A multiple regression results in the fitted equation y= 4 + 1:5x 1 - 1x 2 + 2x 1 x 2 ; where x 1 ranges from 0 to 2 and x 2 ranges from 21 to 1. (a) Plot the fitted regression equation of y versus x1...

A multiple regression results in the fitted equation

y= 4 + 1:5x₁
- 1x₂
+ 2x₁x₂;

where x₁
ranges from 0 to 2 and x₂
ranges from 21 to 1.

(a) Plot the fitted regression equation of y versus x1 using a low value of x₂
and a high value of x₂.

(b) In simple language, describe the relationship between y and x1.

(c) Can you interpret β^ 1 5 1:5 as being the expected change in y if x1 increases by 1? Why or why not?

(d) Suppose the fitted equation had been y= 4 + 1:5x₁
- 1x₂
+ 0x₁x₂. Redraw the plot. How is the description of the relationship simplified?