Econometrics Notes

Descriptive Statistics

Mean

Variance

Standard Deviation

Sample Covariance

If it is greater than zero, upward sloping. This is scale dependent.
Sample Correlation

This is scale independent: between -1 and 1, close to 1 is upward, 0 is central, -1 is downward sloping.

Finding the regression

Regression formula with one regressor

Slope

Intercept

Finding R2

TSS=ESS+SSR

The Coefficient of Determination = R2

This gives the total fit of , between 0 (chance) and 1 (perfect prediction)

Standard Errors

Standard Error of the Regression

Standard error of

Hypothesis Testing 1. 2. Define H0 3. Define H1 4. Define Tcrit/Pcrit a. Note, for Tcrit 2 sided test, half 5. Find Tact/Pact

Tact
,

Pact

For one sided, just

Multiple Regression

Omitted Variable Bias
Ommitted variables may increase the apparent importance of another variable, damaging the ability to prove causality.
Effect of OVB on 1. Find the variable outside of the model 2. Find Corr(ZY) 3. Find Corr (ZX) 4. Multiply the signs 5. If positive, there is an upwards bias ()
Adjusted R2

OLS Wonder Equation

A good model for proving causality has a low , a good model for predicting Y has a low R2

Multiple Variable Tests

Reparametrisation

1. 2. For showing 3. Let 4. Thus, 5. 6. Now, let 7. Thus, 8. Now, run a new regression and do the usual hypothesis tests (: a one sided test). If you can reject H0, then

F-stat tests
Here, the H0 is a joint hypothesis with n restrictions (the number of coefficients equated to 0). 1. Create a restricted regression whereby we assume that H0 is correct 2. We see how the “fit” of the regression changes with the removed variables a. b. c. q is the number of restrictions, n the number of observations and k the number of variables 3. We compare this with an Fcrit value (using