Next section: Confidence intervals and significance tests

The sum of the squared deviations of Y from the mean of Y (Y

The table below shows an example of this partitioning.

X |
Y |
Y-Y _{M} |
(Y-Y _{M})² |
Y' |
Y'-Y _{M} |
(Y'-Y _{M})² |
Y-Y' |
(Y-Y')² |

2 3 4 5 |
5 6 9 10 |
-2.5 -1.5 1.5 2.5 |
6.25 2.25 2.25 6.25 |
4.8 6.6 8.4 10.2 |
-2.7 -0.9 0.9 2.7 |
7.29 0.81 0.81 7.29 |
0.2 -0.6 0.6 -0.2 |
0.04 0.36 0.36 0.04 |

Sum: |
30 |
0.0 |
17.00 |
30.0 |
0.0 |
16.20 |
0.0 |
0.8 |

The regression equation is:

Y' = 1.8X + 1.2

and Y

Defining SSY, SSY' and SSE as:

SSY = Σ(Y - Y

You can see from the table that SSY = SSY' + SSE which means that the sum of squares for Y is divided into the sum of squares explained (predicted) and the sum of squares error. The ratio of SSY'/SSY is the proportion explained and is equal to r². For this example, r = .976, r² = .976² = .95. SSY'/SSY = 16.2/17 = .95.

Next section: Confidence intervals and significance tests