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    Question

    In a regression analysis, if the total sum of squares

    (SST) is 250 and the explained sum of squares (SSR) is 200, the coefficient of determination (RĀ²) is:
    A 0.80 Correct Answer Incorrect Answer
    B 1.25 Correct Answer Incorrect Answer
    C 0.20 Correct Answer Incorrect Answer
    D 0.25 Correct Answer Incorrect Answer
    E 0.50 Correct Answer Incorrect Answer

    Solution

    • TheĀ  Coefficient of Determination (RĀ²) Ā measures the proportion of the total variation in the dependent variable (Y) that is explained by the independent variable(s) (X) in the regression model.
      Formula: RĀ² = SSR / SST
      Where:
      • SSR (Explained Sum of Squares) = Variation explained by the model.
      • SST (Total Sum of Squares) = Total variation in Y.
        Given: SSR = 200, SST = 250.
        RĀ² = 200 / 250 =Ā  0.80 or 80% .
        This means 80% of the variation in Y is explained by X in the model.

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