Linear Regression Model & OLS

Question 1

what does the error term (u_i) capture

Answer 1

-the effect of other variables
-unpredictable elements in human behaviour
-measurement error

this gives us the linear regression model

Question 2

population regression line formula

Answer 2

𝑌_𝑖= 𝑎+𝑏∙𝑋_𝑖+ 𝑢_𝑖

Question 3

what is u_i

Answer 3

the error term

Question 4

OLS assumption 1

Answer 4

the regression function is linear in parameters

Examples – OK, linear
𝑌_𝑖=𝛽_0+𝛽_1 𝑋_𝑖^2+𝑢_𝑖
𝑌_𝑖=𝛽_0+𝛽_1 1/𝑋_𝑖 +𝑢_𝑖

Examples – Not OK, non-linear
𝑌_𝑖=𝛽_0+𝑋_𝑖^(𝛽_1 )+𝑢_𝑖

Question 5

OLS assumption 2

Answer 5

random sampling

Question 6

OLS assumption 3

Answer 6

zero conditional mean

E(u|X) = 0

Since 𝐶𝑜𝑣(𝑢,𝑋)≠0 implies E(𝑢|𝑋)≠0, we can think of this assumption as lack of correlation between the error term and the regressor(s)

Question 7

OLS assumption 4

Answer 7

error term has constant variance (homescedasticity)

V(u|X) = 2

i.e. variance of the error term does not depend on X.

Question 8

the smaller the residual…

Answer 8

the closer the estimated value of Y is to the actual value of Y

𝑌_𝑖=(𝑌_𝑖 )̂+(𝑢_𝑖 )̂

Question 9

what does OLS stand for

Answer 9

Ordinary Least Squares

Question 10

linear regression

Answer 10

TSS = ESS + RSS

TSS - Total sum of squares
ESS - Explained sum of squares
RSS - Residual sum of squares

Question 11

OLS is BLUE - what does BLUE stand for

Answer 11

Best Linear Unbiased Estimator

Question 12

Gauss-Markov theorem

Answer 12

when you take all 4 OLS assumptions or properties together you have what is referred to as the Gauss-Markov theorem

theorem states that OLS estimators are BLUE when the OLS assumptions are satisfied

Question 13

the bigger the difference between the estimate and the actual value…

Answer 13

the worse the fit of your model

we generate this measure by decomposing the variance of the OLS estimates