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    Question

    In a simple linear regression model, Y = a + bX + e, the

    coefficient 'b' represents:
    A The value of Y when X is zero. Correct Answer Incorrect Answer
    B The change in Y for a one-unit change in X, holding other factors constant. Correct Answer Incorrect Answer
    C The error term. Correct Answer Incorrect Answer
    D The standard deviation of X. Correct Answer Incorrect Answer
    E The correlation between X and Y. Correct Answer Incorrect Answer

    Solution

    • In the regression equation Y = a + bX + e:
      • 'a' is the intercept -- the  expected value of Y when X is 0  (option a describes 'a').
      • 'b' is the  slope coefficient . It quantifies the marginal effect: for a  one-unit increase in the independent variable X, the dependent variable Y is expected to change by 'b' units, on average, ceteris paribus (all else held constant) .
      • 'e' is the error term (option c).
        Standard deviation and correlation are measures of dispersion and association, not regression coefficients (options d & e).

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