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

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