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Multiple regression analysis: Definition, example and equation

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Multiple regression analysis: Definition, example and equation Regression Equation
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What is multiple regression?

As the name suggests, multiple regression is a statistical technique applied on datasets dedicated to draw out a relationship between one response or dependent variable and multiple independent variables. Form the definition it is obvious that the study of an event or phenomena will have various factors causing its occurrence. 

Multiple regression works by considering the values of the available multiple independent variables and predicting the value of one dependent variable. 

Example: A researcher decides to study students’ performance from a school over a period of time. He observed that as the lectures proceed to operate online, the performance of students started to decline as well. The parameters for the dependent variable “decrease in performance” are various independent variables like “lack of attention, more internet addiction, neglecting studies” and much more. 

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Why to use multiple regression analysis?

In case of linear regression, although it is used commonly, it is limited to just one independent and one dependent variable. Apart from that, linear regression restricts to the training dataset and does not predict a non-linear regression. 

For the same limitations and to cover them, we use multiple regression. It focuses on overcoming one particular limitation and that is allowing to analyse more than one independent variable. 

Multiple regression equation

We will start the discussion by first taking a look at linear regression equation:

y = bx + a

Where, 

y is a dependent variable we need to find, x is an independent variable. The constants a and b drives the equation. But according to our definition, as the multiple regression takes several independent variables (x), so for the equation we will have multiple x values too:

y = b1x1 + b2x2 + … bnxn + a

Here, to calculate the value of the dependent variable y, we have multiple independent variables x1, x2, and so on. The number of independent variables can grow till n and the constant b with every variable denotes its numeric value. The purpose of the constant a is to denote the dependent variable’s value in case when all the independent variable values turn to zero. 

Example: So for above example, the multiple regression equation would be:

y = b1 * attention + b2 * internet addiction + b3 * technology support + … bnxn + a

[Related read: Regression Analysis]

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Assumptions for multiple regression analysis

  • The variables considered for the model should be relevant and the model should be reliable.
  • The model should be linear and not non-linear. 
  • Variables must have normal distribution
  • The variance should be constant for all levels of the predicted variable.

Benefits of multiple regression analysis

  • Multiple regression analysis helps us to better study the various predictor variables at hand. 
  • It increases reliability by avoiding dependency on just one variable and have more than one independent variable to support the event. 
  • Multiple regression analysis permits you to study more formulated hypotheses that are possible. 

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