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Simple Linear Regression

 Simple Linear Regression

 

Simple linear regression is used to find out the best relationship between a single input variable (predictor, independent variable, input feature, input parameter) & output variable (predicted, dependent variable, output feature, output parameter) provided that both variables are continuous in nature. This relationship represents how an input variable is related to the output variable and how it is represented by a straight line.


After looking at scatter plot we can understand:

  1. The direction
  2. The strength
  3. The linearity

The above characteristics are between variable Y and variable X. The above scatter plot shows us that variable Y and variable X possess a strong positive linear relationship. Hence, we can project a straight line which can define the data in the most accurate way possible.

If the relationship between variable X and variable Y is strong and linear, then we conclude that particular independent variable X is the effective input variable to predict dependent variable Y.

To check the collinearity between variable X and variable Y, we have correlation coefficient (r), which will give you numerical value of correlation between two variables. You can have strong, moderate or weak correlation between two variables. Higher the value of “r”, higher the preference given for particular input variable X for predicting output variable Y. Few properties of “r” are listed as follows:

  1. Range of r: -1 to +1
  2. Perfect positive relationship: +1
  3. Perfect negative relationship: -1
  4. No Linear relationship: 0
  5. Strong correlation: r > 0.85 (depends on business scenario)

Command used for calculation “r” in RStudio is:

> cor(X, Y)

where, X: independent variable & Y: dependent variable Now, if the result of the above command is greater than 0.85 then choose simple linear regression.

If r < 0.85 then use transformation of data to increase the value of “r” and then build a simple linear regression model on transformed data.

Steps to Implement Simple Linear Regression:

  1. Analyze data (analyze scatter plot for linearity)
  2. Get sample data for model building
  3. Then design a model that explains the data
  4. And use the same developed model on the whole population to make predictions.

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