Multiple Regression analysis

What is multiple regression analysis?

Multiple regression analysis is one of the regression models that is available for the individuals to analyze the data and predict appropriate ideas. To actually define multiple regression, is an analysis process where it is a powerful technique or a process that is used to predict the unknown value of a variable out of the recognized value of the available variables. Usually, the known variables are classified as predictors.

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To represent the same aspect of the multiple regression analysis in a form of an equation then it will be as follows:

The multiple regression analysis helps an individual to predict the value of the “Y” parameters for the given predictors, i.e. X1, X2, X3. Etc

The above parameters are compared to a real-time scenario and defining what multiple regression is all about,

For example: 

The yield of rice/acre depends on the following aspects or factors, they are listed below:

  • 1. Quality of the soil
  • 2. Quality of the fertilizers used
  • 3. Amount of water available during the harvest
  • 4. Temperature variations
  • 5. Adequate rainfall during the production

Out of this example,

Y parameter is –“the yield of rice/acre depends on”

The x parameters are the options that are stated above (Quality of soil, Quality of fertilizers, rainfall, etc.)

what is the advantage of multiple regression?

The advantage of multiple regression with this technique is that it gives an opportunity for the individual to study the pattern of these factors and finally able to understand and study the influence of each and every variable which incorporates the yield.

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Dependent and Independent variables in multiple regression analysis:

Let us understand how the dependent is and independent variables come into consideration when we are analyzing multiple regression models. So within the multiple regression modes, we will be having one independent variable and a dependent variable.

An independent variable is nothing but their values are used for prediction in the analysis.

A dependent variable is nothing but where the values are needed to be predicted within the analysis.

Now let’s talk about Multiple Regression models:

In practice, the equation will be similar to that of:

Y = b0 + b1 X1 + b2 X2 + …………………… + bk Xk

Where it goes for exponential values if they are considered.

Out of the above equation

Bo is the intercept of b1, b2, b3, etc. till bk which is nothing but analogous to the slope of linear regression.

The values of the multiple regression models can be appropriately tested as a whole by going through the F-test process in the ANOVA table.

Out of which F indicates the linear relationship between the Y and the X (one of the Xs)

How good is the multiple regression?

Well, to determine this we need to build multiple regression equations.

Once the regression equation is constructed then an individual can evaluate how good the prediction can be. This can be achieved by closely monitoring the coefficient of determination parameters, which is R2.

The value of R2 always lies between o and 1.

No matter whenever the regression is executed, the value of R2 is always close to 1. The better the value is the better the prediction will be.

Further, to answer the question of whether how far the independent variables individually influence the dependent variables significantly is the main point. For us to determine this we need to go through another test, which is the t-test.

Multiple Regression analysis assumptions:

1. Within the multiple regression techniques, it will not check or test whether the data is linear or not.

2. It is basically built out of the pre-defined assumption that the relation between Y and each of the X’s is linear.

3. If the graph is not linear at any point of the time then the individual has to work for attaining linearity.

4. Within multiple regression analysis, it includes homoscedasticity and normality concepts

5. The multiple regression analysis is used only when one needs to continually predict the dependent variable.

6. If in case the multiple regression models are not appropriate then one has to use a logistic regression model.


So we have understood about multiple regression models and how it actually uses the concept of dependent variables and independent variables within their analysis is worth reading. If you have any important points that you think will help other readers, then please suggest your advice in the comment section below.

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Last updated: 03 Apr 2023
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