Estimated Logistic Regression
Qualitative (categorical) dependent variables are the dummy variables used as dependent variables rather than independent variables. Recall that a dummy variable is a variable that takes on the value 0 or 1.The logistic transformation is the most widely used. It…
Model Misspecification
Model specification involves selecting independent variables to include in the regression and the functional form of the regression equation. We say that a model is misspecified when it violates the assumptions underlying linear regression, its functional form is incorrect, or…
Multicollinearity
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 of the independent variables. Multicollinearity…
Heteroskedasticity and Serial Correlation
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: $$E(\epsilon_{i}^{2})=\sigma_{\epsilon}^{2}, i=1,2,…,n$$ In reality, the variance of errors differs across observations. This is…
Hypothesis Testing
Hypothesis testing involves testing an assumption regarding a population parameter. A null hypothesis is a condition believed not to be true. We reject the null hypothesis in the presence of enough evidence against it and accept the alternative hypothesis. Hypothesis…
Dummy Variables in Regression Analysis
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 a value of 0 otherwise. The number of dummy variables…
Analyzing the Regression Output
Most of the regression analysis is done using statistical software. You are mainly supposed to interpret the regression output. ANOVA Table One of the outputs of multiple regression is the ANOVA table. The following shows the general structure of an…
Adjusted Coefficient of Determination
Multiple R2 The multiple coefficients of determination, R2, can be used to test the overall usefulness of the overall set of independent variables in explaining the dependent variable. Multiple R2 can be interpreted as the percentage of the dependent variables’ total…
The F-statistic
The F-test determines whether all the independent variables help explain the dependent variable. It is a test of regression’s overall significance that involves testing the null hypothesis that all the slope coefficients in the regression are jointly equal to zero…
Assumptions of Multiple Regression Model
Multiple regression models are built on the following assumptions. The relationship between the dependent variable, \(Y\), and the independent variables, \(X_{1}, X_{2},…, X_{k}\) is linear. The independent variables \((X_{1}, X_{2},…, X_{k})\) are not random. There exists no definite linear relationship between…
