Multiple linear regression is a statistical method used to model the relationship between two or more independent variables (also known as predictors) and a dependent variable. It is called "multiple" because it involves more than one independent variable.
The main goal of multiple linear regression is to find the best linear relationship between the independent and dependent variables by estimating the regression coefficients' values. The regression coefficients represent the change in the dependent variable for a unit change in the independent variable while holding all other independent variables constant.
Multiple linear regression can be used for forecasting by using the estimated regression equation to predict the dependent variable's values based on the independent variables' values. For example, if you want to forecast sales revenue based on advertising expenditure, price, and consumer income, you can use multiple linear regression to estimate the regression equation that best fits the data and then use that equation to predict sales revenue for different values of advertising expenditure, price, and consumer income.
However, it is important to note that multiple linear regression assumes that the relationship between the independent variables and the dependent variable is linear and that the independent variables are not highly correlated with each other (i.e., they are independent). If these assumptions are violated, the regression analysis results may not be reliable, and other methods may need to be used instead.
Multiple Linear Regression Elements
Multiple linear regression has several components that are important to understand. These components are:
Dependent variable: This is the variable that you want to predict or explain. It is also known as the response variable.
Independent variables: These are the variables that you use to predict or explain the dependent variable. They are also known as the predictor variables or regressors.
Regression equation: This is the equation that describes the relationship between the dependent variable and the independent variables. It takes the form of y = β0 + β1x1 + β2x2 + ... + βnxn, where y is the dependent variable, x1, x2, ..., xn are the independent variables, and β0, β1, β2, ..., βn are the regression coefficients.
Residuals: These are the differences between the predicted values of the dependent variable and the actual values of the dependent variable. They are also known as errors.
Regression coefficients: These are the coefficients that measure the strength and direction of the relationship between the dependent variable and each independent variable. They represent the change in the dependent variable for a one-unit increase in the corresponding independent variable, while holding all other independent variables constant.
R-squared: This is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variables. It ranges from 0 to 1, where 0 means that none of the variance is explained by the independent variables, and 1 means that all of the variance is explained by the independent variables.
Standard error of estimate: This is a measure of the accuracy of the regression equation in predicting the dependent variable. It represents the average difference between the predicted values of the dependent variable and the actual values of the dependent variable.
All of these components are used to build a multiple linear regression model and to analyze the relationship between the dependent variable and the independent variables.
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