Linear Equations · Exercise 3

We are interested in finding the linear relation between the number of widgets purchased at one time and the cost per widget. The following data has been obtained:
X: Number of widgets purchased – 1, 3, 6, 10, 15
Y: Cost per widget(in dollars) – 55, 52, 46, 32, 25
Suppose the regression line is \overset{^}{y} = -2.5 x + 60. We compute the average price per widget if 30 are purchased and observe which of the following?

(a) \overset{^}{y} = 15 \text{dollars}; obviously, we are mistaken; the prediction \overset{^}{y} is actually +15 dollars.
(b) \overset{^}{y} = 15 \text{dollars}, which seems reasonable judging by the data.
(c) \overset{^}{y} = -15 \text{dollars}, which is obvious nonsense. The regression line must be incorrect.
(d) \overset{^}{y} = -15 \text{dollars}, which is obvious nonsense. This reminds us that predicting Y outside the range of X values in our data is a very poor practice.

OpenStax, Introductory Business Statistics 2e · §13.3 Linear Equations · Exercise 3