Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q T3.8. (page 216)

There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least-squares fit of some data collected by a biologist gives the model y^=25.2+3.3x , where x is the number of chirps per minute and y^ is the estimated temperature in degrees Fahrenheit. What is the predicted increase in temperature for an increase of = chirps per minute?

a. 3.3°F

b. 16.5°F

c. 25.2°F

d. 28.5°F

e. 41.7°F

Short Answer

Expert verified

The correct option is (b)16.5°F

Step by step solution

01

Given information

The regression equation for least-squares

y⏜=25.2+3.3x

02

Concept

The least-squares regression line reduces the sum of squares of vertical distances between the observed points and the line to zero.

03

Explanation

replacingxbyx+5y⏜=25.2+3.3(x+5)=(25.2+3.3x)+16.5

It is observed that if x is increased by 5 then the expected value y increases by 16.5F

Hence, the correct option is (b)

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

More crying? Refer to Exercise 16Does the fact that r=0.45 suggest that making an infant cry will increase his or her IQ later in life? Explain your reasoning.

Infant weights in Nahya A study of nutrition in developing countries

collected data from the Egyptian village of Nahyan. Researchers recorded the mean weight (in kilograms) for 170 infants in Nahya 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 looking at the scatterplot first. The result is weight^=4.88+0.267 (age). Use the residual plot to determine if this linear model is appropriate.

Rushing for points What is the relationship between rushing yards and points scored in the National Football League? The table gives the number of rushing yards and the number of points scored for each of the 16 games played by the Jacksonville Jaguars in a recent season.

a. Make a scatterplot with rushing yards as the explanatory variable. Describe what you see.

b. The number of rushing yards in Game 16 is an outlier in the x-direction. What effect do you think this game has on the correlation? On the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this game to confirm your answers.

c. The number of points scored in Game 13 is an outlier in the y-direction. What effect do you think this game has on the correlation? On the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this game to confirm your answers.

Olympic figure skating For many people, the women’s figure skating competition is the highlight of the Olympic Winter Games. Scores in the short program x and scores in the free skate y were recorded for each of the 24 skaters who competed in both rounds during the 2010 Winter Olympics in Vancouver, Canada.28 Here is a scatterplot with least-squares regression line y^=−16.2+2.07x. For this model, s = 10.2 and r2 = 0.736.

Residual gas Refer to Exercise 38. During March, the average temperature was 46.4°F and Joan used an average of 490 cubic feet of gas per day. Calculate and interpret the residual for this month.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Geometry

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