Chapter 12: Q. AP4.29 (page 831)

Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data on weight (in pounds) and neck girth (the distance around the neck in inches) for 10 randomly selected bears. Here is some regression output for these data
A bear has recently captured whose neck girth was $35$ inches and whose weight was $466.35$ pounds. If this bear were added to the data set, what would be the effect on the value of s?
a. It would decrease the value of s because the added point is an outlier.
b. It would decrease the value of s because the added point lies on the least-squares regression line.
c. It would increase the value of s because the added point is an outlier.
d. It would increase the value of s because the added point lies on the least-squares regression line.
e. It would have no effect on the value of s because the added point lies on the least-squares regression line.

Short Answer

Expert verified

The correct option is (b) It would decrease the value of s because the added point lies on the least-squares regression line.

Step by step solution

Given information

The given data is

Explanation

Park rangers are curious about the weight of the bears that live in their area. The question specifies the output of this data. As a result, if we add the bear with a neck girth of $35$ inches and a weight of $466.35$ pounds to the scatterplot, the appropriate point will be added to the scatterplot's top right corner.

Furthermore, this plot will be on the least square regression line because it is an extension of the least square regression line. Also, because the added data has a perfect prediction, the standard error of the estimates will drop.

As a result, our forecasts are more precise, resulting in fewer variations and, as a result, a reduced standard error of prediction.

Option (b) is correct.