A fitted multiple regression equation is Y = 28 + 5X1 – 4X2 + 7X3 + 2X4. When X1 increases 2 units and X2 increases 2 units as well, while X

Question

A fitted multiple regression equation is Y = 28 + 5X1 – 4X2 + 7X3 + 2X4. When X1 increases 2 units and X2 increases 2 units as well, while X3 and X4 remain unchanged, what change would you expect in your estimate of Y? A. Increase by 2
B. Decrease by 4
C. Increase by 4
D. No change in Y

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Nevaeh 2 weeks 2021-10-12T09:43:01+00:00 1 Answer 0

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    2021-10-12T09:44:29+00:00

    Answer:

    A. Increase by 2

    Step-by-step explanation:

    Given that a  fitted multiple regression equation is

    Y = 28 + 5X_1 -4X_2 + 7X_3 + 2X_4

    This is a multiple regression line with dependent variable y and independent variables x1, x2, x3 and x4

    The coefficients of independent variables represent the slope.

    In other words the coefficients represent the rate of change of y when xi is changed by 1 unit.

    Given that x3 and x4 remain unchanged and x1 increases by 2 and x2 by 2 units

    Since slope of x1 is 5, we find for one unit change in x1 we can have 5 units change in y

    i.e. for 2 units change in x1, we expect 10 units change in Y

    Similarly for 2 units change in x2, we expect -2(4) units change in Y

    Put together we have

    10-8 =2 change in y

    Since positive 2, there is an increase by 2

    A. Increase by 2

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27:3+15-4x7+3-1=? ( )