the slope of the simple linear regression equation

The variability in the baseline model is the residual ① Y − Ȳ. The baseline model ( Figure 1A) explains Y using only the mean of Y, which makes a flat line ( Ȳ). Therefore, there is a need for evaluation of the regression line, such as “how much better it is than the baseline model using only the mean of the dependent variable”.įigure 1 depicts baseline and regression models and their difference in variability. Hopefully, we can expect an effective reduction of variability of Y as the result of adding X into the model. However, when we have other information related to the dependent variable, such as a continuous independent variable, X, we can try to reduce the (unexplained) variability of dependent variable by adding X to the model and we model a linear regression line formed by the predicted value by X, Ŷ.

In this situation, we need to model the mean of Y, Ȳ, to explain the variability, which is regarded as a basic or baseline model.

To compare models, we consider a basic situation where we have information on the dependent variable only. An important purpose of data analysis is to explain the variability in a dependent variable, Y.

The slope of the simple linear regression equation