Regression analysis is a form of inferential statistics. It is a measure of the relation between the mean* value of one variable (e.g. output) and corresponding values of other variables (e.g. time and cost). Regression model can help predict sales for a company based on weather, previous sales, GDP growth or other types of conditions. It also helps professionals of business and finance and investment in the similar manner. In finance, the capital asset pricing model (CAPM) is an often-used regression model for pricing assets and discovering costs of capital. For example, Beta is the stock’s risk in relation to the market or index and is reflected as the slope in the CAPM model. The expected return for the stock in question would be the dependent variable Y, while the independent variable X would be the market risk premium.
- ‘Mean’ is an arithmetic average. For example, weights of 4 boys are 45Kg, 55Kg, 60Kg and 60KG=220/4=55 Kg here mean is 55 Kg.
There are different types of regressions. Following are some of the key models of regression:
Linear Regression, Multiple Linear Regressions, Logistic Regression, Polynomial Regression, Stepwise Regression, Ridge Regression, Lasso Regression, Elastic Net Regression
The two basic types of regression are linear regression and multiple linear regression, the others are non-linear regression methods for more complicated data and analysis. Linear regression uses one independent variable to explain or predict the outcome of the dependent variable Y, while multiple regressions use two or more independent variables to predict the outcome.
The general form of linear type of regression is:
Linear Regression: Y = a + bX + u
The general form of Multiple Linear type of regression is:
Multiple Regression: Y = a + b1X1 + b2X2 + b3X3 + … + btXt + u
Y = the variable that you are trying to predict (dependent variable)
X = the variable that you are using to predict Y (independent variable)
a = the intercept
b = the slope
u = the regression residual
Suppose you have the following regression equation: y = 3X + 5. If you enter a value of 6 for the predictor, the fitted value is 23. Fitted values are also called predicted values.
In this equation, +3 is the coefficient*, X is the predictor, and +5 is the constant.
In linear regression, coefficients are the values that multiply the predictor values. The sign of each coefficient indicates the direction of the relationship between a predictor variable and the response variable.
A positive sign indicates that as the predictor variable increases, the response variable also increases.
A negative sign indicates that as the predictor variable increases, the response variable decreases.
Related article:What s the correlation coeeficient R?