Lecture_20Video_20W11D1_20-_20Multicollinearity

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15 Terms

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Multicollinearity

Occurs when two or more predictors in a regression model are highly correlated, leading to redundancy in information.

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Assumption of Independent Predictors

In multiple linear regression, it's assumed that all predictors are independent of one another, not linearly related.

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Perfect Correlation

A condition where two predictors have a correlation of either 1 or -1, making the matrix non-invertible.

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Variance Inflation Factor (VIF)

A measure used to quantify the severity of multicollinearity in an ordinary least squares regression analysis.

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Effects of Multicollinearity

Reduces the stability of coefficient estimates and can make predictions less reliable.

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Redundancy in Predictors

When two predictors provide similar information, making it unnecessary to include both in the model.

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Standard Errors in Regression

The measure of the statistical accuracy of a coefficient estimate; inflated standard errors indicate multicollinearity issues.

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Consequences of High VIF

Indicates that the estimated coefficients are likely to be unreliable due to multicollinearity.

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Dealing with Multicollinearity

Strategies include dropping a highly correlated predictor or combining correlated predictors into one variable.

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Impact of Observational Data on Multicollinearity

In observational studies, perfect independence among predictors is rare, leading to some level of multicollinearity.

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Confounding

A situation in which a third variable influences both the dependent variable and independent variables, skewing results.

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Bias Variance Trade-Off

A principle stating that reducing one type of error may increase the other, especially relevant in the context of multicollinearity.

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Highly Correlated Predictors

Predictors that have a strong linear relationship, often causing redundancy in regression models.

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P-Values in Regression

Indicate the statistical significance of predictors in the presence of other variables; tight correlations may lead to nonsignificant p-values.

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Effects of Adding Predictors

In models with multicollinearity, adding predictors may not lead to significant increases in explained variability.