Quantitative Analysis for Management, 13/e

4.7 Multiple Regression Analysis

The multiple regression model is a practical extension of the model we just observed. It allows us to build a model with several independent variables. The underlying model is

A multiple regression model has more than one independent variable.

$$Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\dots +{\beta }_k{X}_k+ϵ$$ (4-16)

where

$$\begin{array}{lll}\hfill Y& =\hfill & \text{dependent variable (response variable)}\hfill \\ \hfill X_i& =\hfill & i\text{th independent variable (predictor variable or explanatory variable)}\hfill \\ \hfill {\beta }_0& =\hfill & \text{intercept (value of }Y\text{ when all }{X}_i\text{ = 0)}\hfill \\ \hfill {\beta }_1& =\hfill & \text{coefficient of the }i\text{th independent variable}\hfill \\ \hfill k& =\hfill & \text{number of independent variables}\hfill \\ \hfill ϵ& =\hfill & \text{random error}\hfill \end{array}$$

To estimate the values of these coefficients, a sample is taken and the following equation is developed:

$$\widehat{Y}=b_0+b_1{X}_1+b_2{X}_2+\cdots +b_k{X}_k$$(4-17)

where

$$\begin{array}{lll}\hfill \widehat{Y}& =\hfill & \text{predicted value of }Y\hfill \\ \hfill b_0& =\hfill & \text{sample intercept (and is an estimate of ...}\hfill \end{array}$$