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Probability and Stats Review for Econometrics

Understanding mean, variance, standard deviation, expected value
Understanding of hypothesis tests: setting up null vs alternate
Understanding Z-score, t-tests, and p-value
Application of alpha level and confidence intervals
Understanding of Chi squared distribution and F-distribution

Regression Analysis

Simple Regression Model
Nature of data and the need for best fit line/regression line
Terminology and notation
Concept of population regression function
Introduction to the idea of residuals and residual sum of squares (RSS)
Least Squares Simple Regression and minimizing RSS
Conceptual understanding and interpretation of regression slope and intercept coefficients
Gauss Markov properties of Best Linear Unbiased Estimator
Coefficient of Determination and R squared

Classical Normal Linear Regression Assumptions

Probability distribution of the disturbance term
Normality of residuals
Zero covariance between residuals and explanatory variables
Assumption of constant variance of residuals or homoscedasticity

Classical Normal Linear Regression Assumptions

Probability distribution of the disturbance term
Normality of residuals
Zero covariance between residuals and explanatory variables
Assumption of constant variance of residuals or homoscedasticity

Regression Diagnostics

Checking the goodness of fit or R-squared
F-test as the joint hypothesis test for the regression model
Individual t-tests or hypothesis tests for statistical significance of coefficients
Normality of residuals
Checking for heteroscedasticity

Multiple linear regression

Meaning and interpretation of partial regression coefficients
R squared meaning and interpretation with multiple explanatory variables
Issue of multicollinearity
Variance of regression coefficients and the impact on statistical significance

Dummy Variables

Nature of binary/dummy variables
Dummy variable trap
Use of dummy variables in Chow test for structural change
Piecewise linear regression with dummy variables
Interaction variables and intercept dummies

Heteroskedasticity

Issue of heteroscedasticity
OLS remains unbiased but the variance is no longer the minimum variance
Detection of heteroscedasticity with graphical method using scatterplots as well as formal tests
1. Park’s Test
2. Glesjer test
3. Breusch-Pagan hettest
4. White’s test
Fixing for heteroscedasticity using weighted least squares or using White’s robust standard errors

Autocorrelation

Issue of autocorrelation in residuals
OLS is still unbiased but minimum is no longer minimum variance
Graphical detection through scatterplot of residuals
Runs test
Durbin Watson Test and its limitations
Breusch-Godfrey test for autocorrelation
Lagrange multiplier test
Newey west standard errors to fix the issue of autocorrelation

Binary Dependent Variable models

Logit
Probit

Panel Data

Instrumental Variables

Time Series Data

Financial Econometrics

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