Constructing a Confidence Interval Using Regression Results Dohini Manufacturing

Question

Constructing a Confidence Interval Using Regression Results Dohini Manufacturing Company, using 12 months of data on purchasing cost and number of purchase orders, ran a regression equation that yielded the following information on the intercept, X variable 1, and standard error.

Intercept: 15,021

X variable 1: 9.74

Standard error: 513.68

Dohini Manufacturing Company estimates that 430 purchase orders will be processed next month and wants to know the interval into which the actual value will fall with a 95 percent confidence level.

1. Determine the appropriate t-statistic value for constructing Dohini Manufacturing Company's confidence interval.

2. Dohini Manufacturing Company estimates that next month will have 430 purchase orders. Construct a 95 percent confidence interval around the predicted value for purchasing cost

3. Construct a 90 percent confidence interval.

Explanation / Answer

here regression equation is y=15021+9.74*x

SE=513.68

where y=purchasing cost and x=number of purchase order

for x=430, y=15021+9.74*430=19209.2

(1-alpha)*100% confidence interval =estimate±t(alpha/2,n-1)*SE(estimate)

(1) here sample size=n=12 , so t-statistic for 95% confidence interval=t(0.05/2,12-1)=t(0.05,11)=2.2

( using ms-excel command =tinv(0.05,11) , excel is giving two-tailed value of t)

(2) 95% confidence interval =1920.9±2.2*513.68=(18079.1,20339.3)

(3)90% confidence interval =1920.9±1.8*513.68=(18284.6,20133.8)

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