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Residual Plot in Regression: Homoskedasticity v. Heteroskedasticity

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Question 1
What pattern(s) would one like to see in a residual plot and why?
Question 2
a) State in algebraic notation and explain the assumption about the CLRM's disturbances that is referred to by the term homoscedasticity
b) What would the consequence be for a regression model if the errors were not homoscedastic?
c)How might you proceed if you found that (b) was actually the case?

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Solution Summary

Implication of homoskedasticity, consequence of heteroskedasticity and remedy are discussed in the solution.

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Question 1
What pattern(s) would one like to see in a residual plot and why?
Answer: An ideal residuals plot would be showing a constant variance for the error term u, i.e. homoskedasticity (Var(u) = s2).
With the constant variance of the error term, each probability distribution for y (dependent variable) has the same standard deviation regardless of the x-value (independent variables).
This is important as one of the assumptions of the Classical Linear Regression Model (CLRM) that the error term has a constant variance (homoscedastic error). No heteroscedasticity.

Question 2
a) State in ...

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