Question

In a multiple linear regression with 40 observations, the following sample regression equation is obtained:

yˆy^ = 10.0 + 2.7x₁ − 1.4x₂ with s_e = 5.86. Also, when x₁ equals 16 and x₂ equals 7, se(yˆ0)se(y^0) = 2.10.

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

a. Construct the 95% confidence interval for E(y) if x₁ equals 16 and x₂ equals 7. (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.)

Confidence Interval _____ to _____?

b. Construct the 95% prediction interval for y if x₁ equals 16 and x₂ equals 7. (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.)

Prediction interval _____ to _____?

c. Which interval is wider?

• Confidence 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 does not include the variability caused by the error term.

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

Answer 1

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