Quant

Question 1

Multicollinearity

Answer 1

Multicollinearity refers to the condition when two or more of the independent variables, or linear combinations of the independent variables, in a multiple regression are highly correlated with each other. This condition distorts the standard error of estimate and the coefficient standard errors, leading to problems when conducting t-tests for statistical significance of parameters.

Effect: greater probability that we will incorrectly conclude that a variable is not statistically significant (type II error)

Detecting: if the absolute value of the sample correlation between any two independent variables in the regression is greater than 0.7, multicollinerity is a potential problem.

The classic symptom of multicollinearity is a high R^2 and significant F-statistic even though the T statistics on the estimated slope coefficients are not significant

Correcting: omit one or more of the correlated independent variables. Not always easy to detect which variables

Question 2

what does an F test - test

Answer 2

An F-test tests whether at least one of the independent variables is significantly different from zero, where the null hypothesis is that all none of the independent variables are significant.

Question 3

Coefficent of determination

% of variability of Y explained by Xs. Higher R^2 means better fit.

Answer 3

The R^2 is calculated as (SST - SSE) / SST.
or
RSS/SST

Question 4

Standard Error of estimate

Answer 4

SEE= square root of MSE

Question 5

heteroskedasticity

Answer 5

What is it: Occurs when the variance of the residuals is not the same across all observations in the sample.

Effect on regression analysis. 4:
Standard errors are usually unreliable
The coefficient estimates arent affected
F test unreliable
if standard error too small -null hypothesis rejected too often.
If standard error too big - rejected not often enough

Detect it: Looking at scatter plots of the residual and using the Breusch- Pagan chi-square test. Also a scatter plot of the residuals versus one or more of the independent variables can reveal patterns among observations.

Correct: Calculate robust standard errors - (White corrected standard or heteroskedasticity-consistent standard errors).

Or use generalized least squares.

Question 6

Two advantages of using simulation in decision making

Answer 6

The Two advantages of using simulation in decision making are 1) Better input estimation and 2) Simulation yields a distribution for expected value rather than a point estimate. Simulations do not 1) yield better estimates of expected value than conventional risk adjusted value models, nor 2) lead to better decisions.

Question 7

The general format for a confidence interval is:

Answer 7

estimated coefficient ± (critical t-stat x coefficient standard error)

Question 8

What does standard error of the estimate measure

Answer 8

The standard error of the estimate measures the uncertainty in the relationship between the actual and predicted values of the dependent variable. The differences between these values are called the residuals, and the standard error of the estimate helps gauge the fit of the regression line (the smaller the standard error of the estimate, the better the fit).

Question 9

The root mean squared error (RMSE) criterion is used to compare the accuracy of autoregressive models in forecasting out-of-sample values. To determine which model will more accurately forecast future values, we calculate the square root of the mean squared error. The model with the smallest RMSE is the preferred model.

Answer 9

true

Question 10

Spurious correlation

Answer 10

the appearance of a casual linear relationship when in fact there is no relation.

Question 11

limitation of correlation analysis

Answer 11

does not capture strong nonlinear relationships between variables

Question 12

slope coefficent

Answer 12

the estimated slope coefficent b1 for the regression line descrives the change in Y for a one unit change in X.

the predicted change in the dependent variable for 1-unit of change in the independent variable.

b1= cov(xy)/ sigma(x) ^2

Question 13

The coefficient of determination

Answer 13

In a simple regression, the coefficient of determination is calculated as the correlation coefficient squared and ranges from 0 to +1.

cannot decrease as independent variables are added to the model.

is the percentage of the total variation in the dependent variable that is explained by the independent variable.

Question 14

F - Statistic

Answer 14

F = MSR/MSE = (RSS/K) / (SSE/ [n - k - 1])

Question 15

SST
RSS
SSE

Answer 15

Total Sum of Squares - measures total variation in the dependent variable.

Regression sum of Squares - measures the variation in the dependent variable that is explained by the independent variable.

Sum of squared errors - measures the unexplained variation in the dependent variable.

Question 16

Which is more useful T or F - test when we have 1 independent variable

Answer 16

The F-test is not as useful when we only have one independent variable because it tells us the same things as the t-test of the slop coefficient.

Question 17

Limitations of regression analysis include

Answer 17

parameter instability - Linear relationships can change over time

Even if regression model accurately reflects the historical relationship between the 2 variables, limited useful investment use as the market will also know this.

If the data is heterskedastic (non - constant variance of the error terms) or exhibits autocorrelation ( error terms are not independent) regression results may be invalid.

Question 18

Serial Correlation

Answer 18

What is: (autocorrelation) the situation in which the residual terms are correlated one with another. (common in time series data).

Effect: Because of the tendency of the data to cluster together from observation to observation positive serial correlation typically results in coefficient standard errors that are too small, even though the estimated coefficients are consistent. T-statistic will be larger than it should, cause Type I errors: the rejection of the null hypothesis when it is true. F -test will also be unreliable.

Detect: 2 methods - residual plots and Durbin - Watson
ndard errors
Improve the specification of the model. Hansen method

Question 19

Model Misspecification

Answer 19

1. Functional form can be misspecified
   - Variables are omitted
   - Variables should be transformed
   - data is improperly pooled
2. Explanatory variables are correlated with the error term in time series models.
3. Other time-series misspecification that result in nonstationarity.

Question 20

Log-Linear Trend equation

Answer 20

Yt= E^[Bo+B1(t)]

ln(Yt) = Bo+B1(t)

Question 21

Covariance Stationary

Answer 21

A time series is covariance stationary if it satisfies the following 3 conditions.

1. Constant and finance expected value
2. Constant and finite variance
3. Constant and finite covariance between values at any given lag

Question 22

significant T statistic

Answer 22

as a general rule any independent variable must have a T statistic of 2 or more to be significant

Question 23

F = mean regression sum of squares / mean squared error

Answer 23

F = mean regression sum of squares / mean squared error

F = MSR/MSE

MSR = RSS / k
MSE = SSE / (n - k - 1)