eBay Interview Question | Linear Regression

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What are the assumptions required for linear regression? What if some of these assumptions are violated?

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Dhruv2301 55 years 1 Answer 1210 views Great Grand Master 0

Answer ( 1 )

  1. Yash Bagaria
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    There are 5 assumptions of Linear Regression:
    Assumptions:
    1.Auto Correlation:No Auto-Correlation should exist in the residue)
    Test to check the following is the Durbin Watson Score which we get from OLS table.
    If Durbin-Watson==2 then we can say that No Autocorrelation Exist
    If Durbin-Watson>2 then we can say that Postitve Correlation
    If Durbin-Watson<2 then we can say that Negative Correlation
    2.Linearity Test: To check whether the model is linear or not.
    To this we can do Rainbow Test.In the Rainbow Test we take Null Hypothesis: Data is Linear and Alternate Hypothesis as Data is not Linear.
    3.Normality Test:Test to see if the residues are normally distributed or not?
    To test this we use the Jarque-Berra(JB) constant. Over here,
    Null Hypothesis: Residues follow normal distribution
    Alternate Hypothesis: Residues do not follow normal distribution
    4. Multicollinearity: If the Vif(Variance Inflation Factor)=1 then there is no multicollinearity
    5. Homosedasticity: Residues are uniform across all the values of x. For lower values of x we have large residuals and vice -versa.
    We can perform Goldfeld-Quandt Test.
    Null Hypothesis: Residuals sum square is constant across all values of x
    Alternate Hypothesis: Residuals sum square is not constant across all values of x .

    Whenever we violate any of the above linear regression assumptions, the regression coefficient produced by OLS(Ordinary Least Squares Method) will be either biased or the variance of the estimate will be increased.

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