Exercises 11.98 through 11.104 use the CROPS data file, which contains the U.S. yield (bushels/acre) of corn and soybeans from 1957-2013.23
11.103 Do a prediction.
Use the simple linear regression model with corn yield as the response variable and year as the explanatory variable to predict the corn yield for the year 2014, and give the 95% prediction interval. Also, use the multiple regression model where year and year2 are both explanatory variables to find another predicted value with the 95% interval. Explain why these two predicted values are so different. The actual yield for 2014 was 167.4 bushels per acre. How well did your models predict this value?
crops
11.103
For Year alone, , and the prediction interval is (138.8, 181.6901). For Year and Year2: , and the prediction interval is (134.3030, 179.0220). The two predicted values are different because we are near the edge of the data for Year, and as we saw in the previous exercise, this will cause the greatest differences using the quadratic term. The actual yield of 167.4 is not predicted very well by either model but is closer to the predicted value for the linear model than for the quadratic model.