Section 9.3: Regression

  1. Define the terms “response” and “predictor” in the context of predicting one outcome from another, and identify what outcome is the response and what outcome is the predictor when give a prediction problem.
  2. Specify how a regression function is related to the task of predicting one outcome from another.
  3. Specify the form of a simple linear regression of a response \(y\) on a predictor \(x\). Equivalently, identify the form of a simple linear regression model for predicting a response \(y\) using a predictor \(x\).
  4. Perform a simple linear regression using Minitab.
  5. 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.
  6. Identify the slope and intercept from a simple linear regression model, and interpret the slope and intercept in the context of the prediction problem.
  7. Explain, with an example, why the causal interpretation of the slope of a simple linear regression model as ‘the amount that the response increases as the predictor increases by 1 unit’ is generally not correct.
  8. Use a simple linear regression model to identify the best prediction of the response at a given value of the predictor.
  9. Explain, qualitatively, in what sense the line determined by simple linear regression is the ‘line of best fit.’ That is, what do we mean by ‘fit’ and what do we mean by ‘best’?
  10. Determine the error of a prediction given a simple linear regression model, a value for the predictor, and a response at that value of the predictor.

Section 9.4: Variation and Prediction Intervals

  1. Explain why the variation of the frequency histogram for the prediction errors of a simple linear regression gives one indication of how good the model is at prediction.
  2. Define the root-mean-square error (RMSE), aka standard error of prediction (\(S\)), in terms of the distribution of the prediction errors.
  3. Interpret the RMSE / \(S\) in terms of the proportion of errors that fall within \(\pm k \cdot S\) for \(k = 1, 2, 3\).
  4. Give two equivalent definitions of the coefficient of determination, aka \(R^{2}\), aka R-sq.
  5. State the common (though erroneous) way to use \(R^{2}\) as a way to evaluate a simple linear regression model.