please help me. Clearly.

Consider the rainfall data available in the file "ex0915.csv". The file contains data on corn yield and rainfall in six U.S. corn-producing states (Iowa, Nebraska, Illinois, Indiana, Mis- souri and Ohio) recorded for each year from 1890 to 1927. You will find 38 observations on the following 3 variables: Year: year of observation (1890 - 1927) Yield: average corn yield for the six states (in bu/acre) Rainfall: average rainfall in the six states in in/year) 1. Construct a scatterplot of yield vs. rainfall and compute the correlation coefficient between these two variables. Do the plot and correlation coefficient suggest a linear relationship between these two variables? Explain. 2. Fit 3 polynomial regression models for yield vs. rainfall: linear, quadratic and cubic. For each one of these models use the command summary (model) $coef to report the estimated coefficients and P-values. In addition, report the values of Ra and R., for each model. Based on these results, which model seems most appropriate? 3. Use the function anova(.) to conduct the ESS test to compare the linear vs. quadratic models. Use one of the formulas discussed during lecture to obtain the ESS F-statistic and P-value to compare the quadratic vs. cubic models. In each case write down the full and reduced models and clearly state the hypotheses being tested. 4. So far, we have not used the variable year. We can decide whether to add this variable to the model, based on any patterns that remain unexplained in the original model. One way to look at this is to plot the residuals of the original model against the predictor of interest. Construct a scatterplot of the residuals obtained from the linear model versus the variable year. Looking at the scatterplot, do you see any trends or patterns that could perhaps be explained by this new variable? Explain. 5. Suppose a second scientist suggests fitting the model yield rain, year) = Bo + Birain + Bayear + Brain x year. Without doing any analysis, do you think it is reasonable to include the interaction term in the model? Explain. Year Yield Rainfall 1890 24,5 9.6 1891 33.7 12.9 1892 27.9 9.9 1893 27.5 8.7 1891 21.7 6.8 1695 31.9 12.5 1896 36.8 13 1897 29.9 10.1 1899 30.2 10.1 1899 32 10.1 1900 34 10.8 1901 19.4 7.8 1902 36 16.2 1903 30.2 14.1 1904 32.4 10.6 1905 36.4 10 1906 36.9 11.5 1907 31.5 13.6 1908 30.5 12.1 1909 32.3 12 1910 34.9 9.3 1911 30.1 7.7 1912 36.9 11 1913 26.8 6.9 1914 30.5 9.5 1915 33.3 16.5 1916 29.7 9.3 1917 35 9.4 1918 29.9 8.7 1919 35.2 9.5 1920 38.3 11.6 1921 35.2 12.1 1922 35.5 1923 36.7 10.7 1924 26.8 13.9 1925 38 113 1926 31.7 11.6 1927 32.6 10.4