Question

4. The variance of $\hat{\beta_1}$ is A. $\frac{1}{n+1}$ SSE B. $\frac{1}{n+2}$ SSE C. $\frac{1}{\sum_{i=1}^{n} x_i^2} \sigma^2$ D. $\frac{1}{\sum_{i=1}^{n} (x_i - \bar{x})^2} \sigma^2$

          4. The variance of $\hat{\beta_1}$ is
A. $\frac{1}{n+1}$ SSE 	 B. $\frac{1}{n+2}$ SSE 	 C. $\frac{1}{\sum_{i=1}^{n} x_i^2} \sigma^2$ 	 D. $\frac{1}{\sum_{i=1}^{n} (x_i - \bar{x})^2} \sigma^2$

4. The variance of β̂1̂ is
A. (1)/(n+1) SSE B. (1)/(n+2) SSE C. (1)/(∑i=1^n xi^2)σ^2 D. (1)/(∑i=1^n (xi - x̅)^2)σ^2

Added by Samantha H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

10/12/2023

Step 1

Step 1: The variance of the slope coefficient $\hat{\beta_1}$ is given by: $Var(\hat{\beta_1}) = \frac{\sigma^2}{\sum_{i=1}^n (x_i - \bar{x})^2}$ Show more…

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4. The variance of $\hat{\beta_1}$ is A. $\frac{1}{n+1}$ SSE B. $\frac{1}{n+2}$ SSE C. $\frac{1}{\sum_{i=1}^n x_i^2} \sigma^2$ D. $\frac{1}{\sum_{i=1}^n (x_i - \bar{x})^2} \sigma^2$