable for 's;
- dependent variable for 's.

and
.

Here the values , , , and are computed as in the following table.

Variable | Mean | Sum of squares |

Explanatory | ||

Response |

The sample correlation

.

describes the strength of linear relationship for the pair
of data.
Here
is the sum of squares within the response variable 's.
The value
is always between and .
The value
is close to when the pairs lie close to the straight line
with positive slope,
and it is close to when it is aligned with a negative slope.
The fitted linear model