Term 1 Flashcards by Jake Skelton

What are the implications of a statistical relationship?

A causes B
B causes A
A 3rd variable causes both
Random occurrence

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What does the stochastic error include?

Other explanatory variables (X1, X2..) that are missing
Measurement error
Incorrect functional form
Random and unpredictable occurrences

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What does a hat above a variable indicate?

It must be estimated

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How do you calculate the residual and error term

e=Y-YHat

E=Y-E(Y|X)

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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

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How do you estimate a value of B1 using OLS?

Sum(X-XBar)(Y-YBAR)/SUM(X-XBAR)^2

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How do you estimate a value of B0 using OLS?

YBar-B1X

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How do you calculate TSS?

Sum(Y-YBar)^2

TSS=ESS+RSS

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How do you calculate ESS/?

Sum(Yhat-Ybar)^2

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How do you calculate RSS/

Sum(e^2)

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How do you calculate R^2?

ESS/TSS
OR
1-RSS/TSS

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What is the DOF?

The number of observations (N) - Number of coefficients (K)

N-K
N-K-1 for intercept

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How do you calculate Adjusted R^2

(RSS/N-K-1)/(TSS/N-1)

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How can you calculate the correlation coefficient r?

Root R^2

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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

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What is the sampling distribution of Bhat?

The variety of Bhat you get from different samples

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How can the mean reveal bias?

An estimated BHat should have an expected value of B

E(βHat)=β

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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)

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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)

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If the classical assumptions are met., what can be said?

OLS will provide the Best Linear Unbiased Linear Estimator (BLUE)

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What is the formula for the T-Test?

T=(Bk-BH0)/SE(BK)
Bk is the coefficient
Bho is the null, usually 0

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How do you calculate the variance of an estimation?

=Sum(e^2)/N-2

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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