Question

In the least-squares line ŷ = 5 + 6x, what is the marginal change in ŷ for each unit change in x?

a) 5
b) 6
c) 11
d) 30

Answer 1

The marginal change in the predicted value î for each unit change in x in the least-squares line î = 5 + 6x is 6.

Step-by-step explanation:

In the least-squares line î = 5 + 6x, the coefficient of x represents the slope of the line, which is also interpreted as the marginal change in the predicted value î for each unit change in x. Therefore, the marginal change in î for each unit change in x is 6. When x increases by 1 unit, î increases by 6 units. So the correct answer is b) 6.