Question: 29. The regression model is called regression through the origin since it presupposes that the expected response corresponding to the input level x = 0

29. The regression model

is called regression through the origin since it presupposes that the expected response corresponding to the input level x = 0 is equal to 0. Suppose that (xi , Yi ), i = 1, . . . , n is a data set from this model.

(a) Determine the least squares estimator B of β.

(b) What is the distribution of B?

c) Define SSR and give its distribution.

(d) Derive a test of H0 : β = β0 versus H1 : β = β0.

(e) Determine a 100(1 −

a) percent prediction interval for Y (x0), the response at input level x0.

Y = x+e, e~ N(0,0)

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