# 46. Statistics – Multiple Regression

Multiple regression has a similar approach just like a prototypical linear regression would have (see the reference post). But instead of using one variable, this section will encounter and demonstrate when there are multiple variables effecting the regression analysis.

The multiple regression’s approach are as following, similar to the linear regression. Except the matrix formulation will be applied since it’s a linear set of equations. And for the bold letters, this is to indicate it’s in the matrix form.

This is to use the existing values (displayed output and input) to estimate the equation or regression model.

This is to evaluate whether the slope of the regression is sufficient for the estimation of regression model.

Use ANOVA method to calculate the effectiveness of regression while verifying the coefficient of determination (R square value) to see the correlation and matching level between regression and actual data.

This is to finalize the average’s error based on the estimated regression line. Also helps to evaluate the estimate value’s confidence interval zone.

The following reference and examples are the complete procedure from establish regression, effectiveness of coefficients, regression effectiveness via ANOVA and R2 value before finalizing with average’s error of estimates.

*Multiple Regression Estimation Example*

*Multiple Regression’s Hypothesis Testing Example*

*Multiple Regression’s ANOVA Evaluation Example*

*Multiple Regression’s Error Estimation Example*

*Multiple Regression’s Error Estimation with Specific Population/Individual Example*