# Multiple Linear Regression & Stepwise Regression

Can I predict the height of children from the height of their mother and father?

Can I predict product purity from the reaction temperature and reactor residence time?

Can I predict the hardness of a steel bar from the tempering temperature, bar size and time at temperature?

Can I predict a student's university grade point average on the basis of their high school grade point average and SAT score?

Can I predict my ice cream sales based on the temperature and humidity? Multiple linear regression is used to answer these types of questions by finding if there is a linear relationship between an effect (ice cream sales) and possible causes (temperature and humidity).  The SPC for Excel software contains regression as well as stepwise regression.

## Multiple Linear Regression/Stepwise Regression and SPC for Excel

Multiple linear regression is a method used to model the linear relationship between a dependent variable and one or more independent variables.  It allows you to examine what independent variables (x) impact a response variable (y) and by how much. SPC for Excel contains multiple linear regression that allows you to see if a set of x values impact the response variable.   The output from the SPC for Excel software  includes an in-depth analysis of residuals with potential outliers in red as well as multiple charts to analyze the results. You can easily remove independent variables as well as observations from the data and rerun the regression. You can also transform the y variables.  SPC for Excel also contains stepwise regression.  Stepwise regression is process of building a model by successively adding or removing variables based solely on the p values associated with the t statistic  of their estimated coefficients.   A complete list of regression features is given below.

## Multiple Linear Regression Features

ANOVA for Model

Variables Output

Coefficients

Standard error

t statistic, p value

95% confidence limit

VIF

Standardized coefficients

Regression statistics

R2

Mean, standard error

Coefficient of variation

Durbin-Watson statistic

PRESS

R2 prediction

Residuals analysis

Residuals

Leverage

Standardized residuals

Internally studentized residuals

Externally studentized residuals

DFFITS

Cook's distance

Standard error of estimated mean

95% confidence limits of estimate means

Potential outliers in red

Residuals charts (raw, standardized, internally or externally studentized residuals)

Normal plot

Versus predicted values

Versus observation number

Versus predictor variables

Other charts

Predicted vs actual

DFFITS, Cook's distance and leverage versus observation number

Remove variables

Remove observations

Transform y variables

p values < 0.05 in red

## Stepwise Regression Features

Changed p values to enter and to remove variables

Fit intercept

Output lists each step of the regression where a variable is added or removed

Output includes the coefficient, t statistic and p value for each included variable in each step

Output includes sigma, R2 , and R2 adjusted for each step