# 07 Linear Regression Flashcards

σ

Population standard deviation

s

Sample standard deviation:

An estimator of the population standard deviation

s_y

s_y is the estimate of the population standard deviation for the random variable Y of the population from which the sample was drawn

SE()

Standard error of an estimator:

An estimator of the standard deviation of the estimator

SE( ̄Y) = ˆσ_ ̄Y = s_y / √n

μ

Population mean

u

all other factors than X that affects Y

synonyms for “dependent variable” and “independent variable”

dependent variable vs. independent variable

explained variable vs. explanatory variable

predicted variable vs. control variable

response variable vs. control variable

regressand vs. regressor

A normally distributed variable (X) can be made standard normal by:

Z = (X - μ) / ( σ / root(n))

The sample average is normally distributed whenever:

- Xi is normally distributed

- n is large (CLT)

T variable

T = (X - μ) / (s_x / root(n))

SLRM

Simple Linear Regression Model

The sum of squared prediction mistakes over all n observations

sum[(Y - E(β0) - E(β1)X)^2]

E(β0)

E(β0) = avg(Y) - E(β1) * avg(X)

Given by derivation++ of sum[(Y - E(β0) - E(β1)X)^2]

E(β1)

E(β1) = sum[(X - avg(X)) (Y - avg(Y))] /

sum[(X - avg(X)^2]

Given by derivation++ of sum[(Y - E(β0) - E(β1)X)^2]

E(β1) = r_{XY} * s_Y / s_X

If uˆi is positive, the line ____ Yi

If uˆi is positive, the line underpredicts Yi

By the definition of uˆ and the first OLS first order condition the sum of the prediction error is …

By the definition of uˆ and the first OLS first order condition the sum of the prediction error is zero

Sum(û_i) = 0

The sample covariance between the independent variable and the OLS residuals is …

The sample covariance between the independent variable and the OLS residuals is zero.