Quantitative Methods

Question 1

Overfitting

Answer 1

when a machine learning model learns the input and target dataset too precisely, making the system more likely to discover false relationships or unsubstained patterns that will lead to prediction errors.

Question 2

Adjusted R2

Answer 2

goodness of fit measure that adjusts the coefficent of determination, R2, for the number of independent variables in the model

Question 3

Akaike’s Information Criterion (AIC)

Answer 3

a statistic used to compare sets of independent variables for explaining a dependent variable. it is preferred for finding the model that is best suited for prediction.

Question 4

Analysis of Variance (ANOVA)

Answer 4

A table that presents the sums of squares, degrees of freedom, mean squares, and F-statistic for a regression model.

Question 5

Coefficient of Determination

Answer 5

A measure of how well data points fit a linear statistical model, indicated in percentage terms from 0 to 100%. also known as R-squared (R2).

Question 6

General Linear F-Test

Answer 6

A test statistic used to assess the goodness of fit for an entire regression model, so it tests all independent variables in the model.

Question 7

Joint Test of Hypotheses

Answer 7

The test of hypotheses that specify values for two or more independent variables in the hypotheses.

Question 8

Nested Models

Answer 8

Models in which one regression model has a subset of the independent variables of another regression model.

Question 9

Restricted Model

Answer 9

A regression model with a subset of the complete set of independent variables.

Question 10

Schwarz’s Bayesian Information Criterion (BIC or SBC)

Answer 10

A statistic used to compare sets of independent variables for explaining a dependent variable. it is preferred for finding the model with the best goodness of fit.

Question 11

Unrestricted model

Answer 11

A regression model with the complete set of independent variables.

Question 12

What are the principles for proper regression model specification?

Answer 12

Economic reasoning behind variable choices, parsimony, good out-of-sample performance, appropriate model functional form, no violations of regression assumptions

These principles ensure the model is effective and reliable in making predictions.

Question 13

What are common failures in regression functional form?

Answer 13

Omitted variables, inappropriate form of variables, inappropriate variable scaling, inappropriate data pooling

These failures can lead to violations of regression assumptions, impacting model accuracy.

Question 14

What is heteroskedasticity in regression analysis?

Answer 14

When the variance of regression errors differs across observations

It can affect the validity of statistical inferences made from the model.

Question 15

What is unconditional heteroskedasticity?

Answer 15

When the error variance is not correlated with the independent variables

It does not create major problems for statistical inference.

Question 16

What is conditional heteroskedasticity?

Answer 16

When the error variance is correlated with the values of the independent variables

This type of heteroskedasticity can lead to inflated t-statistics and Type I errors.

Question 17

How is conditional heteroskedasticity detected?

Answer 17

Using the Breusch–Pagan (BP) test

This test assesses the correlation between error variance and independent variable values.

Question 18

How can the bias created by conditional heteroskedasticity be corrected?

Answer 18

By computing robust standard errors

This adjustment helps ensure accurate statistical inference.

Question 19

What is serial correlation (or autocorrelation) in regression?

Answer 19

When regression errors are correlated across observations

It is particularly problematic in time-series regressions.

Question 20

What are the consequences of serial correlation?

Answer 20

Inconsistent coefficient estimates, underestimated standard errors, inflated t-statistics

This can lead to misleading conclusions about the relationships between variables.

Question 21

What test is used to detect serial correlation?

Answer 21

The Breusch–Godfrey (BG) test

This test uses residuals from the regression to check for correlation with lagged residuals.

Question 22

What does a variance inflation factor (VIF) measure?

Answer 22

Multicollinearity

It quantifies how much the variance of an estimated regression coefficient increases due to multicollinearity.

Question 23

What does a VIF of 1 indicate?

Answer 23

No correlation between the variable and other regressors

This suggests that multicollinearity is not a concern for that variable.

Question 24

What VIF value indicates serious multicollinearity requiring correction?

Answer 24

VIFj > 10

This level of multicollinearity can significantly affect the reliability of the regression model.

Question 25

What are possible solutions to multicollinearity?

Answer 25

Dropping regression variables, using a different proxy, increasing sample size ## Footnote These strategies help mitigate the effects of multicollinearity on regression analysis.

Question 27

What should the model be grounded in?

Answer 27

Economic reasoning ## Footnote Economic reasoning provides the rationale for the choice of variables in the model.

Question 28

What does it mean for a model to be parsimonious?

Answer 28

Each variable included in regression should play an essential role.

Question 29

What is a key performance expectation for a model?

Answer 29

Model should perform well out of sample ## Footnote This means the model may explain only the specific dataset on which it was trained, indicating potential overfitting.

Question 30

What should the functional form of the model be?

Answer 30

Appropriate ## Footnote If a nonlinear relationship between regressors is expected, the model should incorporate the appropriate nonlinear terms.

Question 31

What must the model satisfy?

Answer 31

Regression assumptions ## Footnote If heteroskedasticity, serial correlation, or multicollinearity are detected, it may be necessary to revise regression variables and/or functional form.

Question 32

What is an omitted variable in regression?

Answer 32

One or more important variables are omitted from the regression. ## Footnote May lead to heteroskedasticity or serial correlation.

Question 33

What is an inappropriate form of variables in regression?

Answer 33

Ignoring a nonlinear relationship between the dependent and independent variable. ## Footnote May lead to heteroskedasticity.

Question 34

What is inappropriate variable scaling in regression?

Answer 34

One or more regression variables may need to be transformed before estimating the regression. ## Footnote May lead to heteroskedasticity or multicollinearity.

Question 35

What is inappropriate data pooling in regression?

Answer 35

Regression model pools data from different samples that should not be pooled. ## Footnote May lead to heteroskedasticity or serial correlation.

Question 37

What is the impact of lagged independent variable on coefficient estimates?

Answer 37

Invalid Coefficient Estimates: Yes

Question 38

What is the impact of lagged independent variable on standard error estimates?

Answer 38

Invalid Standard Error Estimates: Yes

Question 39

What is the impact of independent variable being a lagged value of the dependent variable on coefficient estimates?

Answer 39

Invalid Coefficient Estimates: No

Question 40

What is the impact of independent variable being a lagged value of the dependent variable on standard error estimates?

Answer 40

Invalid Standard Error Estimates: Yes

Question 41

Breusch - Godfrey (BG) test

Answer 41

A test used to detect autocorrelated residuals up to a predesignated order of the lagged residuals

Question 42

Breusch - Pagan (BP) test

Answer 42

A test for the presence of heteroskedasticity in a regression

Question 43

Conditional Heteroskedasticity

Answer 43

A condition in which the variance of residuals of a regression are correlated with the value of the independent variables

Question 44

Durbin - Watson (DW) test

Answer 44

A test for the presence of first-order serial correlation

Question 45

First-order serial correlation

Answer 45

the correlation of residuals with residuals adjacent in time

Question 46

Heteroskedastic

Answer 46

When the variance of the residuals differs across observations in a regression

Question 47

Model Specification

Answer 47

The set of independent variables included in a model and the model's functional form.

Question 48

Multicollinearity

Answer 48

When two or more independent variables are highly correlated with one another or are approximately linearly related

Question 49

Negative serial correlation

Answer 49

A situation in which residuals are negatively related to other residuals

Question 50

Omitted variable bias

Answer 50

Bias resulting from the omission of an important independent variable from a regression model

Question 51

Positive serial correlation

Answer 51

A situation in which residuals are positively related to other residuals

Question 52

Robust standard errors

Answer 52

Method for correcting residuals for conditional heteroskedasticity. also known as heteroskedasticity-consistent standard errors or white-corrected standard errors.

Question 53

Serial Correlation

Answer 53

A condition found most often in time series in which residuals are correlated across observations. also known as autocorrelation

Question 54

serial-correlation consistent standard errors

Answer 54

method for correcting serial correlation. also known as serial correlation and heteroskedasticity adjusted standard errors, Newey-West standard errors, and robust standard errors.

Question 55

unconditional heteroskedasticity

Answer 55

When heteroskedasticity of the error variance is not correlated with the regression's independent variables.

Question 56

Variance inflation factor (VIF)

Answer 56

A statistic that quantifies the degree of multicollinearity in a model.