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EDA > Term 1 > Flashcards

Term 1 Flashcards

1
Q

What are the implications of a statistical relationship?

A

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

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2
Q

What does the stochastic error include?

A

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

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3
Q

What does a hat above a variable indicate?

A

It must be estimated

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4
Q

How do you calculate the residual and error term

A

e=Y-YHat

E=Y-E(Y|X)

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5
Q

How do you illustrate the residual and error term?

A

Difference between sample line and point is residual

Difference between point and true line is error

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6
Q

How do you estimate a value of B1 using OLS?

A

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

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7
Q

How do you estimate a value of B0 using OLS?

A

YBar-B1X

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8
Q

How do you calculate TSS?

A

Sum(Y-YBar)^2

TSS=ESS+RSS

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9
Q

How do you calculate ESS/?

A

Sum(Yhat-Ybar)^2

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10
Q

How do you calculate RSS/

A

Sum(e^2)

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11
Q

How do you calculate R^2?

A

ESS/TSS
OR
1-RSS/TSS

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12
Q

What is the DOF?

A

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

N-K
N-K-1 for intercept

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13
Q

How do you calculate Adjusted R^2

A

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

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14
Q

How can you calculate the correlation coefficient r?

A

Root R^2

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15
Q

What are the steps of applied regression?

A
  1. 5 Choose the dependant variable
  2. Review the literature and develop a theoretical model
  3. Specify the model - expected signs
  4. Hypothesise the expected signs and coefficents
  5. Collect Data, Inspect and Clean
  6. Estimate, evaluate and analyse the equation
  7. Document the Results
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16
Q

What is the sampling distribution of Bhat?

A

The variety of Bhat you get from different samples

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17
Q

How can the mean reveal bias?

A

An estimated BHat should have an expected value of B

E(βHat)=β

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18
Q

What are the classical assumptions of OLS? (1-4)

A

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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19
Q

What are the classical assumptions of OLS? (5-7)

A

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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20
Q

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

A

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

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21
Q

What is the formula for the T-Test?

A

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

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22
Q

How do you calculate the variance of an estimation?

A

=Sum(e^2)/N-2

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23
Q

How do you calculate the variance and SE of a coefficent?

A

VAR(B)=VAR/SUm(X-Xbar)^2

Root for SE

24
Q

How do you calculate a confidence interval?

A

B +- Tc*SE(B)

25
Q

What are the limitations of the T-Test?

A

Does not consider theoretical validity

Does not test importance

26
Q

What are the three potential specificaiton errors?

A

Independent variables
Functional Form
Form of the stochastic error term

27
Q

What is the effect of omitting a revlevant variable?

A

It cannot be held constant therefore biases other coefficents

Violates CA-3
Correlates with error term

28
Q

What is the effect of an irrelevant variable?

A

Does not cause bias
Will increase variance and hence t-scores
Will reduce adjusted R^2

29
Q

What is the four criteria to test whether a variable belongs?

A

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

30
Q

What is the equation for the F-Test?

A

F=(RSSm-RSS)/M
/ (RSS/N-
k-1)
M = Number of constraints

31
Q

What is the equation for the F-Test if the restricted equation is Y=B0

A

F=ESS/K / RSS/N-K-1

32
Q

What is the equation for the F-Test if the restricted equation is Y=B0 using R^2

A

F=R^2/K / 1-R^/N-K-1

33
Q

How do you calculate the critical value for an F-Test

A 
Numerator = Number of Constraints
Denominator = N-k-1
34
Q

What is RESET and how do you execute

A

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

35
Q

What are Akaike’s Information Criterion and the Schwarz Criterion?

A

Methods of comparing alternative specifications
AIC=Log(RSS/N)+2(K+1)/N
SC==Log(RSS/N)+LogN(K+1)/N
Lower the better

36
Q

What are the effects of changing the scale of x?

A

Coefficient must also be multiplied by the scaling factor

SE also

37
Q

What are the effects of scaling y?

A

The whole regression will need to be re-run

38
Q

What are the effects of scaling x and y

A

Intercept and residuals will change,

39
Q

How can we check the distribution of residuals?

A

Diagram
Jarque-Bera

JB=N/6(S^2+ (k-3)^2/4)
s=skewness, k=kurtosis

Critical value is obtained chi-squared

40
Q

What are the three components of B0?

A

The True B0
The constant impact of any specification errors (Omitted variable)
The mean of ε if not equal to zero

41
Q

What happens if you suppress the constant term?

A

You violate classical assumption 2,

The error term has an expected value of zero

42
Q

Discuss linear functional form

A

Linear in the variables
All linear

Not Linear in the coefficients
X^B

43
Q

Discuss Log functional Form

A 
Double log (on both sides)
Still linear in coefficients

Lin-Log- Log of variables
Log-Lin - Log of dependant

44
Q

Discuss Other functional forms

A

Polynominal-x^2

Inverse-1/x

45
Q

What can you not use to compare two different functional forms?

A

R^2

TSS

46
Q

What does an intercept dummy variable do?

A

Change the intercept based on a condition

Use one variable less than the number of conditions

47
Q

What is the omitted condition?

A

The Event not represented by the dummy variable

48
Q

What happens if you use two dummys for two conditions?

A

Violate CS-6 creating perfect co linearity

This is the dummy variable trap

49
Q

What is a slope dummy?

A

Effects both intercept and slope

50
Q

What is an indicator variable?

A

A variable similar to a dummy, but compares the interaction of two variables

51
Q

What is the chow test?

A

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

52
Q

What are the consequences of multi-collinearity

A 
Bias
Larger SE
T-Values go down
Estimates become sensitive to changes
Fit of equation will not change
53
Q

How can you detect collinearity?

A

Hard to detect
Correlation coefficient
High variance inflation factors

54
Q

Why is correlation coefficent not as useful?

A

To given cutoff point

A group of variables, acting together, may cause colinearity despite no test revealing this

55
Q

How would you use high variance inflation factors

A

Run an OLS that has the variable as a function of all others

Do 1/(1-R^2)

If >5, sever mulitcollinearity

56
Q

What are the remidies for multi-collinearity?

A

Do Nothing
Removing a variable may cause spec bias

Drop a redundant variable
Always base this decision on theory
Increase the sample size

EDA (2 decks)

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