Simple linear regression model

The linear regression model for a normally distributed outcome (response) variable and a single predictor (explanatory) variable. The straight line models the mean value of the response variable for each value of the explanatory variable. The major assumption is constant variation of residuals along the fitted line which points out that the model is equally good across all x values. The null hypothesis stating that the explanatory variable has no effect on the response (in other words, the slope of the fitted line is zero) can be tested statistically. The two main aims of regression analysis are to predict the response and to understand the relationships between variables. As in all linear models, the error term is additive (as opposed to multiplicative, i.e. and independent, and they are assumed to have a normal distribution. As an exception, the simple linear regression is a special case for generalized linear models.