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Assumptions underlying linear regression

  • The underlying relationship between the X variable and the Y variable is linear
  • For a given value of Xi the sum of error terms is equal to 0
  • The error term is uncorrelated with the explanatory variable X
  • Error values are normally distributed for any given value of X
  • The probability distribution of the errors for a given Xi is normal
  • The probability distribution of the errors for different Xi has constant variance (homoscedacity)
  • Error values u for given Xi are statistically independent, their covariance is zero


Once we fulfill these assumptions in Linear Regression , we are able to estimate the variance and standard errors of b0 and b1 and this has been possible because of the properties of OLS method.


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