Multiple linear regression

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 MULTIPLE LINEAR REGRESSION

 

INTRODUCTION:

  • It is used to estimate the relationship between two or more independent variables and one dependent variable. The independent variables can be continuous ( or) categorical ( dummy coded as appropriate).
  • You can use MULTIPLE LINEAR REGRESSION ;
  • how strong the relationship is between two ( or) more  independent variables and one dependent variable 
  • the value of dependent variable at certain value of the independent variables .


ASSUMPTIONS:

  • It is also same assumptions as simple linear regression
  • Homoscedasticity : the size of the error in our prediction doesn’t change significantly across the values of independent variable.
  • Independence of observations : the observations in the dataset were collected using statistically valid methods and there are no hidden relationship among variables.
  • In multiple LINEAR REGRESSION, it is possible that some of the independent variable are actually correlated with one another , so it is important to check these before developing the regression model. if two independent variables are too high correlated ( r2> ~0.6) , then only one of them should be used in the regression model.

GOODNESS OF FIT:

  • To find the goodness of fit for each independent variable, MLR calculates three things :
  • the regression coefficients that  lead to the smallest overall model errors.
  • the  t – statistic of the overall model.
  • the  associated p value.
  • It then , calculates the  t – statistic and p value for each regression coefficients in the model . 


ADVANTAGES:

  • By far the most common approach for modelling numeric data
  • Can be adapted to model almost any modeling disk
  • Provides estimates of both the strength and size of the relationship among features and outcome.


DISADVANTAGES:

  • Makes strong assumptions about the data
  • The model ‘s form must be specified by the user in advance 
  • Does not handle missing data 
  • Only works with numeric features, so categorical data requires extra processing.
  • Requires some knowledge of statistics to understand the model.


FORMULAS:




EXAMPLES:


  • Manual calculation sum of MLR






MLR USES:

  • It can be used when one has two continuous variables an independent variable and dependent variable.
  • Independent variable is the parameter that is used to calculate the dependent variable or outcome.

More tests:





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