ID      Year   CornYield       SoyBeanYield
1       1957   48.3    23.2
2       1958   52.8    24.2
3       1959   53.1    23.5
4       1960   54.7    23.5
5       1961   62.4    25.1
6       1962   64.7    24.2
7       1963   67.9    24.4
8       1964   62.9    22.8
9       1965   74.1    24.5
10      1966   73.1    25.4
11      1967   80.1    24.5
12      1968   79.5    26.7
13      1969   85.9    27.4
14      1970   72.4    26.7
15      1971   88.1    27.5
16      1972   97      27.8
17      1973   91.3    27.8
18      1974   71.9    23.7
19      1975   86.4    28.9
20      1976   88      26.1
21      1977   90.8    30.6
22      1978   101     29.4

23      1979   109.5   32.1
24      1980   91      26.5
25      1981   108.9   30.1
26      1982   113.2   31.5

27      1983   81.1    26.2
28      1984   106.7   28.1
29      1985   118     34.1
30      1986   119.4   33.3
31      1987   119.8   33.9
32      1988   84.6    27.0
33      1989   116.3   32.3
34      1990   118.5   34.1
35      1991   108.6   34.2
36      1992   131.5   37.6
37      1993   100.7   32.6
38      1994   138.6   41.4
39      1995   113.5   35.3
40      1996   127.1   37.6
41      1997   126.7   38.9
42      1998   134.4   38.9
43      1999   133.8   36.6
44      2000   136.9   38.1
45      2001   138.2   39.6
46      2002   129.3   38.0
47      2003   142.2   33.9
48      2004   160.3   42.2
49      2005   147.9   43.1
50      2006   149.1   42.9
51      2007   150.7   41.7

Use both predictors. From the previous twoexercises, we conclude that year and soybean may be useful togetherin a model for predicting corn yield. Run this multipleregression.

a)      Explain the results of the ANOVA F test. Give the null andalternate hypothesis, test statistic with degrees of freedom, andp-value. What do you conclude?

b)      Whatpercent of the variation in corn yield in explained by these twovariables? Compare it with the percent explained in the previoussimple linear regression models.

c)      State the regression model. Why do the coefficients for year andsoybean differ from those in the previous exercises?

d)     Summarize the significance test results for the regressioncoefficients for year and soybean yield.

e)      Givea 95% confidence interval for each of these coefficients.

f)        Plot the residualversus year and soybean yield. What do you conclude?