Suppose that we are interested in fitting a simple linear regression model Y = β 0 + β 1 x + ?, where the intercept, β 0 , is known. (a) Find the least squares estimator of β 1 . (b) What is the...

Suppose that we are interested in fitting a simple linear regression model
Y
= β₀+ β₁
x
+ ?, where the intercept, β₀, is known.

(a) Find the least squares estimator of β₁.

(b) What is the variance of the estimator of the slope in part (a)?

(c) Find an expression for a 100(1 - α)% confidence interval for the slope β₁. Is this interval longer than the corresponding interval for the case where both the intercept and slope are unknown? Justify your answer.