For each of the following explain what is wrong and why a Th

For each of the following, explain what is wrong and why.

(a) The parameters of the simple linear regression model are b₀, b₁, and s.

(b) To test H₀: b₁ = 0, use a t test.
(c) For a particular value of the explanatory variable, the confidence interval for the mean response will be wider than the prediction interval for a future observation.

Solution

a)

The parameters are 0,1, and ; b0,b1, and s   are the estimates of those   parameters.

(b)

H0 should refer to 1   (the population slope) rather than   b1   (the estimated slope).

(c)

The confidence interval will be narrower than the prediction interval because the

confidence interval accounts only for the uncertainty in our estimate of the mean response,

while the prediction interval must also account for the random error of an individual

response