Refer to Crop yield Problem 11.25. The observations are listed in time order. Assume that regression model (12.2) with first- and second-order terms for the two predictor variables and no interaction term is appropriate. Test whether or not positive autocorrelation is present; use α = .01. State the alternatives, decision rule, and conclusion.
Problem 11.25
Crop yield. An agronomist studied the effects of moisture (XI, in inches) and temper (X1. in C) on the yield of a new hybrid tomato (Y). The experimental data follow.
The agronomist expects that second-order polynomial regression model (8.7) with independent normal error terms is appropriate here.
a. Fit a second-order polynomial regression model omitting the interaction term and the quadratic effect term for temperature.
b. Construct a contour plot of the fitted surface obtained in part (a).
e. Use the lowess method to obtain a nonparametric estimate of the yield response surface as a function of moisture and temperature. Employ weight function (11.53), q =0 9/25, and a Euclidean distance measure with unscaled variables. Obtain fitted values 
for the
d. Construct a contour plot of the resulting lowess surface. Are the lowess contours consistent with the contour in part (b) for the polynomial model? Discuss.