Calculating Linear Regressions or Correlation Coefficients
Problem
You want to calculate the least-squares regression line for two variables or the correlation coefficient that expresses the strength of the relationship between them.
Solution
Apply summary functions to calculate the necessary terms.
Discussion
When the data values for two variables X and Y are stored in a database, the least-squares regression for them can be calculated easily using aggregate functions. The same is true for the correlation coefficient. The two calculations are actually fairly similar, and many terms for performing the computations are common to the two procedures.
Suppose that you want to calculate a least-squares regression
using the age and test score values for the observations in the
testscore
table:
mysql>SELECT age, score FROM testscore;
+-----+-------+
| age | score |
+-----+-------+
| 5 | 5 |
| 5 | 4 |
| 5 | 6 |
| 5 | 7 |
| 6 | 8 |
| 6 | 9 |
| 6 | 4 |
| 6 | 6 |
| 7 | 8 |
| 7 | 6 |
| 7 | 9 |
| 7 | 7 |
| 8 | 9 |
| 8 | 6 |
| 8 | 7 |
| 8 | 10 |
| 9 | 9 |
| 9 | 7 |
| 9 | 10 |
| 9 | 9 |
+-----+-------+
The following equation expresses the regression line, where
a
and b
are the intercept and slope of the
line:
Y
=bX
+a
Letting age
be
X
and score
be Y
, begin
by computing the terms needed for the regression equation. These
include the number of observations; the means, sums, and sums of
squares for each variable; and the sum of the products of each
variable:[17]
mysql>SELECT
->@n := COUNT(score) AS N, ...
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