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:
Rain and fertilizer and correlated in the data (from part 2 of
your answer).
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.
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.
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 the
booklet:
Rain and fertilizer and correlated in the data (from part 2 of
your answer).
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"? )
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.
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.
