Linear Probability Notes
Estimation is the same as OLS, just remember to add robust after the reg
commend, because we do not have homoscedasticity.
Think about the following questions:
o What is the difference in

Regression with Panel Data Notes
Independently pooled cross section
Panel Data Analysis
o If we observe N samples for T time periods, we have panel data.
o Why is panel data helpful? This is because it will help

First Differencing Model Notes:
(1) Assumption 1:
For each i, the model is
Where
are the parameters to estimate and
is the unobserved effect.
This is very similar to linear parameter assumption in OLS.
(2) Assumption2:
We have a random sample from the cro

Lecture Probability Framework Notes
Probability Framework for Linear Regression
The probability framework for linear regression is summarized by the three least
squares assumptions.
Population
The group of interest (ex: all possible school districts)

Lecture Linear Regression Notes
Linear regression lets us estimate the slope of the population regression line.
The slope of the population regression line is the expected effect on Y of a unit
change in X.
Ultimately our aim is to estimate the causal e

Lecture Nonlinear Regression Functions Notes
Nonlinear regression functions
The regression functions so far have been linear in the Xs
But the linear approximation is not always a good one
The multiple regressi

Lecture Laws and Hypothesis Testing Notes
The Law of Large Numbers:
An estimator is consistent if the probability that its falls within an interval of the
true population value tends to one as the sample size increases.
If (Y1,Yn) are i.i.d. and < , the

Lecture Probability Notes
Review of Probability and Statistics (SW Chapters 2, 3)
Empirical problem: Class size and educational output
Policy question: What is the effect on test scores (or some other outcome
measure) of reducing class size by one student

Lecture Sample Randomness and Distribution Notes
Distribution of a sample of data drawn randomly from a population: YB1B,
YBnB
We will assume simple random sampling
Choose and individual (district, entity) at random from the population
Randomness and d

Lecture Student Distribution Notes
Digression: the Student t distribution
If Yi, i = 1, n is i.i.d. N(Y, ), then the t-statistic has the Student t-
distribution with n 1 degrees of freedom.
The critic