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In: Statistics and Probability

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

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

yˆy^ = 12.5 + 2.4x1 − 1.0x2 with se = 5.41. Also, when x1 equals 16 and x2 equals 5, se(yˆ0)se(y^0) = 2.60.

[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 5. (Round intermediate calculations to at least 4 decimal places, "tα/2,df" value to 3 decimal places, and final answers to 2 decimal places.)



b. Construct the 95% prediction interval for y if x1 equals 16 and x2 equals 5. (Round intermediate calculations to at least 4 decimal places, "tα/2,df" value to 3 decimal places, and final answers to 2 decimal places.)



c. Which interval is wider?

  • 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.

  • 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.

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Expert Solution

orchestra answered 1 year ago
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