Quantitative Analysis for Management, 13/e

4.2 Simple Linear Regression

In any regression model, there is an implicit assumption (which can be tested) that a relationship exists between the variables. There is also some random error that cannot be predicted. The underlying simple linear regression model is

$$Y={\beta }_0+{\beta }_{1}X+ϵ$$(4-1)

where

$$\begin{array}{lll}\hfill Y& =\hfill & \text{dependent variable (response variable)}\hfill \\ \hfill X& =\hfill & \text{independent variable (predictor variable or explanatory variable)}\hfill \\ \hfill {\beta }_0& =\hfill & \text{intercept (value of }Y\text{ when }X\text{ = 0)}\hfill \\ \hfill {\beta }_1& =\hfill & \text{slope of regression line}\hfill \\ \hfill ϵ& =\hfill & \text{random error}\hfill \end{array}$$

The dependent variable is Y and the independent variable is X.

The true values for the intercept and slope are not known, and therefore they are estimated using sample data. The regression equation based on sample data is given as

Estimates of the slope and intercept are found ...