SU4 - Fundamentals Of Linear Regression Flashcards
What are the components of a linear regression model?
The dependent variable, regressors or explanatory variables, error term, intercept, slope coefficients
What is the zero conditional mean assumption?
The expected value of error term ππ conditional on the regressors E(ππ|ππ1,ππ2,β¦,πππ) is zero. To estimate the parameters in a linear regression, we need to assume that the error team averages out to zero.
if zero conditional mean assumption is not available, the parameter can be expressed as two terms. What are the two terms?
The first term consists of variables that are observable, Y and X. Cov(Y,X)
The second term consists of variables that are unobservable, e and X Cov(e,X)
In multiple linear regression, for a one-unit (marginal change) in X, what does the parameter π reflect?
π1,π2,β¦,ππ reflect the marginal responses in the mean of π to π1,π2,β¦,ππ
ΞΈ 1 is not the exact response of Y when X 1 increases by one unit. Rather, it reflects the average response of Y when X 1 increases by one unit.
In ordinary least squares (OLS), why are the values squared?
It is to treat positive and negative distances in the same way. Large positive distances are just as bad as large negative distances.
Remainder term ei = Yi - Y is called residual. If ei > 0, whatβs it called?
Ei > 0, Yi underpredicts Y (Yi < Y)
Ei < 0, Yi overpredicts Y (Yi > Y)
What is the intercept of linear regression?
The expected mean value of Y when X = 0
What is a polynomial regression model?
Polynomial regression is a model where one or more determinants enter as a polynomial It enables us to model the relationship between πand π non linearly through a linear regression model.
If π1is positive and π2is negative, then Ξπ/Ξπwould first be positive for small values of π, then become negative as πincreases beyond a certain point.
(Maggie mee example, poor buy more, rich buy less)
What is log-level model?
πππβπ½πis the percentage change in πwhen πΏπincreases by one unit, while holding other variables
constant
Income and education have a log level relationship. Therefore, an additional year of education is associated with a 100Γ0.0231=2.31percent increase in income, on average.
What is level-log model?
π½π/πππis the change in πwhen πΏπincreases by one percent, while holding other variables constant
what is log-log model?
π½πis the percentage change in πwhen πΏπincreases by 1% (i.e. π½πis the elasticity of πwith respect to πΏπ, while holding other variables constant
Income and parentβs income have log log relationship. Therefore, an additional 1% increase in parentsβ income is associated with a 0.0169 percent increase in ownβs income, on average.
What are the five assumptions of a linear regression model?
1) for linear regression, we have to treat the model as being linear in parameters.
2) the sample of n observations is random
3) No perfect collinearity. (no redundant regressors) None of the independent variables is constant, therefore, Independent variables do not have exact linear RS
4) Zero conditional mean
5) homoskedasticity
What is linear regression?
Linear regression is a statistical model that captures the dependence of one random variable on one or more random variables.
Which component/s in a linear regression function are we interested to estimate?
The coefficients
If the zero conditional mean assumption is violated, what would happen to the covariance between the error term and the explanatory variables?
Cov(e,X) β 0
