It is a statistical method used in data analysis to explore the relationship between a dependent variable and two or more independent variables. It extends the simple linear regression model, which involves predicting a dependent variable based on a single independent variable, to handle situations where multiple factors may influence the outcome.
The multiple regression model aims to estimate the values of the coefficients
that minimizes the sum of squared differences between the observed values of Y and the values predicted by the model. This process is typically done using statistical techniques such as the method of least squares.
Key concepts in multiple regression include:
a) R-squared(R^2): A measure of how well the independent variables explain the variability in the dependent variable. It ranges from 0 to 1, with higher values indicating a better fit.
b) Coefficients and P-values: Coefficients represent the strength and direction of the relationship between each independent variable and the dependent variable. P-values help assess the statistical significance of these relationships.
c) Multicollinearity: The presence of high correlations among independent variables, which can complicate the interpretation of individual coefficients.
d) Adjusted R-squared(R^2): A modified version of R-squared that adjusts for the number of independent variables, providing a more reliable measure of the model's goodness of fit.
Multiple Regression is a type of linear regression that is used mainly when we have more than one independent variable that is used to predict the dependent variables. It is used in economics,social sciences, and natural sciences.