Linear Regression
Linear regression studies linear relationships between a response and one or more predictors. The basic idea is to model the mean response as a linear function of explanatory variables plus an error term.
In general form,
$$y_i = \beta_0 + \beta_1 x_{i1} + \cdots + \beta_p x_{ip} + e_i.$$Key assumptions emphasized in STA305 are linearity in the mean, constant variance, independence of errors, and approximate normality when inference is required.