Question: Consider the simple linear regression model [y=beta_{0}+beta_{1} x+varepsilon] where the intercept $beta_{0}$ is known. a. Find the least-squares estimator of $beta_{1}$ for this model. Does

Consider the simple linear regression model \[y=\beta_{0}+\beta_{1} x+\varepsilon\] where the intercept $\beta_{0}$ is known.

a. Find the least-squares estimator of $\beta_{1}$ for this model. Does this answer seem reasonable?

b. What is the variance of the slope $\left(\hat{\beta}_{1}\right)$ for the least-squares estimator found in part a?

c. Find a $100(1-\alpha)$ percent CI for $\beta_{1}$. Is this interval narrower than the estimator for the case where both slope and intercept are unknown?

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