Question

A farmer is having problems with birds eating her crops. She tries putting up different numbers of scarecrows to keep the birds away. The average number of crops eaten is 200, and the average number of scarecrows she has put up is 20.

The farmer finds some of the linear regression equation:
number of crops eaten = a - 0.8*(number of scarecrows).
What is the value of the intercept?

Answer 1

The value of the intercept is a=216.

Explanation:

We define "s" as the number of scarecrows and "C" the number of crops eaten.

The farmer finds the linear regression equation:

`C=a-0.8s`

We have a linear function, for which we only know the slope (m=0.8) and a point within it (when s=20, C=200).

We can find a replacing the variables C asn s with the known point (20, 200):

`C=a-0.8s\\\\C(20)=a-0.8(20)=200\\\\a=200+0.8*20=200+16\\\\a=216`

The value of the intercept is a=216.