What is Ŷ?
An estimated value of Y calculated from the regression at the i-th observation
What can cause stochastic error?
1. OVB 2. Measurement error 3. A misspecified function 4. Random occurrences
What can we use to quantify the severity of multicollinearity in our model?
We use the variance inflation factor (VIF)
What is the VIF(ß1 hat?)
Which hypothesis test do we use for the following situations?: 1. Single parameter (one restriction) 2. Multiple parameter (linear combination) 3. Multiple parameter (non-linear combination) 4. Multiple parameter (multiple restrictions)
1. t-test (of one variable) 2. lincom (or t-test comparing two variables) 3. t-test/Taylor approximation (if one restriction) 4. F-test
What does ß0 equal? (Univariate)
Ybar - ß1(Xbar)
How do you know if you have OVB?
1. Use economic theory/knowledge of the subject 2. Run a robustness check
What is TSS?
Sum of the squared differences between actual values and the mean
What is RMSE?
1. Another goodness of fit measurement 2. Sqrt of SSR/(n-k-1)
What is the advantage of BIC over AIC?
BIC gives you consistent estimates
What should you do if you are asked about an effect? A change?
Effect = derivative
Change = difference
What is a residual?
The difference between the estimated and actual values of the dependent variable
What is R2?
The % of variation in Y explained by the model
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 is the formula for the adj. R2?
1. 1 - [(n-1)/(n-k-1)] x SSR/TSS
What do you need to look at after running an F-test to determine if it is statistically significant?
The Chi-square critical values
What does ß1 equal? (Univariate)
What is the formula for an F-test?
(SSRr - SSRu/r) ÷ (SSRu/n-k-1)
If our causal effect depends on the level of another independent variable, what do we do?
Take the natural log of the variable
What must "t" be greater than equal to for: 1. 90% confidence 2. 95% confidence 3. 99% confidence
1) 1.645 2) 1.96 3) 2.58 ^^ For two-tailed tests
If our causal effect depends on another variable (but not the level) what do we do?
Use an interaction terms
Formula for t-test?
(ß1 hat)-(H0: ß1) / SE(ß1 hat) p = 2(cdf)(-l t l)
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 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)
For a hypothesis test, what is the significance level and confidence level?
Significance = p Confidence = 1-p
What is iteratively re-weighted least squares?
Feasible GLS repeated until weights converge to a value
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)
Why is a high degree of freedom desired?
It is likely that the errors will balance out
What type of GLS do we use when the form of heteroskedasticity is unknown?