# Econometrics

### Probability and Stats Review for Econometrics

• Understanding mean, variance, standard deviation, expected value
• Understanding of hypothesis tests: setting up null vs alternate hypothesis
• 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

• Correlation vs causation
• 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 regression as the minimizing of 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

• Logit
• Probit

#### Panel Data

• Fixed effectsRandom EffectsFirst Differencing

#### Instrumental Variables

• Endogeneity and finding appropriate instruments