# 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 calculate 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 data-sets A and D is a correlation (Row Correl p <0.05) and the regression is 0.51X + 0.49.

Data file

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

# Multiple linear Regression

## Interpretation

• The resulting formula is the fitted line between the two or more data sets. With this formula you can calculate the Y value out of a given X value.
• The p value of the T-test of the predictor indicates if a predictor is significant
• The P value of the Anova is an indication if there is at least one significant predictor.
• RÂ²adj indicates how good the data is fitting the regression model the higher the value the more significant.
• For a good regression calculation the residual must be normally distributed Normally p higher than 0.10.

### 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

### Example

To use the Multiple Regression test "Menu: Tools=> Multiple Linear Regression". Then select the input data-sets and a response data set. In this example the regression is a significant.
According the Anova there is at least one predictor significant. Looking to the T-test predictor A is significant. And the the normality of the residual is OK it is bigger than 0.10.

Data file