Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q.21 (page 161)

Hot dogs Are hot dogs that are high in calories also high in salt? The figure below is a scatterplot of the calories and salt content (measured as milligrams of sodium) in 17brands of meat hot dogs.

(a) The correlation for these data is r=0.87. Explain what this value means.

(b) What effect would removing the hot dog brand with the lowest calorie content have on the correlation? Justify your answer.

Short Answer

Expert verified

a). In a hot dog, there is a very significant positive relationship between calories and salt.

b). The linear association would become more significant.

Step by step solution

01

Part(a) Step 1: Given Information

The calories and salt content (measured as milligrams of sodium) in 17brands of meat hot dogs.

02

Part(a) Step 2: Explanation 

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

In a hot dog, there is a very significant positive relationship between calories and salt.

03

Part(b) Step 1: Given Information

The calories and salt content (measured as milligrams of sodium) in 17brands of meat hot dogs.

04

Part(b) Step 2: Explanation 

The point in the bottom left corner (corresponding to the lowest calorie content) does not follow the same general linear trend as the other data points in the scatterplot.

Thus, deleting this point from the data set would make the data look more linear, resulting in a rise in the linear correlation coefficient r. (close to 1).

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

The figure below is a scatterplot of reading test scores against IQ test scores for 14 fifth-grade children. The line is the least-squares regression line for predicting reading scores from IQ scores. If another child in this class has an IQ score of 110, you predict the reading score to be close to

(a)50.(b)60.(c)70.(d)80.(e)90.

Nahya infant weights A study of nutrition in developing countries collected data from the Egyptian

village of Nahya. Here are the mean weights (in kilograms) for 170 infants in Nahya who were

weighed each month during their first year of life:

A hasty user of statistics enters the data into software and computes the least-squares line without plotting the data. The result is weight=4.88+0.267(age) A residual plot is shown below. Would it be appropriate to use this regression line to predict y from x? Justify your answer.

The scatterplots below show four sets of real data:

(a) repeats the manatee plot in Figures

(b) shows the number of named tropical storms and the number predicted before the start of hurricane season each year between 1984and 2007by William Gray of Colorado State University;

(c) plots the healing rate in micrometers (millionths of a meter) per hour for the two front limbs of several newts in an experiment; and

(d) shows stock market performance in consecutive years over a 56-year period.

For each graph, estimate the correlation r. Then interpret the value of r in context.

(a)

(b)

(c)

(d)

Do heavier people burn more energy? Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. We have data on the lean body mass and resting metabolic rate for 12women who are subjects in a study of dieting. Lean body mass, given in kilograms, is a person’s weight leaving out all fat. Metabolic rate is measured in calories burned per 24hours. The researchers believe that lean body mass is an important influence on metabolic rate.

(a) Make a scatterplot on your calculator to examine the researchers’ belief.

(b) Describe the direction, form, and strength of the relationship.

Do students with higher IQ test scores tend to do better in school? The figure below shows a scatterplot of IQ and school grade point average (GPA) for all 78seventh-grade students in a rural midwestern school. (GPA was recorded on a 12-point scale with , A+=12,A=11,A-=10,B+=9,…,D-=1,andF=0.)2

(a) Say in words what a positive association betweenIQ and GPA would mean. Does the plot show a positive association?

(b) What is the form of the relationship? Is it very strong? Explain your answers.

(c) At the bottom of the plot are several points that we might call outliers. One student, in particular, has a very low GPA despite an average IQ score. What are the approximate IQ and GPA of this student?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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