econometrics

Ordinary Least Squares OLS

the method that chooses coefficients to minimize the sum of squared residuals.

Residual

the difference between the actual value of Y and the predicted value.

Fitted value or predicted value

the value of Y predicted by the regression line.

Sum of squared residuals SSR

the sum of all squared residuals from the model.

R squared

the share of variation in Y explained by the model.

Adjusted R squared

R squared corrected for the number of predictors in the model.

Standard error of regression SER

the average size of a typical residual.

Standard error of a coefficient

the estimated uncertainty of a coefficient used to form t statistics and confidence intervals.

t statistic

coefficient divided by its standard error.

F statistic

a test of multiple restrictions at once.

P value

the probability of seeing your estimated statistic if the null hypothesis is true.

Confidence interval

a range of plausible values for a parameter based on a chosen confidence level.

Sampling distribution

the distribution a statistic takes across repeated samples.

Linear model

Y equals B0 plus B1X.

Quadratic model

Y equals B0 plus B1X plus B2X squared.

Log linear model

log Y equals B0 plus B1X.

Linear log model

Y equals B0 plus B1 log X.

Log log model

log Y equals B0 plus B1 log X.

Interpretation log linear

a one unit increase in X changes Y by roughly one hundred times B1 percent.

Interpretation linear log

a one percent increase in X changes Y by B1 divided by one hundred.

Interpretation log log

B1 is the elasticity. It is the percent change in Y from a one percent change in X.

Expected value

the long run average of a random variable.

Variance

the average squared distance from the mean.

Standard deviation

the square root of the variance.

Coefficient of variation

standard deviation divided by the mean.

Z score

the number of standard deviations an observation is from the mean.

Conditional probability

the probability of A given B.

Law of total probability

the weighted average of conditional probabilities across all groups.

Binomial distribution

the distribution for repeated independent trials with two outcomes.

Entropy

a measure of unpredictability or spread in categorical data.

Covariance

a measure of how two variables move together.

Correlation

a scaled version of covariance that ranges from negative one to one.

Slope coefficient

B1 in Y equals B0 plus B1X. It is the change in Y for a one unit change in X.

Intercept

B0 in the regression. It is the predicted value of Y when X equals zero.

OLS identifying assumption

the error term is uncorrelated with the independent variable.

Multicollinearity

when predictors are strongly correlated with each other.

Omitted variable bias

bias caused when a relevant variable is left out and is correlated with both X and Y.

Instrument

a variable used in IV that affects X but does not affect Y except through X.

Two stage least squares

the method used in IV regression using predicted X from the first stage.

Weak instrument

an instrument that is weakly correlated with the endogenous regressor.

Linear probability model

a regression where the dependent variable equals zero or one.

Logit model

a nonlinear model that uses a logistic function to keep predicted probabilities between zero and one.

Probit model

a model that uses the normal CDF to generate probabilities.

Marginal effect

the change in predicted probability from a small change in a regressor.