{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Slides_Econ140A_Regression_Continued

Slides_Econ140A_Regression_Continued - Regression continued...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Regression continued… Copyright Dick Startz 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Goals Prove OLS is unbiased Derive variance Hypothesis tests t- test versus z More on reading what a regression really tells us Copyright Dick Startz 2
Background image of page 2
Regression as a theoretical model Assumptions 1. ? ? = ?? ? + 𝜀 ? , true model of DGP 2. 𝑋 nonrandom (or exogenous) 3. ? 𝜀 ? = 0 ∀? 4. ? 𝜀 ? 𝜀 ? = 𝜎 2 , ? = ? 0, ? ≠ ? 5. (sometimes) 𝜀~????𝑎? Copyright Dick Startz 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Substitute in the DGP ? = ∑?? ∑? 2 = ?? + 𝜀 ? ∑? 2 = ∑?? 2 + ∑𝜀? ∑? 2 ? = ? + ∑𝜀? ∑? 2 ? = ? + 𝜀 1 ? 1 ∑? 2 + 𝜀 2 ? 2 ∑? 2 + ⋯ + 𝜀 𝑛 ? 𝑛 ∑? 2 Copyright Dick Startz 4
Background image of page 4
Prove OLS is unbiased ? = ? + 𝜀 1 ? 1 ∑? 2 + 𝜀 2 ? 2 ∑? 2 + ⋯ + 𝜀 𝑛 ? 𝑛 ∑? 2 ? ? = ? + ? 𝜀 1 ? 1 ∑? 2 + ? 𝜀 2 ? 2 ∑? 2 + ⋯ + ? 𝜀 𝑛 ? 𝑛 ∑? 2 ? ? = ? + 0 + 0 … + 0 = ? Copyright Dick Startz 5
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
var ? for ? = 2 ? = ? + 𝜀 1 ? 1 ? 1 2 + ? 2 2 + 𝜀 2 ? 2 ? 1 2 + ? 2 2 var ? = ? ? − ? ? 2 = ? 𝜀 1 ? 1 ? 1 2 + ? 2 2 + 𝜀 2 ? 2 ? 1 2 + ? 2 2 2 = ? 𝜀 1 2 ? 1 2 ? 1 2 + ? 2 2 2 + 𝜀 2 2 ? 2 2 ? 1 2 + ? 2 2 2 + 2𝜀 1 𝜀 2 ? 1 ? 2 ? 1 2 + ? 2 2 2 Copyright Dick Startz 6
Background image of page 6
var ? for ? = 2 continued ? 𝜀 1 2 ?
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}