An agribusiness performed a regression of wheat yield (bushels per acre) using o

Question

An agribusiness performed a regression of wheat yield (bushels per acre) using observations on 23 test plots with four predictors (rainfall, fertilizer, soil acidity, hours of sun). The standard error was 1.39 bushels.

(a) Find the approximate width of a 95% prediction interval for wheat yield. (Round your answer to 2 decimal places.)

y ± _______

(b) Find the approximate width using the quick rule. (Round your answer to 2 decimal places.)

y ± ________

(c) The quick rule gives a similar result.

No or Yes

Explanation / Answer

Solution:- Given that n = 23,standard error = 1.39 , k = 4

df = n-k-1 = 23-4-1 = 18

t =  2.101

a) the approximate width of a 95% prediction interval for wheat yield = y ± t(SE)

= y ± 2.101(1.39)

=  2.92

b) => y ± 2(SE) =  = y ± 2(1.39) = 2.78

c) yes

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