ANOVA Table and Measures of Goodness of Fit
R-squared \(\bf{(R^2)}\) measures how well an estimated regression fits the data. It is also known as the coefficient of determination and can be formulated as: $$ R^2=\frac{\text{Sum of regression squares}}{\text{Sum of squares total}}=\frac{{\sum_{i=1}^{n}{(\widehat{Y_i}-\bar{Y})}}^2}{{\sum_{i=1}^{n}{(Y_i-\bar{Y})}}^2} $$ Where: \(n\) = Number of observations….
What Multiple Regression is and How It Works
Example: Multiple Regression in Investment World James Chase, an investment analyst, wants to determine the impact of inflation rates and real rates of interest on the price of the US Dollar index (USDX). Chase uses the multiple regression model below:…
A Review of Multiple Linear Regression’s Uses
Multiple linear regression describes the variation of the dependent variable by using two or more independent variables. When used properly, it can improve predictions. However, if used incorrectly, it can create spurious relationships that can undermine predictions. Typically, a multiple…
Mortgages and Mortgage-Backed Securities
After completing this reading, you should be able to: Describe the various types of residential mortgage products. Calculate fixed-rate mortgage payment and its principal and interest components. Describe the mortgage prepayment option and the factors that influence prepayments. Summarize the…
Corporate Bonds
After completing this reading, you should be able to: Understand what a bond is and describe the methods of issuing bonds. Describe the features of bond trading and explain the behavior of bond yield. Describe a bond indenture and explain…
Regression with a Single Regressor – Hypothesis Tests and Confidence Intervals
After completing this reading you should be able to: Calculate and interpret confidence intervals for regression coefficients. Interpret the \(p-value\). Interpret hypothesis tests about regression coefficients. Evaluate the implications of homoskedasticity and heteroskedasticity. Determine the conditions under which the OLS…
Properties of Options
After completing this reading, you should be able to: Identify the six factors that affect an option’s price. Identify and compute upper and lower bounds for option prices on non-dividend and dividend-paying stocks. Explain put-call parity and apply it to…
Bayesian Analysis
After completing this reading you should be able to: Describe Bayes’ theorem and apply this theorem in the calculation of conditional probabilities. Compare the Bayesian approach to the frequentist approach. Apply Bayes’ theorem to scenarios with more than two possible…
Linear Regression
After completing this reading, you should be able to: Describe the models that can be estimated using linear regression and differentiate them from those which cannot. Interpret the results of an OLS regression with a single explanatory variable. Describe the…
Validating Rating Models
After completing this reading, you should be able to: Explain the process of model validation and describe the best practices for the roles of internal organizational units in the validation process. Compare qualitative and quantitative processes to validate internal ratings…
