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….
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…
