Linear Regression

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Purpose

Linear regression is used to estimate the parameters of an equation relating a particular variable (dependent variable or "Y") to another variable (independent variable or "X"), where the resulting equation is called a "regression equation" or "regression model". Simple linear regression is applied when the dependent variable is linearly proportional to just one independent variable.


Anatomy

Linear Regression

Reference: Juran's Quality Control Handbook

Terminology

A. Regression equation – expressing the predicted value as a function of the "X" and coefficients.

B. A sufficiently small p-value (e.g. p<alpha) is indicative that the coefficient is statistically significant.

C. R-Sq - (r2) Coefficient of Determination is the ratio of SS regression/SStotal and is a measure of the fit of the regression to the data. It suggests a very good fit when "R-Sq" approaches 100%, and a poor fit when it is small. R-Sq(adj) is adjusted for the degrees of freedom.

D. Analysis of Variance – standard interpretations apply to the Sum of Squares (SS), Mean Sum of Squares (MS), the F-value and P-value corresponding to the F-Test.

E. A sufficiently small p-value (e.g. p<alpha) is indicative that the regression is statistically significant.


Major Considerations

Linear regression is applied with the assumption that the dependent variable is linearly proportional to the independent variable, and the data has to be paired.

Simple regression is applicable to one independent variable, while multiple regression is used for cases with more than one independent variable.

Application Cookbook

1. Collect data samples.

2. Enter the data corresponding to the independent variable and dependent variable into two separate columns in Minitab.

3. Select Stat – Regression – Regression.

4. In the Response field, select column corresponding to the dependent variable.

5. In the Predictors field, select column corresponding to the independent variable.

6. For Options, select "Fit Intercept" but leave all other settings unchecked for basic applications.

7. Carry out residual analysis (see tool Residual Plots).

8. Check if the P value is sufficiently small (i.e. P<alpha) to conclude that the regression is statistically significant.

From Linear Regression to Six Sigma Tools.

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