Correlation And Regression

Question 0

Test statistic for significance of correlation coefficient

Answer 0

t = r sqrt(n - 2)
————–
sqrt(1 - r^2)

r = correlation coefficient 
n = number of samples

Question 1

What is correlation coefficient

Answer 1

Measure of strength of linear relationship between two variables
x>0 = positive correlation
x<0 = negative correlation
X=0 = no correlation

Question 2

Regression assumptions

Answer 2

Independent variable:

• linearly related to dependent var
• uncorrelated with residual

Residual term:

• exp value = 0
• constant variance
• independently and normally distributed

Question 3

Confidence interval of y value

Answer 3

Predicted Y value +/- (critical t-value)*(standard error)

Question 4

Difference between t-test and F-test

Answer 4

T-test: assesses statistical significance of individual regression parameters

F-test: assesses model effectiveness

Question 5

How to test for heteroskedasticity

Answer 5

Using Breusch-Pagan test on regressed squared residuals
Lagrange Multiplier LM = n*R^2
Will be x^2 random variable w/df= num independent variables in regression
Or White Test?

Question 6

How to test for serial correlation

Answer 6

Durbin-Watson test

If it differs sufficiently from 2, then regression errors have significant serial correlation

Question 7

How to test for multicollinearity

Answer 7

No specific test

Identify whether R^2 is high with significant F-stat despite insignificant t-tests

Drop one of correlated variables

Question 8

What are two types of tests for significance in multiple regression?

Answer 8

Whether each independent variable explains dependent (t stat)

Whether some or all independent variables explain dependent (F stat)

Question 9

What is t stat formula for multiple regression

Answer 9

t = est regression param
—————————————
Std error of regression param

With n - k - 1 df

Question 10

What info is included in an ANOVA table? (analysis of variance)

Answer 10

Degrees of freedom 
Sum of squares 
Mean square (ss / df)

For regression and error and total

Question 11

How to calc MSR (mean squared regression)

Answer 11

                k

Question 12

How to calc MSE (mean squared error)

Answer 12

        n - k - 1

Question 13

What is coefficient of determination and how to calc (R^2)

Answer 13

% variation in dep var explained by indep vars
R^2 = regression sum of squares
——————————
total sum of squares

    = SST - SSE
       ------------
            SST

Question 14

What does adjusted R^2 measure

Answer 14

Goodness of fit that adjusts for the number of independent variables included in the model

Question 15

What is standard error of estimate and how to calc

Answer 15

Measures uncertainty of values of dependent variable around regression line

= Sqrt (mean squared error)

Question 16

How to calculate F stat

Answer 16

mean squared error

With k and n-k-1 df

Reject H0 if F > Fcritical

Question 17

Confidence interval for regression coefficient

Answer 17

Regression coefficient +- (critical t-value)(standard error of regression coefficient)

If zero is included in conf interval, slope not statistically significant

Question 18

What is conditional heteroskedasticity

Answer 18

Residual variance related to level of independent variables

Question 19

What is serial correlation

Answer 19

Residuals are correlated

Question 20

What is multicollinearity

Answer 20

Two or more independent variables correlated

Question 21

What are six common misspecifications of a regression model?

Answer 21

Omitting a variable
Transforming variable 
Incorrectly pooled data
Using lagged dependent var as an independent var
Forecasting the past
Measuring independent vars with error

Question 22

What do model misspecifications result in?

Answer 22

Biased and inconsistent regression coefficients
No confidence in hypothesis tests of coefficients
No confidence in predictions

Question 23

When do you use a linear trend model?

Answer 23

Data points equally distributed above and below line

Mean is constant

Question 24

When do you use a log-linear model?

Answer 24

When dependent variable grows at constant rate (to a power) Residuals may be correlated Mean is non constant Seasonality

Question 25

When do you use an auto regressive model?

Answer 25

When dependent variable is regressed against previous values of itself Autocorrelation a of residuals are not statistically signif Use t test to identify correlation between residuals

Question 26

What is autocorrelation?

Answer 26

When residuals exhibit serial correlation Used to test for seasonality

Question 27

What are 3 conditions required to be covariance stationary

Answer 27

Required for time series models Three conditions: - constant and finite expected value - constant and finite variance - constant and finite covariance with leading or lagged values

Question 28

Three steps to determine whether a time series is covariance stationary and how to correct

Answer 28

Plot data; mean /variance constant? Run AR model; test correlation Dickey fuller test (for unit root) Can correct with first differencing

Question 29

What is mean reversion

Answer 29

b0/(1 - b1) For AR(1) model

Question 30

What is a unit root and how to identify

Answer 30

Unit root is when value of lag coefficient = 1 Use Dickey-Fuller test to identify Cov stationary Random walk

Question 31

How to convert random walk to covariance stationary

Answer 31

Use first differencing (model change in value vs value) Var y = xt - x(t- 1) = error term

Question 32

What is root mean squared error used for

Answer 32

Used to assess predictive accuracy of autoregressive models Lower RMSE is better Out of sample RMSE tests forecasting ability

Question 33

What is a structural change?

Answer 33

A significant shift in plotted data dividing in two distinct patterns Results in coefficient instability Run two diff models before and after change

Question 34

What is cointegration

Answer 34

When two time series are economically linked Related to same macro variable

Question 35

How to test for cointegration

Answer 35

Regress one time series on other Test residuals for unit root; if test rejects unit root, two series are cointegrated If cointegrated, results in covariance stationary error term and reliable t tests

Question 36

What is autoregressive conditional heteroskedasticity (ARCH) and what does it result in

Answer 36

Variance of residuals in one time period dependent on variance of residuals in another time period Results in invalid reg coeff standard errors and hypothesis tests

Question 37

How to correct for ARCH

Answer 37

Use Generalized least squares Or use model to predict variance of residuals in following periods