Formulate and Interpret a Logistic Regression Model
Qualitative (categorical) dependent variables are dummy variables used as dependent rather than independent variables. Remember that a dummy variable is a variable that takes on the value 0 or 1. The logistic transformation takes the probability that an event happens,…
Formulate and Interpret a Multiple Regression Model That Includes Qualitative Independent Variables
Dummy variables are binary variables used to quantify the effect of qualitative independent variables. A dummy variable is assigned a value of 1 if a particular condition is met and, otherwise, a value of 0. The number of dummy variables…
Describe Influence Analysis and Methods of Detecting Influential Data Points
In statistics, regression analysis is a method of modeling the relationships between a dependent variable (also called an outcome variable) and one or more independent variables (also called predictor variables). Regression analysis aims to find the best-fitting line or curve…
Explain Multicollinearity and How It Affects Regression Analysis
Multicollinearity occurs when two or more independent variables are significantly correlated to each other. It results from the violation of the multiple regression assumptions that there is no apparent linear relationship between two or more independent variables. Multicollinearity is common…
Explain Serial Correlation and How It Affects Statistical Inference
Serial Correlation (Autocorrelation) Serial correlation, also known as autocorrelation, occurs when the regression residuals are correlated with each other. In other words, it occurs when the errors in the regression are not independent of each other. This can happen for…
Explain the Types of Heteroskedasticity and How It Affects Statistical Inference
One of the assumptions underpinning multiple regression is that regression errors are homoscedastic. In other words, the variance of the error terms is equal for all observations: $$ E\left(\epsilon_i^2\right)=\sigma_\epsilon^2,\ i=1,2,\ldots,n $$ In reality, the variance of errors differs across observations….
Model Misspecification
Model specification involves selecting independent variables to include in the regression and the functional form of the regression equation. Here, comprehensive guidelines are provided for accurately defining a regression, followed by an explanation of common model misspecifications. Exhibit 1 succinctly…
The Use of Multiple Regression for Forecasting
Multiple regression uses the same process employed in simple regression for predicting the dependent variable’s value. It, however, does so with more items summed up, as shown below: $$ \widehat{Y_f}={\hat{b}}_0+{\hat{b}}_1X_{1f}+{\hat{b}}_2X_{2f}+\ldots+{\hat{b}}_kX_{kf}={\hat{b}}_0+\sum_{j=1}^{k}{{\hat{b}}_jX_{jf}} $$ Where: \({\hat{Y}}_f\) = Predicted (forecasted) value of the dependent…
Joint Hypotheses Testing
In multiple regression, the intercept in simple regression represents the expected value of the dependent variable when the independent variable is zero, while in multiple regression, it’s the expected value when all independent variables are zero. The interpretation of slope…
Assumptions Underlying Multiple Linear Regression
The following assumptions are used to build multiple regression models: The relationship between the dependent variable, and the independent variables, is linear. The independent variables are not random. There is no definite linear relationship between two or more independent variables….
