Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q.22 (page 162)

All brawn? The figure below plots the average brain weight in grams versus average body weight in kilograms for 96species of mammals. There are many small mammals whose points at the lower-left overlap.

(a) The correlation between body weight and brain weight isr=0.86. Explain what this value means.

(b) What effect would removing the elephant have on the correlation? Justify your answer.

Short Answer

Expert verified

a). Body weight in kilogram and brain weight in gram have a very significant positive relationship.

b). Ther coefficient of linear correlation would decrease.

Step by step solution

01

Part (a) Step 1: Given Information 

The average brain weight in grams versus average body weight in kilograms for 96 species of mammals.

02

Part (a) Step 2: Explanation

The stronger the positive relationship, the closer the correlation, r, is to 1.

Body weight in kilogram and brain weight in gram have a very significant positive relationship.

03

Part (b) Step 1: Given Information 

The average brain weight in grams versus average body weight in kilograms for 96species of mammals.

04

Part (b) Step 2: Explanation

The point in the top right corner (Elephants) follows the same basic linear trend as the rest of the scatterplot's data points.

When this point is removed from the data set, the data appears less linear, and the linear correlation coefficient rdecreases.

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.

Start your free trial

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

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?

Does social rejection hurt? We often describe our emotional reaction to social rejection as “pain.” Does social rejection cause activity in areas of the brain that are known to be activated by physical pain? If it does, we really do experience social and physical pain in similar ways. Psychologists first included and then deliberately excluded individuals from a social activity while they measured changes in brain activity. After each activity, the subjects filled out questionnaires that assessed how excluded they felt. The table below shows data for 13subjects.7“Social distress” is measured by each subject’s questionnaire score after exclusion relative to the score after inclusion. (So values greater than 1show the degree of distress caused by exclusion.) “Brain activity” is the change in activity in a region of the brain that is activated by physical pain. (So positive values show more pain.)

Discuss what the data show. Follow the four-step process.

Teaching and research A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says, “The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero.” The paper reports this as “Professor McDaniel said that good researchers tend to be poor teachers, and vice versa.” Explain why the paper’s report is wrong. Write a statement in plain language (don’t use the word “correlation”) to explain the psychologist’s meaning.

Stats teachers’ cars A random sample of AP Statistics teachers were asked to report the age (in years) and mileage of their primary vehicles. A scatterplot of the data, a least-squares regression printout, and a residual plot are provided below.

(a) Give the equation of the least-squares regression line for these data. Identify any variables you use.

(b) One teacher reported that her 6-year-old car had65,000 miles on it. Find its residual.

(c) Interpret the slope of the line in context.

(d) What’s the correlation between car age and mileage? Interpret this value in context.

(e) How well does the regression line fit the data? Justify your answer using the residual plot and s.

One of nature’s patterns connects the percentage of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are data for 13colonies of sparrow-hawks:

Make a scatterplot by hand that shows how the number of new adults relates to the percentage of returning birds.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation
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