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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 byQuestion 5 options: 10 42 –1 29

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 byQuestion 5 options 10 42 1 29 class=

Respuesta :

Given:

y' = –11 + 5x1 + 21x2 + 11x3 + 3x4

y' = –11 + 5x1 + 21x2 + 11x3 + 3x4 (we are to focus on the x1 term)

y' = –11 + 5(x1) + 21x2 + 11x3 + 3x4 (let's surround the x1 in parenthesis)

y' = –11 + 5(x1+2) + 21x2 + 11x3 + 3x4 ( let's replace x1 by 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 + 5*2

We can see that we have gotten a new y' value from what we did above.

Note how we simply add 10 to the old y' value to get the new y' value.

Therefore, y' is changing by 10 when x1 changes by 2

So, the correct option is the first option which is 10.

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