\[Y=\beta_0+\beta_1 X+\beta_2 X^2+...+\beta_d X^d+\epsilon\]
Question 1 How much more effort is required to estimate \(\beta_i\) when compared to the other regression models that we have discussed?
Question 2 In the text, the authors note that while you can theoretically let d be anything that you want, it is unusual to use a value greater than what? Why?
Question 3 Assume we have a dataset consisting of an outcome variable, Y, 3 numeric input variables, X1, X2, X3, and 1 categorical variable with 4 potential states. If we allow d to be up to 3 and we allow for interaction terms (but no other transformations such as log, and no interactions between the same variable, e.g. no X1:X1\(^3\) terms), how many possible parameters \(\beta\) are there in the full model?
In the labs over the last two weeks, we covered Linear Regression including: