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Develop a 98% confidence interval for the population slope coefficient β2 if the following simple regression...

Develop a 98% confidence interval for the population slope coefficient β2 if the following simple regression information are given: estimated slope b2= 23.5, se(b2)=5.488, and n = 25.

A. 23.5 +/- 13.68

B. 23.5 +/- 13.72

C. 23.5 +/- 11.95

D. 23.5 +/- 11.92

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Answer #1

The correct option is

  • B. .

The confidence interval would be . Standard error and slope coefficients are given. We have to find the t-value at 99% or 0.99, as it would be a two tail confidence interval, and the right side would be at , and the left side would be , ie at 99% and 1%, so that their difference would be 98% (the alpha). As the distribution is symmetric, we may compute only the t value at 99% at degree of freedom n-2=23, as there are two estimates including the intercept.

We can use any online calculator, or simple R-command as below to compute the required t-value.

> qt(0.99,df=23)
[1] 2.499867

Hence, we have the required confidence interval as or .

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