Regression analysis

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 Regression analysis

  • Regression like , relation is a study of a relationship between variables 
  • Simple regulation : single explanatory variable 
  • Multiple regression : includes any  number of explanatory variables
  • Dependent  variables : The single variable being explained/ predicted by the regression model
  • Independent variable: Explanatory  variables used to predict the dependent variable
  • Residuals :Portions of dependent variables  is not explained by the model
  • Correlation  tests or closeness and direction of relationship between the two phenomena . Regression  gives the nature and extent of this  relation, so that prediction  can be made about dependent variable, for any value of independent variable.
  • Clearly designates one  variable as cause and the other effect , unlike the correlation
  • Linear regression :straight line relationship, Y=mx+c
  •  In least square method of regulation ‘m’ and ‘b’ are calculated by equating the differencal of Loss Function (Yi-Pi) to zero
  • Formula:-

Y_i=f(X_i, \beta)+e_i
Y_i= dependent variable
f= function
X_i= independent variable
\beta= unknown parameters
e_i= error terms


  • Non linear regression : implies third relationships. e.g Logarithmic relationships
  • Cofficient of determination(R^2) : Sum of sq explained by a regression /total number sum of Squares. It lies between 0 and 1 .if R^2=1 it means 100% of variation in Y is explained by variation in X
Graph :-






Application:-

  • Spectrophotometry and similarother and analytical techniques
  • Used to model real life situation for which outcomes is  uncertain. Modelling the appropriate probability distribution can help to make predictions and inferences.
  • Probability of an event varies between 0 and 1 

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