Regression Analyses

Numerous disciplines, including economics, social sciences, finance, and marketing, heavily rely on regression analysis. It helps forecast outcomes, offers useful insights into the interactions between factors, and allows researchers to test ideas and reach conclusions based on actual data.

1. Dependent and Independent Variables: The result or response variable we are interested in forecasting or explaining is known as the dependent variable in regression analysis. To predict or explain the variance in the dependent variable, independent variables—also referred to as predictor or explanatory variables—are utilized.
2. Linear Regression: Regression analysis most frequently takes the form of linear regression. It presupposes that the dependent and independent variables have a linear relationship. In multiple regression, the objective is to identify the line (or hyperplane) that minimizes the difference between the observed data points and the projected values.
3. Ordinary Least Squares (OLS): OLS is a technique for calculating the regression equation’s coefficients. It reduces the total squared difference between the values anticipated and observed. The degree and direction of the link between the independent factors and the dependent variable are represented by the estimated coefficients.
4. Multiple Regression: Examining the link between a dependent variable and two or more independent variables at the same time is known as multiple regression. While accounting for the impacts of other factors, it enables the identification of the distinctive contribution of each independent variable.
5. Assumptions of Regression Analysis: The linearity, independence, homoscedasticity, and absence of multicollinearity (strong correlation between independent variables) are among the assumptions that underpin regression analysis. The reliability of the regression findings may be impacted by violations of these presumptions.
6. Interpretation of Coefficients: When other variables are held constant, the coefficients in a regression equation indicate the change in the dependent variable resulting from a one-unit change in the corresponding independent variable. Indicating a positive or negative association, respectively, are positive and negative coefficients.
7. Goodness of Fit: The regression model’s “goodness of fit” evaluates how well the data fits the model. The coefficient of determination (R-squared), which shows the percentage of variation in the dependent variable that can be accounted for by the independent variables, and modified R-squared, which accounts for the number of variables and sample size, are common metrics.
8. Diagnostic Tests: Diagnostic tests are carried out to evaluate the regression’s presumptions and find any breaches or problems. These tests involve looking for outliers, looking for patterns in the residuals, and determining whether any significant observations are present.

To analyze the correlations between economic variables, forecast outcomes, or test hypotheses, regression analysis is essential in economics. Demand and Supply Analysis, Macroeconomic Analysis, Labor Economics, Financial Econometrics, Economic Growth and Development, Econometric Modelling, and Policy Evaluation are a few examples of how regression analysis is used in economics.