For these data, fit the quadratic polynomial assuming Var(LCPUE|Day = x) = σ2 . Draw a scatterplot of LCPUE versus Day, and add the fitted curve to this plot. Using the delta method described in...

For these data, fit the quadratic polynomial

assuming Var(LCPUE|Day = x) = σ2 . Draw a scatterplot of LCPUE versus Day, and add the fitted curve to this plot.

Using the delta method described in Section 7.6, obtain the estimate and variance for the value of Day that maximizes E(LCPUE|Day).

Another parameterization of the quadratic polynomial is
 where the θs can be related to the βs by
 In this parameterization, θ₁
is the intercept, θ₂
is the value of the predictor that gives the maximum value of the response, and θ₃
is a measure of curvature. This is a nonlinear model because the mean function is a nonlinear function of the parameters. Its advantage is that at least two of the parameters, the intercept θ₁
and the value of x that maximizes the response θ₂, are directly interpretable. Use nonlinear least squares to fit this mean function. Compare your results with the first two parts of this problem.