Rain, food, and orange yield

Topic: Regression examples · more questions on this topic
‹ Birth weight and mother’s age

A fit of yield in kilograms on rainfall in millimetres and citrus-food supplement in grams is

\widehat{\mathrm{yield}}=99.504+0.01763\times\mathrm{rainfall}+0.04020\times\mathrm{food},

with residual standard error 4.991 on 97 degrees of freedom and R^2=0.454.

  1. Predict the yield at 1000 mm of rain and 500 g of food.

  2. A 95% prediction interval at that point is (127.38,\,147.18). Why is this wider than a confidence interval for the mean yield at the same point?

99.504+0.01763\times 1000+0.04020\times 500=137.3

kilograms. A prediction interval covers a new tree, which still has variance \sigma^2 even if the mean yield were known. A confidence interval covers only the mean, so it is shorter.