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How would heteroskedasticity impact the results of regression?
Heteroscedasticity tends to produce p-values that are smaller than they should be. This effect occurs because heteroscedasticity increases the variance of the coefficient estimates but the OLS procedure does not detect this increase.
What are the consequences of using least squares when heteroskedasticity is present?
In the presence of heteroskedasticity, there are two main consequences on the least squares estimators: The least squares estimator is still a linear and unbiased estimator, but it is no longer best. That is, there is another estimator with a smaller variance.
What problems does heteroskedasticity cause?
Heteroskedasticity has serious consequences for the OLS estimator. Although the OLS estimator remains unbiased, the estimated SE is wrong. Because of this, confidence intervals and hypotheses tests cannot be relied on. In addition, the OLS estimator is no longer BLUE.
What causes the OLS estimator to be biased?
This is often called the problem of excluding a relevant variable or under-specifying the model. This problem generally causes the OLS estimators to be biased. Deriving the bias caused by omitting an important variable is an example of misspecification analysis.
What makes OLS unbiased?
In order to prove that OLS in matrix form is unbiased, we want to show that the expected value of ˆβ is equal to the population coefficient of β. First, we must find what ˆβ is. Then if we want to derive OLS we must find the beta value that minimizes the squared residuals (e).
Is there no heteroscedasticity in linear regression?
As mentioned above that one of the assumption (assumption number 2) of linear regression is that there is no heteroscedasticity. Breaking this assumption means that OLS (Ordinary Least Square) estimators are not the Best Linear Unbiased Estimator (BLUE) and their variance is not the lowest of all other unbiased estimators.
Why does heteroscedasticity occur in a mathematical model?
While there are numerous reasons why heteroscedasticity can exist, a common explanation is that the error variance changes proportionally with a factor. This factor might be a variable in the model.
How is heteroscedasticity related to crop yield loss?
It is nevertheless very common to see nonlinear regressions fit through these kind of data and then see subsequent model and/or data set comparison. Here is an imaginary example where weed biomass influences crop yield loss. Issues of heteroscedasticity. The uncertainty is clearly and regularly related to the predictor value.
Why is heteroscedasticity less variable in lower income households?
Lower income households are less variable in absolute terms because they need to focus on necessities and there is less room for different spending habits. Higher income households can purchase a wide variety of luxury items, or not, which results in a broader spread of spending habits. You can categorize heteroscedasticity into two general types.