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The following data are observations y on a dependent random

The following data are observations y on a dependent random variable Y taken at various levels of an independent variable x. [It is assumed that E(Yi׀xi) = A + Bxi, and the Yi are independent normal random variables with mean 0 and variance σ2.]

(a) Estimate the linear relationship by the method of least squares, and forecast the value of Y when x = 10.

(b) Find a 95 percent confidence interval for the expected value of Y at x* = 10.

(c) Find a 95 percent prediction interval for a future observation to be taken at x+ = 10.

(d) For x+ = 10, P+ = 0.90, and 1 – α = 0.95, find a simultaneous Tolerance interval for the future value of Y+. Interpolate if necessary.

(a) Estimate the linear relationship by the method of least squares, and forecast the value of Y when x = 10.

(b) Find a 95 percent confidence interval for the expected value of Y at x* = 10.

(c) Find a 95 percent prediction interval for a future observation to be taken at x+ = 10.

(d) For x+ = 10, P+ = 0.90, and 1 – α = 0.95, find a simultaneous Tolerance interval for the future value of Y+. Interpolate if necessary.

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