Pvn Why is OLS Assumption #1 important for a single linear regression with dependent variable Y andindependent variable X?Guarantees the residuals in a regression have a N(0,1) distributionNecessary to ensure that the population regression line corresponds to the conditional (on X) mean functionof YYields the most precise OLS estimates given a random sample with N observationsO Without it, the R-Squared of a regression will fail to correspond to the Standard Error of the Regression (SER)

Answered: Why is OLS Assumption #1 important for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Pvn

Why is OLS Assumption #1 important for a single linear regression with dependent variable Y and
independent variable X?
Guarantees the residuals in a regression have a N(0,1) distribution
Necessary to ensure that the population regression line corresponds to the conditional (on X) mean function
of Y
Yields the most precise OLS estimates given a random sample with N observations
O Without it, the R-Squared of a regression will fail to correspond to the Standard Error of the Regression (SER)

Expert Solution

Step 1: simple linear regression

In the context of a simple linear regression, the assumption is that the relationship between the dependent variable Y and the independent variable X can be expressed as:

$Y i equals beta subscript 0 plus beta subscript 1 X i plus epsilon i$

The assumption implies that the average value of the error term is zero E(ei)=0 and this ensures that the regression line accurately represents the conditional mean of Y given X, as expressed by:

$E left parenthesis Y vertical line X right parenthesis equals beta subscript 0 plus beta subscript 1 X a s space E left parenthesis e i right parenthesis equals 0$

This linear assumption is important because it allow us to estimate $beta subscript 0 space a n d space beta subscript 1$ through the least squares method