Assumptions of Linear Regression- Homoscedasticity

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Another assumption of linear regression is ‘Homoscedasticity’. In a linear model the variation in the value of dependent variable ‘y’ is calculated by the Error term- which should be identically and independently distributed.

It means that the variation in the value of the dependent variable ‘y’ (i.e. error term) should be constant for all values of the independent variables ‘X’. This is checked by plotting the value of ‘y’ against the predicted probability calculated using the independent variables.

Example: the variation in expenditure is same with the increase in income.

The opposite of Homoscedasticity is’ Hetroscedasticity’ which means that the variation in the value of ‘y’ (i.e. error term) is not constant against the values of the independent variables ‘x’, which makes the independent variables inefficient and they are no longer Best Linear Unbiased Estimator(BLUE)

Example: The variation in expenditure is not same with the increase in income.

Income Expenditure Absolute Variation Relative Variation Log Variation
100 80
100 70 -10 -13% 0.13
100 85 5 6% -0.06
1000 800
1000 700 -100 -13% 0.13
1000 850 50 6% -0.06

Log Transformation tends to keep the variation the dependent variable ‘y’ constant.

Homo1

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