An agribusiness performed a regression of wheat yield bushel

An agribusiness performed a regression of wheat yield (bushels per acre) using observations on 30 test plots with four predictors (rainfall, fertilizer, soil acidity, hours of sun). The standard error was 1.08 bushels.

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

Solution

An agribusiness performed a regression of wheat yield (bushels per acre) using observations on 30 test plots with four predictors (rainfall, fertilizer, soil acidity, hours of sun).

The standard error was 1.08 bushels.

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

c = confidence level = 0.95

alpha = 1 - 0.95 = 0.05

The prediction interval is,

y^ + - tc * se

where y^ is the predicted value.

tc is the critical value form t-distribution with n-2 degrees of freedom.

se is the standard error.

n = number of test plots = 30

critical value we can find by using EXCEL

syntax : =tinv(probability,d.f.)

probability = 0.05

d.f. = 30-2 = 28

tc = 2.05

lower limit = y^ - tc * se = y^ - 2.05 * 1.08 = y^ - 2.21

upper limit = y^ + tc * se = y^ + 2.05 * 1.08 = y^ + 2.21