Regression

If Correlation test is selected and and the comparing column contains 4 or more values in the same row the regression formula is calculated.
Calculates the linear regression formula between two comparing columns.
The correlation does not work in DOE mode because there are no pairs in this mode.

Interpretation

• The resulting formula is the fitted line between the two data sets. With this formula you can calulate the Y value out of a given X value.
• For a good regression calculation there must be an Correlation between the data sets.

Formula for calculating the linear regression formula.

Legend

x = Current column
y = Comparing column

Example

Between datasets A and D is a correlation (Row Correl p <0.05) and the regression is 0.51X + 0.49.

External links

http://en.wikipedia.org/wiki/Simple_linear_regression

Multiple linear Regression

Formula

Correlation coefficients

The formula is put in to matrices.





To Calculate the factors the following formula is used



To calculate the correlation coefficient the following formulas are used.

Anova table

	df	SS	MS
Total	n-1
Regression	k
Error	n-k-1

Legend

=Transposed matrix
=inverse matrix
= y value predicted by the formula
= Average y value
= error
= multiple correlation coefficient

External links

• http://en.wikipedia.org/wiki/Linear_regression
• http://en.wikipedia.org/wiki/Matrix_%28mathematics%29