What is the stochastic error term?

A term added to the regression equation to account for any variation in Y that is not explained by X

What does TSS equal?

ESS+SSR

What is the SE?

Sq.Rt. of RSS/{(n-k-1) ∑(Xi-Xbar)^{2}}

What are the four assumptions of the error term?

1. The variation does not change as X changes 2. Its distribution is normal 3. Conditional mean=0 4. Independent for any two observations (i,j)

What can cause stochastic error?

1. OVB 2. Measurement error 3. A misspecified function 4. Random occurrences

When are dummy variables useful?

When we want to quantify something that is inherently qualitative (race, gender, etc.)

What is Ŷ?

An estimated value of Y calculated from the regression at the i-th observation

What is a residual?

The difference between the estimated and actual values of the dependent variable

What changes between observations?

The values of Y, Xs, and error terms (but not the coefficients)

While adding a variable may not change TSS...

It will likely reduce SSR and, thus likely increase R-squared

OLS seeks to minimize....

The sum of squared residuals (or SSE)

K = ?

The # of independent variables

Why is a high degree of freedom desired?

It is likely that the errors will balance out

Y_{i} - Ŷ is....

The residual (prediction mistake)

What are the three properties of estimators?

1. Unbiasedness: The estimator is correct (on avg.) 2. Consistency: As observations increase, so does the probability that the estimator is close to the pop. parameter Efficiency: Estimator has smaller relative variance (converges to the pop. parameter more quickly)

How do we adjust for degrees of freedom?

Divide by (n-1)

What does ß_{0} equal? (Univariate)

Ybar - ß_{1}(Xbar)

What does ß_{1} equal? (Univariate)

∑(Y_{i}-Ybar)(X_{i}-Xbar)/∑(X_{i}-Xbar)^{2}

What is the formula for sample variance?

1/(n-1) ∑(X_{i}-Xbar)^{2}

What is the formula for sample covariance?

1/(n-1) ∑(X_{i}-Xbar)(Y_{i}-Ybar)

What are the 7 OLS assumptions?

1. The population regression function (DGP) is linear in parameters 2. Observations are randomly drawn from the population and i.i.d 3. X[vector] is fixed in repeated samples (no measurement error) 4. The error term has a conditional mean of 0 5. Homoskedasticity 6. Errors are independent (for every i, j) 7. Outliers are unlikely

If you specify a dummy variable for each possible outcome.....

You will induce perfect multicollinearity (nothing to compare dummy to)

If the omitted variable is correlated with a regressor and it has an effect on the dependent variable....

We have OVB

If the effect of the OV on Y and the correlation between OV and regressor are moving in the same direction...

Your estimator is too big

How do you know if you have OVB?

1. Use economic theory/knowledge of the subject 2. Run a robustness check

What is ESS?

Sum of the squared differences between predicted values and the mean

What is TSS?

Sum of the squared differences between actual values and the mean

What is R^{2}?

The % of variation in Y explained by the model

What are the formulas for R^{2}?

1. ESS/TSS 2. 1 - SSR/TSS

What is the formula for the adj. R^{2}?

1. 1 - [(n-1)/(n-k-1)] x SSR/TSS