Flashcards in Term 1 Deck (56):

1

## What are the implications of a statistical relationship?

###
A causes B

B causes A

A 3rd variable causes both

Random occurrence

2

## What does the stochastic error include?

###
Other explanatory variables (X1, X2..) that are missing

Measurement error

Incorrect functional form

Random and unpredictable occurrences

3

## What does a hat above a variable indicate?

### It must be estimated

4

## How do you calculate the residual and error term

###
e=Y-YHat

E=Y-E(Y|X)

5

## 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

6

## How do you estimate a value of B1 using OLS?

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

7

## How do you estimate a value of B0 using OLS?

### YBar-B1X

8

## How do you calculate TSS?

###
Sum(Y-YBar)^2

TSS=ESS+RSS

9

## How do you calculate ESS/?

### Sum(Yhat-Ybar)^2

10

## How do you calculate RSS/

### Sum(e^2)

11

## How do you calculate R^2?

###
ESS/TSS

OR

1-RSS/TSS

12

## What is the DOF?

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

N-K

N-K-1 for intercept

13

## How do you calculate Adjusted R^2

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

14

## How can you calculate the correlation coefficient r?

### Root R^2

15

## What are the steps of applied regression?

###
0.5 Choose the dependant variable

1. Review the literature and develop a theoretical model

2. Specify the model - expected signs

3. Hypothesise the expected signs and coefficents

4. Collect Data, Inspect and Clean

5. Estimate, evaluate and analyse the equation

6. Document the Results

16

## What is the sampling distribution of Bhat?

### The variety of Bhat you get from different samples

17

## How can the mean reveal bias?

###
An estimated BHat should have an expected value of B

E(βHat)=β

18

## 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)

19

## 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)

20

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

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

21

## What is the formula for the T-Test?

###
T=(Bk-BH0)/SE(BK)

Bk is the coefficient

Bho is the null, usually 0

22

## How do you calculate the variance of an estimation?

### =Sum(e^2)/N-2

23

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

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

Root for SE

24

## How do you calculate a confidence interval?

### B +- Tc*SE(B)

25

## What are the limitations of the T-Test?

###
Does not consider theoretical validity

Does not test importance

26

## What are the three potential specificaiton errors?

###
Independent variables

Functional Form

Form of the stochastic error term

27

## 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

28

## What is the effect of an irrelevant variable?

###
Does not cause bias

Will increase variance and hence t-scores

Will reduce adjusted R^2

29

## 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

30

## What is the equation for the F-Test?

###
F=(RSSm-RSS)/M

/ (RSS/N-

k-1)

M = Number of constraints

31

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

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

32

## 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

33

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

###
Numerator = Number of Constraints

Denominator = N-k-1

34

## 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

35

##
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

36

## What are the effects of changing the scale of x?

###
Coefficient must also be multiplied by the scaling factor

SE also

37

## What are the effects of scaling y?

### The whole regression will need to be re-run

38

## What are the effects of scaling x and y

### Intercept and residuals will change,

39

## 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

40

## 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

41

## What happens if you suppress the constant term?

###
You violate classical assumption 2,

The error term has an expected value of zero

42

## Discuss linear functional form

###
Linear in the variables

All linear

Not Linear in the coefficients

X^B

43

## Discuss Log functional Form

###
Double log (on both sides)

Still linear in coefficients

Lin-Log- Log of variables

Log-Lin - Log of dependant

44

## Discuss Other functional forms

###
Polynominal-x^2

Inverse-1/x

45

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

###
R^2

TSS

46

## What does an intercept dummy variable do?

###
Change the intercept based on a condition

Use one variable less than the number of conditions

47

## What is the omitted condition?

### The Event not represented by the dummy variable

48

## What happens if you use two dummys for two conditions?

###
Violate CS-6 creating perfect co linearity

This is the dummy variable trap

49

## What is a slope dummy?

### Effects both intercept and slope

50

## What is an indicator variable?

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

51

## 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

52

## 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

53

## How can you detect collinearity?

###
Hard to detect

Correlation coefficient

High variance inflation factors

54

## 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

55

## 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

56