Quantitative Methods

Question 1

Formula for Multiple Regression

Answer 1

Question 2

Coefficient of Determination

Answer 2

R²
Measure of Goodness of Fit
Sum of Squares Regression / Sum of Squares Total

Question 3

Adjusted R²

Answer 3

Adjusts R² by the degrees of freedom;
Does not automatically increase when variables are added

Question 4

Akaike’s Information Criterion (AIC)

Answer 4

Measure of Model Parsimony ie. Lower is better fitting model

Preffered model for prediction purposes

Question 5

Schwarz’s Bayesian Information Criteria (BIC or SBC)

Answer 5

Allows us to choose the best model among a set of models

Preffered when Goodness of Fit is Desired

Question 6

Unrestricted Model

Answer 6

Full model with all independent variables

Question 7

Restricted Model

Answer 7

Also called nested Models, they take the unrestricted model and exclude one or more variables

Question 8

F-Distributed Test Statistic When Comparing Restricted & Unrestricted Models

Answer 8

q is the number of restrictions

Question 9

General Linear F-test

Answer 9

Question 10

Heteroskedasticity

Answer 10

The variance of the residuals differ across observations

Arises from Ommited Variables, Incorrect Functional Form, Extreme Values

Use Breusch-Pagan (BP) Test

Question 11

Unconditional Heterskedasticity

Answer 11

Error variance is not correlated with Independent Variables

Not a problem for statistical inference

Question 12

Conditional Heterskedasticity

Answer 12

Error Variance is correlated to independent variables

Inflated T-Statistics

Use Breusch-Pagan (BP) Test

Question 13

Breusch-Pagan (BP) Test

Answer 13

Used to test for Heterskedasticity;
1. Run Regression
2. Run another regression with the Dependent variable being the residuals squared from step 1
3. Use Chi Squared Statistic to solve Null Hypothesis that there is no Heteroskedasticity

Question 14

Robust Standard Errors

Answer 14

Computed to correct for the effects of Heteroskedasticity

Question 15

Serial Correlation

Answer 15

Regression Errors are correlated across observations

Typically seen in Time-Series Regressions

Use Durbin Watson (DW) Test or Breusch-Godfrey (BG) Test

Question 16

Breusch-Godfrey (BG) Test

Answer 16

Used to Test for Serial Correlation;
1. Run the initial regression
2. Run Fitted Residuals from Step 1 as the Dependent Variable against the initial regressors + one or more lagged residuals
3. Test Hypothesis using Chi-Square Test

Question 17

Correcting for Serial Correlation

Answer 17

Serial-correlation consistent standard errors

Computed by Software Packages

Question 18

Multicollinearity

Answer 18

Independent Variables are correlated to each other

Use variance inflation factor (VIF) to quantify multicollinearity issues

Question 19

Variance Inflation Factor (VIF) Formula

Answer 19

Used to test for Multicollinearity

VIF>5 Prompts Investigation
VIF>10 Serious Multicollinearity issues

Question 20

Correcting Multicollinearity

Answer 20

• Excluding 1 or more variables
• Using a different proxy for one of the variables
• Increasing sample size

No easy way to fix

Question 21

High Leverage Point

Answer 21

Extreme Value of a Independent Variable

Question 22

Outlier

Answer 22

Extreme Value of Dependent Variable

Question 23

Leverage

Answer 23

Difference between nth independent variable and the mean of all the independent variables

Rule of Thumb: Leverage above 3(K+1/N) is potentially influential

Question 24

Studentized Residual

Answer 24

Way of testing for outliers

Question 25

Cook's Distance

Answer 25

Metric for identifying influential data points; How the estimated value if the regression changes after deleting an observation

Question 26

Logistic Transformation

Answer 26

Transforms Qualitative Dependent Variable into a Linear relationship with the independent variables

Question 27

Logistic Regression

Answer 27

Question 28

Likelihood Ratio (LR) Test

Answer 28

Method to assess the fit of Logistic Regression models | Higher values (closer to 0) are better

Question 29

Linear Trend Model Formula

Answer 29

Time Series with Linear Trend

Question 30

Log-Linear Model Formula

Answer 30

Commonly used with time series that have exponential growth

Question 31

Autoregressive (AR) Model Formula

Answer 31

Time series model regressed on its own past values

Question 32

Covariance Stationary

Answer 32

1. The expected value of the Time Series must be constant and finite in all periods 2. The variance in the time series must be constant and finite in all periods 3. The covariance of the time series to itself must be constant and finite in fixed periods in the future and the past

Question 33

Mean Reversion level for AR (1) Model

Answer 33

Question 34

Random Walk

Answer 34

The value of a time series in one period is the same as the one in the previous time period, with an error term added. ## Footnote Use Dickey Fuller Test

Question 35

Dickey-Fuller Test

Answer 35

Used to test for a Unit root; If there is a unit root, then the time series is a random walk. | Test for g=0

Question 36

*n*-period Moving Average Formula

Answer 36

Used to smooth out period to period fluctuations in time series models

Question 37

Moving Average Time-Series (MA1) Model

Answer 37

Question 38

AR1 Model Adjusted for Quarterly Seasonality

Answer 38

Question 39

Autoregressive Moving Average Models (ARMA)

Answer 39

Combines Autoregressive and Moving Average Time Series ## Footnote Can be very unstable

Question 40

Autoregressive Conditional Heteroskedasticity (ARCH1) Model

Answer 40

Way of Testing if an AR Model has Heterskedasticity

Question 41

Cointegration

Answer 41

Long Term finanical or economic relationship exists and don't diverge in the long run

Question 42

Test of Conitegration between two time series that have a unit root

Answer 42

Question 43

Supervised Learning

Answer 43

Infers patterns between inputs (features) and Outputs (targets); uses labeled data

Question 44

Unsupervised Learning

Answer 44

Seeks to identify strucure in unlabeled data; Used in 1. Dimesion Reduction (reduce number of features) 2. Clustering

Question 45

Guide to ML Algorithms

Answer 45

Question 46

Overfitting

Answer 46

Does not generlize well to new data

Question 47

Bias Error

Answer 47

Degree to which the model fits the training data; produces underfitting and in-sample errors

Question 48

Variance Error

Answer 48

How much the model's results change in response to new data; Causes overfitting and out-of-sample errors

Question 49

Base Error

Answer 49

Due to Randomness of Data

Question 50

Cross-Validation

Answer 50

Method of reducing overfitting

Question 51

K-Fold Cross Validation

Answer 51

Used to randomize the data into training and validation samples

Question 52

LASSO (Least Absolute Shrinkage and Selection Operator)

Answer 52

A type of Penalized Regression that applies as features are added to the regression

Question 53

Hyperparameter

Answer 53

Paramater selcted by the researcher before learning begins

Question 54

Support Vector Machine

Answer 54

Optimally separates the data into two sets

Question 55

*k*-Nearest Neighbor (KNN)

Answer 55

Supervised learning technique used mostly for classification and sometimes for regression

Question 56

Classification and Regression Tree (CART)

Answer 56

Supervised learning used in both classificatio and regression. Commonly applied to binary classification or regression

Question 57

Ensemble Learning

Answer 57

Combining the predictions from a collection of models

Question 58

Bootstrap Aggregation (Bagging)

Answer 58

Technique where orignial dataset is used to create *n* number of datasets

Question 59

Random Forrest Classifier

Answer 59

Large number of decision trees trained via a bagging method

Question 60

Principal Component Analysis (PCA)

Answer 60

Transform many highly correlated features of data into a smaller number of uncorrelated composite variables

Question 61

Eigenvectors

Answer 61

Mutual uncorrelated composite variables that are linear combinations of the original features | Represents a direction

Question 62

Eigenvalue

Answer 62

Represetns the proportion of the total variance explained by the eigenvectors

Question 63

*k*-Means Clustering

Answer 63

A form of Unsupervised learning

Question 64

Hierarchical Clustering

Answer 64

A form of unsupervised learning

Question 65

Choosing an ML Algorithm Flowchart

Answer 65

Question 66

ML Model Building Steps

Answer 66

1. Conceptualization of the Modeling Task 2. Data Collection 3. Data Preperation and Wrangling 4. Data Exploration 5. Model Training

Question 67

Text ML Model Building Steps

Answer 67

1. Text Problem Formulation 2. Data (Text) Curation 3. Text Preperation and Wrangling 4. Text Exploration

Question 68

Trimming

Answer 68

When extreme values and outliers are removed from the dataset | Also called truncation

Question 69

Winsorization

Answer 69

When extreme values or outliers are replaced by the maximum (minimum) values that are not outliers

Question 70

Normalization Formula

Answer 70

Process of rescaling numeric variables in the range of [0,1]

Question 71

Standardization Formula

Answer 71

Process of both centering and scaling the variables ## Footnote Data must be normally distributed to be effective

Question 72

Confusion Matrix

Answer 72

Question 73

Precision Formula

Answer 73

Question 74

Recall Formula

Answer 74

Question 75

Accuracy Formula

Answer 75

Question 76

F1 Score Formula

Answer 76

Question 77

Root Mean Squared Error

Answer 77