Keypoints

• Linear regression is a statistical method to build a model where one or more predictor variables explain a response variable (in this course we only study the situation with one predictor variable). Even though a causal relation between predictor and response may be plausible, the statistical method itself will only give evidence for correlation, not a causal relationship.

• A regression model can be used to make predictions for the response variable at any value for the predictor variable and provides confidence bounds around this regression line as well.

• Apart from providing a model, the regression framework provides a hypothesis test for the linear association between the predictor and response variable as well. The null-hypothesis is that there is no linear association between the two variables.

• For the model to be reliable and the results of the hypothesis test to be valid, the assumptions that underly the regression model need to be met: 1) linearity, 2) homoscedasticity, 3) normality of residuals and 4) absence of influential datapoints. These assumptions can be checked via diagnostic plots.