Abstract
We study the simple linear regression model which, except for random error, assumes a straight-line relationship between a response and an input variable. We use the method of least squares to estimate the parameters of this model. Assuming that the random error is normal with mean 0 and variance σ2σ2, we show how to test hypotheses concerning the parameters of the model. The concept of regression to the mean is introduced; we explain when it arises and how one must be careful to avoid the regression fallacy in its presence. We explain the coefficient of determination. Finally, we introduce the multiple linear regression model, which relates a response variable to a set of input variables.
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