Born to be old? Is there a relationship between the gestational period (time from conception to birth) of an animal and its average life span? The figure shows a scatterplot of the gestational period and average life span for 43 species of animals.

(a) Describe the direction, form, and strength of the scatterplot.

(b) Three “unusual” points are labeled on the graph: Point A is for the hippopotamus, Point B is for the giraffe, and Point C is for the Asian elephant. In what way is each of these animals “unusual”?

Short Answer

Expert verified

Part (a) Direction: positive

Form: slightly curved

Strength: Moderately strong.

Part (b) Point A: unusual because of its high life span.

Point B: unusual because of the combination of a long gestation period and a low life span

Point C: unusual because of its high life span and its long gestation period

Step by step solution

01

Part (a) Step 1: Given information

02

Part (a) Step 2: Concept

A regression line is a straight line that depicts the change in a response variable y when an explanatory variable x changes. By putting this x into the equation of the line, you may use a regression line to predict the value of y for any value of x

03

Part (a) Step 3: Explanation

The general pattern moves from bottom left to higher right, as shown in the graph. That is, animals with a longer gestation time have a longer life expectancy. There is a strong link between the two variables. The relationship has a somewhat curved shape. Overall, there is a reasonably strong relationship: animals with similar gestation times have about similar life lengths.

Direction: positive

Form: slightly curved

Strength: moderately strong.

04

Part (b) Step 1: Explanation

The hippopotamus, giraffe, and Asian elephant are the three creatures that stand out in the scatterplot: point A for the hippopotamus, point B for the giraffe, and point C for the Asian elephant. These points are known as outliers because they deviate from the broader pattern.

Point A: unusual because of its high life span.

Point B: unusual because of the combination of a long gestation period and a low life span

Point C: unusual because of its high life span and its long gestation period

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Measurements

on young children in Mumbai, India, found this least-squares line for predicting height y from the arm span y=6.4+0.93xMeasurements are in centimeters (cm).

By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is

(a) greater than zero.

(b) less than zero.

(c) 0.93

(d) 6.4

(e) Can’t tell without seeing the data.

Merlins breeding Exercise 13 (page 160) gives data on the number of breeding pairs of merlins in an isolated area in each of nine years and the percent of males who returned the next year. The data show that the percent returning is lower after successful breeding seasons and that the relationship is roughly linear. The figure below shows the Minitab regression output for these data.

(a) What is the equation of the least-squares regression line for predicting the percent of males that

return from the number of breeding pairs? Use the equation to predict the percent of returning males after a season with 30 breeding pairs.

(b) What percent of the year-to-year variation in the percent of returning males is explained by the straight-line relationship with a number of breeding pairs the previous year?

(c) Use the information in the figure to find the correlation r between the percent of males that return and the number of breeding pairs. How do you know whether the sign of r is + or −?

(d) Interpret the value of s in this setting.

Rank the correlations Consider each of the following relationships: the heights of fathers and the heights of their adult sons, the heights of husbands and the heights of their wives, and the heights of women at age 4and their heights at age 18. Rank the correlations between these pairs of variables from highest to lowest. Explain your reasoning.

In the chapter-opening Case Study (page 141), the Starnes family arrived at Old Faithful after it had erupted. They wondered how long it would be until the next eruption. Here is a scatterplot that plots the interval between consecutive eruptions of Old Faithful against the duration of the previous eruption, for the month prior to their visit.

What information does the Starnes family need to predict when the next eruption will occur?

What form does the relationship take? Why are there two clusters of points?

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free