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When there exists very high correlation among independent variables in a multiple linear regression model, it is said to suffer from the problem of:
Question



When there exists very high correlation among independent variables in a multiple linear regression model, it is said to suffer from the problem of:

A.

Autocorrelation

B.

Multicollinearity

C.

Homoscedasticity

D.

Heteroscedasticity

Correct option is B


Multicollinearity:
· Multicollinearity occurs when two or more independent variables in a regression model are highly correlated.
· This high correlation makes it difficult to determine the individual effect of each independent variable on the dependent variable.
· It leads to unstable coefficient estimates and increases the standard errors of the coefficients, reducing the reliability of hypothesis tests.
Other Terms in the Options:
· (a) Autocorrelation: Refers to correlation between residuals (errors) of a regression model, often occurring in time-series data.
· (c) Homoscedasticity: Refers to the condition where the variance of residuals is constant across all levels of the independent variable(s).
· (d) Heteroscedasticity: The opposite of homoscedasticity; it occurs when the variance of residuals changes across different levels of the independent variable(s).
Impact of Multicollinearity in Regression Models:
· Results in inflated variance inflation factors (VIFs).
· Makes regression coefficients unreliable and challenging to interpret.
Information Booster: 1. Multicollinearity affects the predictive accuracy and interpretability of regression models.
2. Detection:
· Variance Inflation Factor (VIF): A VIF > 10 indicates high multicollinearity.
· Correlation Matrix: Shows high correlation between independent variables.
3. Solutions:
· Remove highly correlated variables.
· Use principal component analysis (PCA) to combine correlated variables.
· Regularization techniques like Ridge or Lasso regression.

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