In a Simple Linear Regression Model yi=beta0+beta1 xi+varepsiloni; i=1,2,… n where E(varepsiloni)=0, Var(varepsiloni)=sigma^2 and Cov(varepsiloni,varepsilonj)=0, ine j. What is Var(hatbeta0) equal to?

(D) sigma^2/n+sigma^2(bar x)^2/sumi=1^n(xi-bar x)^2

Q58Section I (Objective (Q1–Q80))57 of 79

Linear Models — variance of the regression intercept

In a Simple Linear Regression Model $y_i=\beta_0+\beta_1 x_i+\varepsilon_i$ ; $i=1,2,… n$ where $E(\varepsilon_i)=0$ , $\mathrm{Var}(\varepsilon_i)=\sigma^2$ and $\mathrm{Cov}(\varepsilon_i,\varepsilon_j)=0$ , $i\ne j$ . What is $\mathrm{Var}(\hat\beta_0)$ equal to?

Pick an option to check your answer. In a mock test a wrong answer here costs 0.83 mark.

Keyboard: A–D answer · S solution · ←/→ previous/next