University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Administration Courses and Curricula, HSPM J716,

Assignment 3 comment advice

The multiple regression and the simple regression give you different numbers for the effect of fertilizer on yield. Here are some ideas that you can use in your comment:

1. Rain and fertilizer and correlated in the data (from part 2 of your answer).
2. The difference in rain, between plots that had a lot of fertilizer and plots that had a little, may have contributed to the effect that fertilizer showed in the simple regression.
3. The multiple regression tried to separate the effects of fertilizer and rain. It gave some of the effect on yield to rain, taking it away from fertilizer.
4. If your rain coefficient in the multiple regression was not statistically significant, the difference between the fertilizer coefficients in the two methods is not be significant either. The difference is "within the margin of error," as the pollsters like to say.

To explain the difference in prediction between the two methods, you can use these ideas, in addition to (or instead of) the ideas in Assignment 3:

1. Rain and fertilizer and correlated in the data (from part 2 of your answer).
2. The simple regression "expects" that the rain and fertilizer will continue to move together. This means that if you give a plot 800 pounds of fertilizer, the simple regression expects it to get 30 inches of rain. (Can you do better than my vague term "expects"? )
3. You were predicting for 800 pounds of fertilizer but only 20 inches of rain. The simple regression could not deal with that. The multiple regression could.
4. If your rain coefficient is not statistically significant, the difference between the two predictions will not be statistically significant either. If you compare the confidence intervals of the predictions, you'll see that each prediction is inside the other prediction's 95% confidence interval.

Here's another way to think about it:

Imagine that, instead of rain from heaven, the different amounts of water on the different fields came from a practical joker who deliberately put more water on the fields on which you put more fertilizer. He wants to fool you into thinking that the fertilizer's effect is bigger than it really is. (Maybe he sells fertilizer for a living!) If you use the simple regression to predict, you will fall for his scheme. If you then apply 800 pounds of fertilizer -- an amount that is way above the average of the other fields -- to a new field, and if the joker doesn't add a corresponding above-average amount of water, the yield will disappoint you. You won't get as much as the simple regression predicted.