ECON 104 Lecture Notes - Lecture 28: Statistical Hypothesis Testing, Bias Of An Estimator
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Slide 10 b) c) d) e) f) g) h) i) j) This looks kind of like a linear relationship if we ignore that it"s x 1 ^ 2 and different powers. The fact that one variable x 1 ^2 is a square of another variable. Have different columns, name it x 2 /x 3 /x 4 , and equate it to the respective powers of x. Can have unbiased estimator of beta 0, beta 1, beta 2,can still make confidence intervals around the numbers of betas. But beta"s no longer mean unit change of y on unit change in x. Suppose you want to regress test scores on district incomes. From slide 5, it"s probably not a linear relationship. If you do a quadratic specification, have a positive beta 1, and when income is small then income dominates, but negative beta 2, so it will dominate as income increases.
