Statistics

Suppose a data set has a linear regression line of y = 6 -0.8x. If the mean of the x's is 5, what is the mean of the y's?


2

5

10

6

None of the above

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  1. The mean of the y's = 2

    Use this equation:
    predicted y = (rSy/Sx)X - (rSy/Sx)xbar + ybar
    ...where r = correlation, Sy = sd of y, Sx = sd of x, and X is the variable in 'a + bx' equation.
    Note: xbar = mean of x; ybar = mean of y.

    Substituting what is known:
    predicted y = (-0.8)X - (-0.8)5 + ybar
    predicted y = (-0.8)X - (-4) + ybar
    predicted y = (-0.8)X + 4 + ybar
    predicted y = (-0.8)X + 4 + 2
    predicted y = (-0.8)X + 6

    Therefore: ybar = 2

    I hope this helps.

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