solution

 

. We need a new variable to model the curved relation that we see between corn yield and year in the residual plot of the last exercise. Let year2 = (year − 1982)2. (When adding a squared term to a multiple regression model, we sometimes subtract the mean of the variable being squared before squaring. This eliminates the correlation between the linear and quadratic terms in the model and thereby reduces collinearity.)

(a) Run the multiple linear regression using year, year2, and soybean yield to predict corn yield. Give the fitted regression

equation.

(b) Give the null and alternative hypotheses for the ANOVA F test. Report the results of this test, giving the test statistic,

degrees of freedom, P-value, and conclusion.

(c) What percent of the variation in corn yield is explained by this multiple regression? Compare this with the model in the previous exercise.

(d) Summarize the results of the significance tests for the individual regression coefficients.

(e) Analyze the residuals and summarize your conclusions.