SOLUTION: In a multiple regression model y' = - 10 + 2x1 + 19x2 + 14x3 + 2x4, if the x1 value changes by 2, then the predicted value for y will change by

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Question 1202914: In a multiple regression model y' = - 10 + 2x1 + 19x2 + 14x3 + 2x4, if the x1 value changes by 2, then the predicted value for y will change by

Found 3 solutions by MathLover1, ikleyn, math_tutor2020:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!

' =

if the value changes by , we will have

' =

' =

' =

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

So ' is changing by when changes by

Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website!
.
In a multiple regression model y' = - 10 + 2x1 + 19x2 + 14x3 + 2x4, if
the x1 value changes by 2, then the predicted value for y will change by
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As I read your post, I do not see variable y in it, at all.

What I see in it, is variable y', instead.

So, in my view, the problem's formulation is INCORRECT and MUST be EDITED.

Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

The x1 variable is attached to the coefficient 2, as indicated by the notation 2x1 aka
The subscript 1 is to give x a different name so to speak. It's to help distinguish it from the other variables x2, x3, and x4 (aka , , and )

If x1 increases by 2, then we replace x1 with x1+2
Therefore 2x1 becomes 2(x1+2) = 2x1+4
It shows that the entire expression increases by 4.
We don't have to worry about the other input variables since we're only changing x1.