Exercise 6: Polynomial Regression

Note

Polynomial Regression

  1. Consider the values of x shown below: \[x = 1.00, 1.70, 1.25, 1.20, 1.45, 1.85, 1.60, 1.50, 1.95, 2.00\] Suppose that we wish to fit a second-order model using these levels for the regressor variable \(x\). Calculate the correlation between \(x\) and \(x^2\). Do you see any potential difficulties in fitting the model?
  1. Is there evidence of non-linear association between any of the predictors and the response crim in the Boston data set? To answer this question, for each predictor \(X\), fit a model of the form \[Y = \beta_0 + \beta_1X+\beta_2X^2+\beta_3X^3+\epsilon\]