Standardized Multiple Regression is a method that helps to control round-off errors in normal calculations, and it also allows the estimated regression coefficients to be compared in common units.
Correlation Transformation is the transformation that obtains the standardized regression model by helping to control round-off errors and by expressing the coefficients in the same units.
Standardizing a variable involves centering and scaling.
Centering is the method of taking the difference between each observation and the mean of all the observations.
Scaling expresses the centered observation in the units of the standard deviation of the observations.
Some of the difficulties with the non-standardized regression equation are:
Rounding errors may occur when:
the number of X variables is considerably large (even if you use many digits in the calculations)
the inverse
of
is taken or if:
has
a determinant close to 0
the
elements of
vary greatly in the order of magnitude
the X
variables have different magnitudes which causes the entries for the
matrix to cover a broad range.
The differences in the units involved make it hard to compare the regression coefficients.
First, let's look at an example to see the output that should be expected.
Regression Tutorial Menu Dictionary