For the Loblolly tree height growth data, fit the nonlinear model (given at the end of the lecture notes) to the data (Seed ==329 only) using the following approaches. For each approach superimpose a plot of the estimated model prediction on a plot of the data (Height vs. age). Drop a dashed line from each data point to the prediction line:
- Least squares estimation using a user-defined function for RSS and the optim() function
- Provide estimates of the parameters and the minimized RSS
- MLE estimation using a user-defined function for a Normal likelihood and the optim() function
- Provide estimates of the parameters and their asymptotic standard errors. Note that sigma (the Normal scale parameter) is a parameter to be estimated
- Least squares estimation via the nls() function.
- Provide estimates of the parameters and their standard errors