Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q.42 (page 191)

How much gas? Refer to Exercise 40. Would it be appropriate to use the regression line to predict Joan’s natural-gas consumption in a future month with an average temperature of 65°F? Justify your answer

Short Answer

Expert verified

we can surely predict J's natural gas consumption in the future months with an average temperature of65°F

Step by step solution

01

Given Information

It is given in the question 40, y^=1425−19.87x

Would it be appropriate to use the regression line to predict Joan’s natural-gas consumption in a future month with an average temperature of65°F

02

Explanation

A regression line is extrapolated to make predictions far beyond the interval of values of the explanatory variable Xused to obtain the regression line. These predictions are often incorrect.

Here is the equation for the least squares when considering how much gas there is:

y^=1425−19.87x

Our data shows that the average temperature of localid="1649399013276" 65∘Fis not too far outside our x- values.

Joan's natural gas consumption can therefore be predicted in a future month if the weather averages65°F.

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

55. Bird colonies Refer to Exercise 53.
(a) Use your calculator to make a residual plot. Describe what this graph tells you about how well the line fits the data.
(b) Which point has the largest residual? Explain what this residual means in context.

The British government conducts regular surveys of household spending. The average weekly household spending (in pounds) on tobacco products and alcoholic beverages for each of 11 regions in Great Britain was re- corded. A scatterplot of spending on alcohol versus spending on tobacco is shown below. Which of the following statements is true?

(a) The observation (4.5,6.0) is an outlier.

(b) There is clear evidence of a negative association between spending on alcohol and tobacco.

(c) The equation of the least-squares line for this plot would be approximately y⏜=10−2x

(d) The correlation for these data is r=0.99

(e) The observation in the lower-right corner of the plot is influential for the least-squares line.

IQ and reading scoresData on the IQ test scores and reading test scores for a group of fifth-grade children give the following regression line: predicted reading score -33.4+0.882(IQ score).

(a) What’s the slope of this line? Interpret this value in context.

(b) What’s the intercept? Explain why the value of the intercept is not statistically meaningful.

(c) Find the predicted reading scores for two children with IQ scores of 90and 130, respectively.

What affects correlation? Make a scatterplot of the following data:

The correlation for these data is 0.5. What is responsible for reducing the correlation to this value despite a strong straight-line relationship between xand yin most of the observations?

Do heavier people burn more energy? The study of dieting described in Exercise 10 collected data on the lean body mass (in kilograms) and metabolic rate (in calories) for 12female and7male subjects. The figure below is a scatterplot of the data for all 19subjects, with separate symbols for males and females.

Does the same overall pattern hold for both women and men? What is the most important difference between the sexes?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

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