Rainfall and Corn Yield. The data on corn yields and rainfall, discussed in Section 9.3.1, appear in Display 9.18. (Data from M. Ezekiel and K. A. Fox, Methods of Correlation and Regression Analysis, New York: John Wiley & Sons, 1959; originally from E. G. Misner, "Studies of the Relationship of Weather to the Production and Price of Farm Products, I. Corn" [mimeographed publication, Cornell University, March 1928].)(a) Fit the multiple regression of corn yield on rain and rain^2 (squared)(b) Plot the residuals versus year. Is there any pattern evident in this plot? What does it mean? (Anything to do, possibly, with advances in technology?)(c) Fit the multiple regression of corn yield on rain, rain^2 (squared) , and year. Write the estimated model and report standard errors, in parentheses, below estimated coefficients. How do the coef- ficients of rain and rain^2 differ from those in the estimated model in (a)? How does the estimate of differ? (larger or smaller?) How do the standard errors of the coefficients differ? (larger or smaller?) Describe the effect of an increase of one inch of rainfall on the mean yield over the range of rainfalls and years.(d) Fit the multiple regression of corn yield on rain, rain^2 , year, and year rain. Is the coefficient of the interaction term significantly different from zero? Could this term be used to say something about technological improvements regarding irrigation?Year Yield Rainfall1890 24.5 9.61891 33.7 12.91892 27.9 9.91893 27.5 8.71894 21.7 6.81895 31.9 12.51896 36.8 131897 29.9 10.11898 30.2 10.11899 32 10.11900 34 10.81901 19.4 7.81902 36 16.21903 30.2 14.11904 32.4 10.61905 36.4 101906 36.9 11.51907 31.5 13.61908 30.5 12.11909 32.3 121910 34.9 9.31911 30.1 7.71912 36.9 111913 26.8 6.91914 30.5 9.51915 33.3 16.51916 29.7 9.31917 35 9.41918 29.9 8.71919 35.2 9.51920 38.3 11.61921 35.2 12.11922 35.5 81923 36.7 10.71924 26.8 13.91925 38 11.31926 31.7 11.61927 32.6 10.4