what is cross-sectional data
observations on many units at a single point in time
what is time-series data
observations on one unit across multiple time periods
what is pooled cross-section
different cross-sections at different times (not the same units)
what is panel data
repeated observations on the same units across time
in the linear model y=β0+β1x+u what does u capture
all other (unobserved) factors affecting y with E(u|x)=0.
interpret β0 (intercept) in a regression
predicted value of y when all regressors equal zero
Interpret β1 (slope) in a regression
change in E[y|x] for a one-unit increase in x, holding others fixed
What is the sample residual?
ûi=yi−ŷi (the part of yi not explained by the regressors)
what is the population regression function (PRF) idea
The Population Regression Function (PRF) expresses the expected value of the dependent variable ( y ) given the independent variable(s) ( X ).
E[y|X]=Xβ and individual y deviates by u with E(u|X)=0
Law of Iterated Expectations statement
The Law of Iterated Expectations says that the overall expected value of y can be found by first taking the expected value of y given X,and then taking the expected value of that result over X
E[y]=E_X{E[y|X]