13.3 Exercise 9

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?

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