Econometrics Notes & R Code (UCSC Econ113)

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Econometrics Notes & R Code (UCSC Econ113)

Very much in development. Hopefully helpful resources.

Econometrics Topics to Know

Basic Statistics Review

Expected Value

Expected value of a random variable [Video 3:31]

Expected value of a function of a random variable [Video 2:41]

Expected value rules [Video 3:01]

Central Tendency

Mean - equation. outliers problem?

videos Mean - Sample v Population Mean
Median - equation. how does this correct for the outlier problem?
Mode - what is the mode? wikipedia
Example of finding the mean, median and mode by hand

Histogram - be prepared to draw a very simple histogram.

hist in R - Video Histogram Intro

Dispersion

Population variance of a discreet random variable [Video 3:50]

Alternative expression for population variance [Video 2:39]

Sample mean and variance [Video 13:53]

Videos: Population Variance, Sample Variance
Standard Deviation - equation in terms of variance? [Video 13:07]

Example of variance and standard deviation calc by hand

Relatedness of Two Variables

Covariance, Rules for Covariance and Variance [Video 15:54]

Estimators of variance, covariance, and correlation [Video 4:07]

Normal Distribution

The normal distribution [LSE Video 5:45]
Probability Density Function [Video 10:01]

Normal Distribution Videos: Vid1, Vid2, Vid3(example), Vid4 (more z-table examples), Vid5(abstract example), Vid6.

Central Limit Theorem [Video 9:49]

Econometrics - the goal of causal inference. Using data to test a theory.

Data-set Types: Cross Section, Time Series, Panel Data.

Simple Regression Model

Ordinary Least Squares (OLS) Estimator.

what is the problem OLS solves?

Videos: Intro, OLS Proof Pt1, Pt2, Pt3, Pt4 (the Punchline)

- Tying it all together with a regression line

- Know dependent and independent variables. Know 'u' the error term.

- Derivation for \beta^hat_1 & \beta^hat_0

Gauss Markov Assumptions required for "\beta\hat\_0" and "\beta\hat_1" to be an unbiased estimator for for the population "\beta_0" & "\beta_1" terms.

"Unbiased Estimate" means...

Interpreting Beta - how to interpret your estimate of beta given a level-level, log-level & log-log regression.

How to Interpret a Level-Level Regression Model (video 5:00)
How to Interpret a Log-Level Regression Model (video 6:40)
How to Interpret a Level-Log Regression Model (video 6:50)
How to Interpret a Log-Log Regression Model (video 5:30)

Goodness of Fit and R-Squared.

Videos: Finding R-Squared, Pt2(numerical ex), Pt3(calc example),

Homoskedasticity Assumption

Hypothesis Testing & P-Values

Intro to Hypoth Testing Video

Video: one-sided vs two-sided test

Notes:

LSE Intro to Econometrics (see email)

R examples: http://www.mayin.org/ajayshah/KB/R/index.html

Intro to applied Stats: R code: http://www.stanford.edu/class/stats191/helpR.html

Helpful R Code

Reference Websites for R

Download R Software
"Try R" from Code School
A quick (and free), two-hours-or-less tutorial introducing the basics of R software.
Quick-R (Reference for the basics of R)
Dumbed-down R-Software documentation. Check out the right navigation window.
Resources for R (More Example R Code)
Examples - getting started with R

Getting Started with R Software
Too often, the hardest part.

Basic Statistics & Visualization

Getting a sense of your data with R (video)
Simple code that gives you a sense of your R data. Mean, median, structure, variance and standard deviation.
Find the Mode Using R
Using R to find the Mode - unfortunately, finding the Mode(s) requires a couple lines of code -- not as easy as summary statistics.
Creating Histograms in R Software
The hist() function (video)
A simple histogram using R software. Also Kernel Density plots, and comparing two kernal densities.
Create Simple Plots with R
TA Kevin McLaughlin's Website (two simple screenshots)
R-Software Documentation for Simple X-Y Plots (technical, but comprehensive)

Econometrics with R Software

Do a Regression (with R) (video 16:40)
Short video that walks through the code to do a linear regression with R. This works for a univariate and multivariate model. It'll deliver regression coefficient estimates, standard error, t-statistic, P-values, R-squared, adjusted R-squared, omnibus F-test statistic and more.

SSE, SSR & SST with R-Code A solid explanation for R-Squared and the inputs of R^2 through R-software. Handy R-Code under "Definition of R^2" too.

Detailed overview of the lm(..) function for OLS estimation.

Simple Regression with R - Ordinary Least Squares solved by hand and in R Software. Introduction to R-regression summary. How to run a regression where data is inputed manually.

Multivariate Regression with R - with a walk-through R's OLS Regression Summary Output.

lm(...) function

Hypothesis Testing, Significance Test - testing whether or not a model's variable is statistically significant.

Hypothesis Testing, Other Hypotheses - testing whether or not a model's variable has some specific effect on the dependent variable.

Confidence Interval - calculation and interpretation.

P-Value - hand calculation. R-software's P-Value. Interpretation of P-Value.

Hypothesis Testing - Testing Hypothesis about Linear Combination of Parameters -- testing whether or not two variable have identical effects on the dependent variable.

Hypothesis Testing - F-Statistics - Testing General Linear Restrictions.

testing whether or not multiple variables are jointly statistically significant determinants of the dependent variable.

Hypothesis Testing - F-Statistic - Testing Overall Significance of a Regression.

Standardizing Variables in a Regression Model.

Dummy variables

Interaction terms

Dummy variables in interaction terms

Categorical variables. - running regression over 'factor' vector, dummy variable trap, interpretation.