SOLUTION: In a multiple regression model y' = –11 + 5x1 + 21x2 + 11x3 + 3x4, if the x1 value changes by 2, then the predicted value for y will change by
10
42
–1
29
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Question 1088261: In a multiple regression model y' = –11 + 5x1 + 21x2 + 11x3 + 3x4, if the x1 value changes by 2, then the predicted value for y will change by
10
42
–1
29
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
y' = –11 + 5x1 + 21x2 + 11x3 + 3x4
y' = –11 + 5x1 + 21x2 + 11x3 + 3x4 ... focus on the x1 term
y' = –11 + 5(x1) + 21x2 + 11x3 + 3x4 ... surround the x1 in parenthesis
y' = –11 + 5(x1+2) + 21x2 + 11x3 + 3x4 ... Replace x1 with x1+2 (to indicate a change by 2)
y' = –11 + 5(x1+2) + 21x2 + 11x3 + 3x4
y' = –11 + 5x1+5*2 + 21x2 + 11x3 + 3x4
y' = –11 + 5x1 + 21x2 + 11x3 + 3x4 + 5*2
y' = –11 + 5x1 + 21x2 + 11x3 + 3x4 + 10
y' = –11 + 5x1 + 21x2 + 11x3 + 3x4 + 10
The portion in blue of the equation above represents the old y' value before x1 changed to x1+2.
Note how we simply add 10 this old y' value to get the new y' value.
So y' is changing by 10 when x1 changes by 2
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Answer: Choice A) 10
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