Question

1.      The U.S. Department of Agriculture publishes data annually on various selected farm products. Shown here are the unit production figures (in millions of bushels) for three farm products for 10 years during a 20-year period. (leave 3 decimal places)

Corn	Soybeans	Wheat
4152	1127	1352
6639	1798	2381
4175	1636	2420
7672	1861	2595
8876	2099	2424
8226	1940	2091
7131	1938	2108
4929	1549	1812
7525	1924	2037
7933	1922	2739

(4). Based on the following output, given alpha = 0.05, manually test if the built regression model is better than the average (y) model (lazy model). (Written)

call:

aov(formula= farm_model)

terms:

soybeans wheat residuals

sum of squares 20769458    421189    5205899

degree of freedom 1    1    7

residual standard error: 862.3804

stimated effects may be unbalanced

Write down the correct R command to find F statistic value and p value, what is the statistic decision and conclusion from the R output. (R)

(5). In order to test each one of the independent variables (Soybeans and Wheat) and see if they are providing significant predictive power to the dependent variable (Corn), write down the null hypotheses and alternative hypotheses for all the hypotheses testing. (Written)

Given alpha = 0.05, write down the correct R command to find t statistic values and p value. Based on the R output, write down the t value, p value, your statistic decision and conclusion for all independent variables. (Written)

(6). Based on the regression model, given Soybeans = 1127 and Wheat = 1352 (the first example), what is the estimated Corn production? What is the residual of this example? (Written)

Answer 1

The fitted model is

Y stands for Corn

X1 stands for Soybeans

X2 for Wheat