Simple regression from moments

Problem

In simple linear regression with an intercept, $\operatorname{Var}(X)=4$ and $\operatorname{Cov}(X,Y)=6$ . Find the population least-squares slope. If $\mathbb{E}[X]=2$ and $\mathbb{E}[Y]=5$ , find the intercept.

Reveal answer or reference solution

The slope is

\frac{\operatorname{Cov}(X,Y)}{\operatorname{Var}(X)} = \frac{3}{2}.

The intercept is

\mathbb{E}[Y] - \frac{3}{2}\mathbb{E}[X] = 2.

Local history

Loading attempts saved in this browser…

Use with your agent

Share this URL and your attempt. Ask the agent to start with a clarifying question or the smallest useful hint.

Tutor me on https://mlprep.iwase.dev/mathematics/statistics/original-stats-regression/. If window.mlPrepAgent is available, read attempts for item original-stats-regression before tutoring. Inspect my attempt, keep the item ID, and do not reveal the full answer first. After a real attempt, append its record and read it back.

Appears in

Statistics Practice