Regression Analysis

A regression analysis is the process of identifying and analyzing the relationship among variables. It can help you understand the characteristic value of the dependent variable changes, if any one of the independent variables is varied. This means one variable is dependent on another, but it is not vice versa. It is generally used for prediction and forecasting.

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Regression takes a group of random variables, thought to be predicting Y, and tries to find a mathematical relationship between them. This relationship is typically in the form of a straight line (linear regression) that best approximates all the individual data points. In multiple regression, the separate variables are differentiated by using subscripts.

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The two basic types of regression are simple linear regression and multiple linear regression, although there are non-linear regression methods for more complicated data and analysis. Simple linear regression uses one independent variable to explain or predict the outcome of the dependent variable Y, while multiple linear regression uses two or more independent variables to predict the outcome.

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• Simple linear regression: Y = a + bX + u

• Multiple linear regression: Y = a + b1X1 + b2X2 + b3X3 + … + btXt + u

Where:

• 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.

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 Scatterplot of cricket chirps in relation to outdoor temperature