Term 1 Flashcards
What are the implications of a statistical relationship?
A causes B
B causes A
A 3rd variable causes both
Random occurrence
What does the stochastic error include?
Other explanatory variables (X1, X2..) that are missing
Measurement error
Incorrect functional form
Random and unpredictable occurrences
What does a hat above a variable indicate?
It must be estimated
How do you calculate the residual and error term
e=Y-YHat
E=Y-E(Y|X)
How do you illustrate the residual and error term?
Difference between sample line and point is residual
Difference between point and true line is error
How do you estimate a value of B1 using OLS?
Sum(X-XBar)(Y-YBAR)/SUM(X-XBAR)^2
How do you estimate a value of B0 using OLS?
YBar-B1X
How do you calculate TSS?
Sum(Y-YBar)^2
TSS=ESS+RSS
How do you calculate ESS/?
Sum(Yhat-Ybar)^2
How do you calculate RSS/
Sum(e^2)
How do you calculate R^2?
ESS/TSS
OR
1-RSS/TSS
What is the DOF?
The number of observations (N) - Number of coefficients (K)
N-K
N-K-1 for intercept
How do you calculate Adjusted R^2
(RSS/N-K-1)/(TSS/N-1)
How can you calculate the correlation coefficient r?
Root R^2
What are the steps of applied regression?
- 5 Choose the dependant variable
- Review the literature and develop a theoretical model
- Specify the model - expected signs
- Hypothesise the expected signs and coefficents
- Collect Data, Inspect and Clean
- Estimate, evaluate and analyse the equation
- Document the Results
What is the sampling distribution of Bhat?
The variety of Bhat you get from different samples
How can the mean reveal bias?
An estimated BHat should have an expected value of B
E(βHat)=β
What are the classical assumptions of OLS? (1-4)
The regression model is linear, is correctly specified, and has an additive error term
The error term has a zero population mean
All explanatory variables are uncorrelated with the error term
Observations of the error term are uncorrelated with each other (no serial correlation)
What are the classical assumptions of OLS? (5-7)
The error term has a constant variance (no heteroskedasticity)
No explanatory variable is a perfect linear function of any other explanatory variable(s) (no perfect multicollinearity)
The error term is normally distributed (this assumption is optional but usually is invoked)
If the classical assumptions are met., what can be said?
OLS will provide the Best Linear Unbiased Linear Estimator (BLUE)
What is the formula for the T-Test?
T=(Bk-BH0)/SE(BK)
Bk is the coefficient
Bho is the null, usually 0
How do you calculate the variance of an estimation?
=Sum(e^2)/N-2
How do you calculate the variance and SE of a coefficent?
VAR(B)=VAR/SUm(X-Xbar)^2
Root for SE
How do you calculate a confidence interval?
B +- Tc*SE(B)
What are the limitations of the T-Test?
Does not consider theoretical validity
Does not test importance
What are the three potential specificaiton errors?
Independent variables
Functional Form
Form of the stochastic error term
What is the effect of omitting a revlevant variable?
It cannot be held constant therefore biases other coefficents
Violates CA-3
Correlates with error term
What is the effect of an irrelevant variable?
Does not cause bias
Will increase variance and hence t-scores
Will reduce adjusted R^2
What is the four criteria to test whether a variable belongs?
Theory: Is the variables place theoretically sound
t-Test: Is the variables estimated coefficient significant in the expected direction
Adjusted R^2: Does the overall fit of the equation improve when the variable is added
Bias: Do other variables coefficients change significantly when the variable is added
What is the equation for the F-Test?
F=(RSSm-RSS)/M
/ (RSS/N-
k-1)
M = Number of constraints
What is the equation for the F-Test if the restricted equation is Y=B0
F=ESS/K / RSS/N-K-1
What is the equation for the F-Test if the restricted equation is Y=B0 using R^2
F=R^2/K / 1-R^/N-K-1
How do you calculate the critical value for an F-Test
Numerator = Number of Constraints Denominator = N-k-1
What is RESET and how do you execute
Ramsey Regression Specification Error Test
Add Y2 Y3 and Y4 variables
Compare R^2 of old and new
Perform a F-Test to test significance of New variables
What are Akaike’s Information Criterion and the Schwarz Criterion?
Methods of comparing alternative specifications
AIC=Log(RSS/N)+2(K+1)/N
SC==Log(RSS/N)+LogN(K+1)/N
Lower the better
What are the effects of changing the scale of x?
Coefficient must also be multiplied by the scaling factor
SE also
What are the effects of scaling y?
The whole regression will need to be re-run
What are the effects of scaling x and y
Intercept and residuals will change,
How can we check the distribution of residuals?
Diagram
Jarque-Bera
JB=N/6(S^2+ (k-3)^2/4)
s=skewness, k=kurtosis
Critical value is obtained chi-squared
What are the three components of B0?
The True B0
The constant impact of any specification errors (Omitted variable)
The mean of ε if not equal to zero
What happens if you suppress the constant term?
You violate classical assumption 2,
The error term has an expected value of zero
Discuss linear functional form
Linear in the variables
All linear
Not Linear in the coefficients
X^B
Discuss Log functional Form
Double log (on both sides) Still linear in coefficients
Lin-Log- Log of variables
Log-Lin - Log of dependant
Discuss Other functional forms
Polynominal-x^2
Inverse-1/x
What can you not use to compare two different functional forms?
R^2
TSS
What does an intercept dummy variable do?
Change the intercept based on a condition
Use one variable less than the number of conditions
What is the omitted condition?
The Event not represented by the dummy variable
What happens if you use two dummys for two conditions?
Violate CS-6 creating perfect co linearity
This is the dummy variable trap
What is a slope dummy?
Effects both intercept and slope
What is an indicator variable?
A variable similar to a dummy, but compares the interaction of two variables
What is the chow test?
Tests the equivalence of two regressions
Create an indicator intercept and slope variable for every interaction
Seenotes
F-Test that they are all equal to zero
What are the consequences of multi-collinearity
Bias Larger SE T-Values go down Estimates become sensitive to changes Fit of equation will not change
How can you detect collinearity?
Hard to detect
Correlation coefficient
High variance inflation factors
Why is correlation coefficent not as useful?
To given cutoff point
A group of variables, acting together, may cause colinearity despite no test revealing this
How would you use high variance inflation factors
Run an OLS that has the variable as a function of all others
Do 1/(1-R^2)
If >5, sever mulitcollinearity
What are the remidies for multi-collinearity?
Do Nothing
Removing a variable may cause spec bias
Drop a redundant variable
Always base this decision on theory
Increase the sample size
