Question

An agribusiness performed a regression of wheat yield (bushels per acre) using observations on 22 test plots with four predictors (rainfall, fertilizer, soil acidity, hours of sun). The standard error was 1.18 bushels.

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

yˆiyi

±

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

yˆiyi

±

(c)	The quick rule gives a similar result.
	Yes No

Answer 1

SOLUTION:

From given data,

An agribusiness performed a regression of wheat yield using observations on 22 test plots with four predictors . The standard error was 1.18 bushels.

n = Sample size = 22

se = standard error = 1.18 bushels

(a) Find the approximate width of a 95% prediction interval for wheat yield.

The approximate width of a 95% prediction interval for wheat yield is

= Y_i t _/2,n-1 * se

= Y_i t _0.025,21 * 1.18

= Y_i t _0.025,21 * 1.18

= Y_i   2.413845 * 1.18

= Y_i   2.8483371

Yi   2.8483371

(b) Find the approximate width using the quick rule.

the approximate width using the quick rule is

= width   z_{/2 ,} * se where,   z_/2 = 1.96 for 95%

= width   1.96 * 1.18

= width   2.3128

width   2.3128

(c) The quick rule gives a similar result.

Answer : No.