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Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
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    Including highly correlated predictor variables in multiple regression models is often discouraged. However, this approach is justifiable when theoretical or empirical evidence supports their inclusion, especially with squared variables.

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    Area of Science:

    • Statistics
    • Econometrics
    • Social Sciences

    Background:

    • Multiple regression analysis commonly excludes highly correlated predictor variables.
    • The exclusion is based on the argument that these variables account for redundant variance.

    Purpose of the Study:

    • This study defends the inclusion of highly correlated predictor variables in specific circumstances.
    • It focuses on the use of squared elements of original variables as predictors.

    Main Methods:

    • The study discusses scenarios where including correlated predictors is appropriate.
    • It examines the justification based on group membership vectors and theoretical/empirical support.

    Main Results:

    • The inclusion of highly correlated variables is defended under specific conditions.
    • Theoretical or empirical justification is a key factor for their inclusion.

    Conclusions:

    • The practice of including highly correlated predictor variables, particularly squared terms, can be statistically valid.
    • Researchers should consider theoretical and empirical justifications when deciding on variable inclusion in regression models.