Quantitative Methods

Question 0

What does correlation measure?

Answer 0

Strength of the linear relationship between two variables

= (Covx,y)/(σx*σy)

Question 1

What does covariance measure?

Answer 1

The direction in which variables move

= [Σ(x-X)(y-Y)]/(n-1), where X and Y are the mean values

Question 2

Slope of the regression line

Answer 2

= covariance/variance

Test for statistical significance

Question 3

Standard error of estimate

Answer 3

• Standard deviation of the error terms
• Measures degree of variability between actual and estimate values from the regression line

= SQRT[SSE/(n-2)]

Question 4

Total sum of squares (SST)

Answer 4

• Sum of squared differences between actual values of Y and the mean of Y
• Total variation in Y

Question 5

Regression sum of squares (RSS)

Answer 5

• Sum of the squared differences between predicted values of Y and the mean of Y
• Variation in Y explained by X

Question 6

Sum of squared errors (SSE)

Answer 6

• Sum of squared differences between actual values of Y and predicted values of Y
• Unexplained variation in Y

Question 7

R-squared (coefficient of determination)

Answer 7

• Percent of total variation in the dependent variable explained by the independent variable

= (SST - SSE)/SST or RSS/SST

Question 8

What does F test assess?

Answer 8

If at least one independent variable within a set explains variation in values of Y

Question 9

F-statistic

Answer 9

= MSR/MSE

= (RSS/k)/[SSE/(n-k-1)]

One-tailed test

Question 10

What is ρ value? How is it used?

Answer 10

• Smallest level of significance for which the null hypothesis can be rejected
• Reject if ρ value is less than significance level

Question 11

Setting up a t-test for regression coefficients

Answer 11

= (estimated coefficient - hypothesized value)/standard error

Question 12

Why is it necessary to adjust R squared? How?

Answer 12

• R squared always increases with more variables, even if contribution is insignificant

= 1 - (1-Rsq)(n-1)/(n-k-1)

Question 13

Heteroskedasticity

Answer 13

• Variance of the residuals is not equal across all observations in the sample
• Correct using White-corrected standard errors

Question 14

How to detect heteroskedasticity

Answer 14

• scatter plot

- Breusch-Pagan chi-square test (n*Rsq)

Question 15

Serial correlation (autocorrelation)

Answer 15

• Residual terms are correlated with one another

- Correct using the Hansen method by adjusting the coefficient standard errors

Question 16

How to detect serial correlation

Answer 16

Durbin-Watson test

• close to 2 if not correlated
• positively correlated if 2
• reject if less than d1 (unless model is autoregressive),

If autoregressive, use t-test on the residual autocorrelations over several lags

Question 17

What is multicollinearity

Answer 17

Two or more independent variables are correlated with one another

Question 18

How to detect multicollinearity

Answer 18

F test and R-sq show significance but p-values don’t

Question 19

Autoregressive model

Answer 19

When a dependent variable is regressed against one or more lagged values of itself

Question 20

Mean-reverting level for a time series

Answer 20

b0/(1-b1)

• indicate if time series to be covariance stationary

Question 21

ARCH (autoregressive conditional heteroskedasticity)

Answer 21

Variance of the residuals in one period is dependent of the variance of the residuals in a previous period

Question 22

What does the Dickey Fuller test check?

Answer 22

Covariance stationary and cointegration (two time series are economically linked)

Question 23

How to test for ARCH

Answer 23

• Regression of squared residuals on their lagged values

- If coefficient is statistically different from zero, then time series exhibits ARCH

Question 24

Testing covariance stationarity for a time series

Answer 24

• run an AR model

- Dickey Fuller test

Question 25

How to adjust for seasonality

Answer 25

Incorporate a seasonal lag term in the AR model

Question 26

Unit root - what it means, how to detect and how to fix

Answer 26

• means time series is not covariance stationary
• if coefficient on lagged dependent variable is equal to one
• first difference data before using in time series model