Question

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

Answer 1

In a multiple regression model, if x1 changes by 2, the predicted value for y will change by 10, based on the coefficient of x1 which is 5 (2*5=10).

Step-by-step explanation:

The question asks how the predicted value of y in a multiple regression model will change if the value of x1 changes by 2. The given regression equation is y' = –11 + 5x1 + 21x2 + 11x3 + 3x4. Since only x1 is changing and we know that its coefficient is 5, we can determine the change in y' by multiplying the change in x1 (which is 2) by its coefficient (which is 5).

Therefore, the change in y' is 10 (2*5=10).This inference is drawn from the coefficient of x being 5 in the regression equation, indicating a proportional impact on the predicted value for every unit change in x,

Answer 2

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.