Question

In a simple linear regression based on 27 observations, the following information is provided:

yˆy^ = −6.53 + 1.22x and s_e = 2.95. Also, se(yˆ0)se(y^0) evaluated at x = 27 is 1.14.

[You may find it useful to reference the t table.]

a. Construct the 95% confidence interval for E(y) if x = 27. (Round intermediate calculations to at least 4 decimal places, "t_α/2,df" value to 3 decimal places, and final answers to 2 decimal places.)

b. Construct the 95% prediction interval for y if x = 27. (Round intermediate calculations to at least 4 decimal places, "t_α/2,df" value to 3 decimal places, and final answers to 2 decimal places.)

c. Which interval is narrower?

• Confidence interval, since it does not include the variability caused by the error term.

• Prediction interval, since it includes the variability caused by the error term.

• Prediction interval, since it does not include the variability caused by the error term.

• Confidence interval, since it includes the variability caused by the error term.

Answer 1

a)predicted value =-6.53+1.22*27=26.41

for 95% CI ; crtiical t =2.060

95% confidence interval for E(y) =26.41 -/+ 2.060*1.14 =24.06 , 28.76

b)

95% prediction interval =26.41 -/+ 2.060*sqrt(1+1.14²) =23.29 ; 29.53

c)

Confidence interval, since it does not include the variability caused by the error term.