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Multivariate regression: Definition, Example and steps Survey

Multivariate regression: Definition, Example and steps

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What is multivariate regression?

Most of the statistically analysed data does not necessarily have one response variable and one explanatory variable. In most cases, the number of variables can vary depending on the study. To measure the relationships between these multidimensional variables, multivariate regression is used.

Multivariate regression is a technique used to measure the degree to which the various independent variable and various dependent variables are linearly related to each other. The relation is said to be linear due to the correlation between the variables. Once the multivariate regression is applied to the dataset, this method is then used to predict the behaviour of the response variable based on its corresponding predictor variables. 

Multivariate regression is commonly used as a supervised algorithm in machine learning, a model to predict the behaviour of dependent variables and multiple independent variables.

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Characteristics of multivariate regression

  • Multivariate regression allows one to have a different view of the relationship between various variables from all the possible angles. 
  • It helps you to predict the behaviour of the response variables depending on how the predictor variables move.
  • Multivariate regression can be applied to various machine learning fields, economic, science and medical research studies.
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Example of multivariate regression

An agriculture expert decides to study the crops that were ruined in a certain region. He collects the data about recent climatic changes, water supply, irrigation methods, pesticide usage, etc. To understand why the crops are turning black, do not yield any fruits and dry out soon. 

In the above example, the expert decides to collect the mentioned data, which act as the independent variables. These variables will affect the dependent variables which are nothing but the conditions of the crops. In such a case, using single regression would be a bad choice and multivariate regression might just do the trick. 

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Steps to achieve multivariate regression

Step 1: Select the features 

First, you need to select that one feature that drives the multivariate regression. This is the feature that is highly responsible for the change in your dependent variable. 

Step 2: Normalize the feature

Now that we have our selected features, it is time to scale them in a certain range (preferably 0-1) so that analysing them gets a bit easy. 

To change the value of each feature, we can use:

Step 3: Select loss function and formulate a hypothesis

A formulated hypothesis is nothing but a predicted value of the response variable and is denoted by h(x). 

A loss function is a calculated loss when the hypothesis predicts a wrong value. A cost function is a cost handled for those wrongly predicting hypotheses.  

Step 4: Minimize the cost and loss function 

Both cost function and loss function are dependent on each other. Hence, in order to minimize both of them, minimization algorithms can be run over the datasets. These algorithms then adjust the parameters of the hypothesis.

One of the minimization algorithms that can be used is the gradient descent algorithm.

Step 5: Test the hypothesis

The formulated hypothesis is then tested with a test set to check its accuracy and correctness.

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Advantages and disadvantages of multivariate regression

Advantages: 

  • The multivariate regression method helps you find a relationship between multiple variables or features. 
  • It also defines the correlation between independent variables and dependent variables. 

Disadvantages: 

  • Multivariate regression technique requires high-level mathematical calculations.
  • It is complex. 
  • The output of the multivariate regression model is difficult to analyse.
  • The loss can use errors in the output.
  • Multivariate regression yields better results when used with larger datasets rather than small ones. 

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