Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Q.26 (page 793)

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of 25students was selected from a large high school. For each student, x=footlength&y=heightere recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

26. Which of the following is the best interpretation of the value 0.4117in the computer output?

a. For each increase of 1cmin foot length, the average height increases by about0.4117cm

b. When using this model to predict height, the predictions will typically be off by about 0.4117cm.

c. The linear relationship between foot length and height accounts for 41.17%of the variation in height.

d. The linear relationship between foot length and height is moderate and positive.

e. In repeated samples of size 25the slope of the sample regression line for predicting height from foot length will typically vary from the population slope by about 0.4117.

Short Answer

Expert verified

The correct option is option (e)

In repeated samples of size25the slope of the sample regression line for predicting height from foot length will typically vary from the population slope by about 0.4117

Step by step solution

01

Given Information

Given in the question that

we have to determine the correct option.

02

Explanation 

The number 0.4117is mentioned in the column "SE Coef" and in the row "foot length," indicating that 0.4117is the standard error of the slope SEb1

The average deviation of the slope of the sample regression line from the population regression line is shown by the standard error of the slope.

As a result, the best solution is (e)

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

Tattoos: What per cent of U.S. adults have one or more tattoos? The Harris Poll conducted an online survey of 2302adults and found 29% of respondents had at least 1 tattoo. According to the published report, “Respondents for this survey were selected from among those who have agreed to participate in Harris Interactive surveys.” Explain why it would not be appropriate to use these data to construct a 95% confidence interval for the proportion of all U.S. adults who have tattoos.

Students in Mr. Handford’s class dropped a kickball beneath a motion detector. The detector recorded the height of the ball (in feet) as it bounced up and down several times. Here is a computer output from a linear regression analysis of the transformed data of log(height) versus bounce number. Predict the highest point the ball reaches on its seventh bounce.

a. 0.35feet

b. 2.26feet

c. 0.37feet

d. 2.32feet

e. 0.43feet

Braking distance How is the braking distance for a motorcycle related to the speed at which the motorcycle was traveling when the brake was applied? Statistics teacher Aaron Waggoner gathered data to answer this question. The table shows the speed (in miles per hour) and the distance needed to come to a complete stop when the brake was applied (in feet).

Speed (mph)Distance (ft)Speed (mph)Distance (ft)61.423252.0894.924084191848110.333044.75

a. Transform both variables using logarithms. Then calculate and state the least-squares regression line using the transformed variables.

b. Use the model from part (a) to calculate and interpret the residual for the trial when the motorcycle was traveling at 48 mph.

Do taller students require fewer steps to walk a fixed distance? The scatterplot shows the relationship between x=height (in inches) and y=number of steps required to walk the length of a school hallway for a random sample of 36 students at a high school.

A least-squares regression analysis was performed on the data. Here is some computer output from the analysis

Long legs Do these data provide convincing evidence at the α=0.05level that taller students at this school require fewer steps to walk a fixed distance? Assume that the conditions for inference are met.

SAT Math scores Is there a relationship between the percent of high school graduates in each state who took the SAT and the state’s mean SAT Math score? Here is a residual plot from a linear regression analysis that used data from all 50states in a recent year. Explain why the conditions for performing inference about the slope β1 of the population regression line are not met.

See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Decision 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