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# 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

Accepted Solution

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Answer:A. Increase by 2Step-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 x4The 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 unitsSince slope of x1 is 5, we find for one unit change in x1 we can have 5 units change in yi.e. for 2 units change in x1, we expect 10 units change in YSimilarly for 2 units change in x2, we expect -2(4) units change in YPut together we have$$10-8 =2$$ change in ySince positive 2, there is an increase by 2A. Increase by 2