1. Nonlinear models Hill et al Chapter 10

2. Types of nonlinear models Linear in the parameters. –Includes models that can be made linear by transformation: Nonlinear in the parameters –Require nonlinear least squares.

3. Polynomial terms in a regression For U-shaped curve we expect 2 0 U-shaped marginal cost curve 2 >0, 3 0

4. Interactions between continuous variables Is it reasonable that these effects are independent of income and age?

5. An alternative model

6. Empirical example

7. Nonlinear least squares Minimise sum of squared errors b = 1.1612 se(b) = 0.129 Simple expressions for the value of beta that minimises S cannot be found. Similarly expressions for the se(beta) cannot be found. The problem is solved numerically.

8. A logistic growth curve

9. Example: proportion of steel produced with electric arc furnace

10. The poisson regression Number of visits to a lake: count data Does not have a normal distribution Poisson distribution is an alternative: is the average or mean number of visits per year, for all households Number of visits 01234567891013 Frequency615541312319872111

11. Estimating the conditional mean function in the Poisson regression define the zero-mean error term

12. Computing probabilities in the Poisson regression What is the probability that a household located 50 miles from the Lake, with income of $60,000, and 3 family members, visits the park less than 3 times per year?