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…
The Predicted Value of a Dependent Variable
The Predicted Value of the Dependent Variable The following steps are followed to predict the value of a dependent variable in a multiple regression model. Determine the regression coefficient estimates. Obtain the forecasted values of the independent variables. Calculate the…
Interpreting the Results of Hypothesis Tests of Regression Coefficients
The following results are obtained from regressing the price of the US Dollar Index (USDX) on inflation rates and real interest rates. $$\small{\begin{array}{l|c}\textbf{Regression Statistics}\\ \hline\text{Multiple R} & 0.8264\\ \hline\text{R Square} & 0.6830\\ \hline\text{Adjusted R Square} & 0.5924\\ \hline\text{Standard Error} &…
Estimated Regression Coefficients
The intercept term is defined as the value of the dependent variable when the independent variables are zero. On the other hand, each slope coefficient is the estimated change in the value of the dependent variable for a one-unit change…
Multiple Regression Equation
Multiple regression allows us to evaluate the effect of two or more independent variables on a given dependent variable. Multiple regression with two explanatory variables and one intercept term can be represented in the following 3D diagram: Mathematically, a multiple…
Functional Forms for Simple Linear Regression
Most Financial and economic data exhibit non-linear relationships between the dependent and independent variables. Estimating such data using a simple linear regression model would lead to the dependent variable being understated for some ranges of the independent variable. Thus, we…
