Refer to Exercise 12.35. Fit a single model to the data that relates y to x and x2 with separate coefficients for each of the three crops.
a. Does there appear to be a difference in slopes for the three crops?
b. Does there appear to be a difference in intercepts for the three crops?
c. Does a quadratic model appear to provide and adequate fit the data?
In exercise

Type of Crop MerCon Corn Wheat Barley 133.3 25.8 24.6 15.1 18.0 174 92 10.0 259 8.6 1 231 9. 45 82 2 314 35.7 145 409 22.9 105 34.6 234 184 24.9 21. 4.3 9.6 6.4 23.2 3 404 352 52.1 307 46.9 27 135 303 19.3 336 308 22.0 12.9 35 27.9 4 65.6 74.7 77.3 64.2 713 50.6 53.9 552 48.6 352 36.6 34 68 27.7 39.5 5 94.4 949 88. 100.1 1048 849 77.6 933 643 742 56.7 42.8 49.0 47.9 45.2 6 1234 158.6 137.3 1567 1335 1075 919 87.7 106.2 108. 708 75.7 100.3 64.6 70.1 1