# 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.