Chapter 4

The least-squares regression line

1. Specify how a regression function is related to the task of predicting one outcome from another.
2. Specify the form of a simple linear regression of a response variable \(y\) on an explanatory variable \(x\). Equivalently, identify the form of a simple linear regression model for predicting a response variable \(y\) using a predictor variable \(x\).
3. Recall, from either high school or college algebra / precalculus, the equation for a line and the interpretation of the slope and intercept of the line.
4. Identify the slope and intercept from a simple linear regression model, and interpret the slope and intercept in the context of a prediction problem.
5. Use a simple linear regression model to predict a response variable at a given value of the predictor.
6. Determine the residual / error of a prediction given a simple linear regression model, a value for the explanatory variable, and a response variable at that value of the explanatory variable.

Association does not imply causation

1. Give examples where an observed association between two variables does not result from a causal influence from one variable to the other.
2. Explain the motto “association does not imply causation,” or its more popular counterpart “correlation does not imply causation.”

R

1. Perform a simple linear regression using R.
2. Relate the output of lm to the slope and intercept of the fitted simple linear regression equation.