Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 13.1, Problem 5E
A sample of small cars was selected, and the values of x = horsepower and y = fuel efficiency (mpg) were determined for each car. Fitting the simple linear regression model gave the estimated regression equation ŷ = 44.0 − 0.150x.
- a. How would b = −0.150 be interpreted?
- b. Substituting x = 100 gives ŷ ＝ 29.0. Give two different interpretations of this number.
- c. What happens if the efficiency for a car with a 300-horsepower engine is predicted? Why does this occur?
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
The admissions officer for a certain college developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high school GPA.
ŷ = −1.39 + 0.0234x1 + 0.00482x2
where
x1
=
high-school grade point average
x2
=
SAT mathematics score
y
=
final college grade point average.
#1)A high-school average 84 corresponds to x1 = 84
and a score of 535 on the SAT mathematics test corresponds to
x2 = 535. Substitute these values into the estimated regression equation to find the final college GPA, rounding the result to two decimal places.
GPA
=
−1.39 + 0.0234x1 + 0.00482x2
=
-1.39 +0.0234 (_____________) + 0.00482 (535)
=
__________________
Consider the following regression analysis between sales (Y in $1,000) and social media advertising (X in dollars).Ŷ = 55,000 + 7XThe regression equation implies that an ________.
Multiple Choice
increase of $7 in advertising is associated with an increase of $7,000 in sales
increase of $1 in advertising is associated with an increase of $7 in sales
increase of $1 in advertising is associated with an increase of $62,000 in sales
increase of $1 in advertising is associated with an increase of $7,000 in sales
In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the midterm exam. The equation of the least‑squares regression line was ?̂ =10+0.9?, where ?y represents the final exam score and ?x is the midterm exam score. Suppose Joe scores an 80 on the midterm exam. What would be the predicted value of his score on the final exam?
Chapter 13 Solutions
Introduction To Statistics And Data Analysis
Ch. 13.1 - Let x be the size of a house (in square feet) and...Ch. 13.1 - Consider the variables and population regression...Ch. 13.1 - The flow rate in a device used for air quality...Ch. 13.1 - The paper Predicting Yolk Height, Yolk Width,...Ch. 13.1 - A sample of small cars was selected, and the...Ch. 13.1 - Prob. 6ECh. 13.1 - Suppose that a simple linear regression model is...Ch. 13.1 - a. Explain the difference between the line y x...Ch. 13.1 - Prob. 9ECh. 13.1 - Hormone replacement therapy (HRT) is thought to...
Ch. 13.1 - Consider the data and estimated regression line...Ch. 13.1 - A simple linear regression model was used to...Ch. 13.1 - Consider the accompanying data on x = Advertising...Ch. 13.2 - What is the difference between and b? What is the...Ch. 13.2 - The largest commercial fishing enterprise in the...Ch. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - An experiment to study the relationship between x...Ch. 13.2 - The paper The Effects of Split Keyboard Geometry...Ch. 13.2 - The authors of the paper Decreased Brain Volume in...Ch. 13.2 - Do taller adults make more money? The authors of...Ch. 13.2 - Researchers studying pleasant touch sensations...Ch. 13.2 - Prob. 24ECh. 13.2 - Acrylamide is a chemical that is sometimes found...Ch. 13.2 - Prob. 26ECh. 13.2 - Exercise 13.18 described a regression analysis...Ch. 13.2 - Consider the accompanying data on x = Research and...Ch. 13.2 - Prob. 29ECh. 13.2 - In anthropological studies, an important...Ch. 13.3 - The graphs accompanying this exercise are based on...Ch. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - The article Vital Dimensions in Volume Perception:...Ch. 13.3 - Prob. 35ECh. 13.3 - An investigation of the relationship between x =...Ch. 13.4 - Prob. 37ECh. 13.4 - Prob. 38ECh. 13.4 - In Exercise 13.19, we considered a regression of y...Ch. 13.4 - Prob. 40ECh. 13.4 - A subset of data read from a graph that appeared...Ch. 13.4 - Prob. 42ECh. 13.4 - Prob. 43ECh. 13.4 - The article first introduced in Exercise 13.34 of...Ch. 13.4 - The shelf life of packaged food depends on many...Ch. 13.4 - For the cereal data of the previous exercise, the...Ch. 13.4 - The article Performance Test Conducted for a Gas...Ch. 13.5 - Prob. 48ECh. 13.5 - Prob. 49ECh. 13.5 - A sample of n = 353 college faculty members was...Ch. 13.5 - Prob. 51ECh. 13.5 - Prob. 52ECh. 13.5 - The accompanying summary quantities for x =...Ch. 13.5 - Prob. 54ECh. 13.5 - Prob. 55ECh. 13.6 - Prob. 56ECh. 13 - Prob. 1CRECh. 13 - Prob. 2CRECh. 13 - Prob. 3CRECh. 13 - Prob. 4CRECh. 13 - Prob. 5CRECh. 13 - The accompanying graphical display is similar to...Ch. 13 - Prob. 7CRECh. 13 - Prob. 8CRECh. 13 - Consider the following data on y = Number of songs...Ch. 13 - Many people take ginkgo supplements advertised to...Ch. 13 - Prob. 11CRECh. 13 - Prob. 12CRECh. 13 - Prob. 13CRECh. 13 - Prob. 14CRECh. 13 - The discharge of industrial wastewater into rivers...Ch. 13 - Many people take ginkgo supplements advertised to...Ch. 13 - It is hypothesized that when homing pigeons are...Ch. 13 - Prob. 18CRECh. 13 - Prob. 57CRCh. 13 - Prob. 58CRCh. 13 - Prob. 59CRCh. 13 - The article Photocharge Effects in Dye Sensitized...Ch. 13 - Prob. 61CRCh. 13 - Prob. 62CRCh. 13 - Prob. 63CRCh. 13 - Prob. 64CRCh. 13 - Prob. 65CRCh. 13 - The article Improving Fermentation Productivity...Ch. 13 - Prob. 67CRCh. 13 - Prob. 68CRCh. 13 - Prob. 69CR
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardA biologist wants to predict the height of male giraffes, y, in feet, given their age, x1, in years, weight, x2, in pounds, and neck length, x3, in feet. She obtains the multiple regression equation yˆ=7.36+0.00895x1+0.000426x2+0.913x3. Predict the height of a 12-year-old giraffe that weighs 3,100 pounds and has a 7-foot-long neck, rounding to the nearest foot.arrow_forward
- A company has a set of data with employee age (X) and the corresponding number of annual on-the-job-accidents (Y). Analysis on the set finds that the regression equation is Y=60-0.5*X. What can be said of the correspondence (relation) between age and accidents? Are younger workers safer or more prone to accident? What is the likely number of accidents for someone aged 25?arrow_forwardA group of students looked to see if there was a linear relationship between the number of hours spent on social media per day (x) and number of sit-ups a person can do in one minute (y).After gathering data from their class, the students ran LinReg regression on their calculator, which gave them: y = ax + b a = -1.794 b = 36.334 Based on that result, how many sit-ups would you expect a person who spends 6 hours of on social media to be able to do in one minute? Round to the nearest whole number of sit-ups.arrow_forward.The worker has noticed that the more time he spends at work (x), the less money he is likely to make (y) in conducting transactions for his firm. Which of the regression equations MOST suggests such a possibility?arrow_forward
- Assume that there is a positive linear correlation between the variable R (return rate in percent of financial investment) and the variable t (age in years of the investment) given by the regression equation R = 2.5t + 5.3. 1- Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment?arrow_forwardSuppose that a researcher studying the weight of female college athletes wants to predict the weights based on height, measured in inches, and the percentage of body fat of an athlete. The researcher calculates the regression equation as (weight) = 3.544*(height) + 1.064*(percent body fat) - 87.076. If a female athlete is 64 inches tall and has a 21 percentage of body fat, what is her expected weight? Question 24 options: 1) 55.444 2) We do not know the observations in the data set, so we cannot answer that question. 3) 162.084 4) 249.16 5) 336.236arrow_forwardA social science professor wants to determine if the amount of time that a student, who is in a relationship, spends with his or her partner is related to that same student’s academic performance. A random sample of students who are in a relationship has been taken, and the table below shows the amount of time (in hours) spent by each sample on his or her partner in a week, as well as the average grade (with 75.00 as the passing mark). a. Find the regression equation and construct the scatter plot diagram.b. Predict the grade of a student who spends 118.72 hours per week on his or her partner.c. Calculate the total variation.d. Compute the standard deviation of the estimate.arrow_forward
- Assume that there is a positive linear correlation between the variable R (return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R = 2.3t + 4.8. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? If the investment continues to grow at a constant rate, what is the expected return rate when the investment is 7 years old? If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?arrow_forwardA surgery intern has conducted a study of the sleeping habits of her colleagues and has developed a following regression equation: y-hat = 6 + 0.1X, where X is the number of hours working on one shift, and Y is the number of hours sleeping at night after that shift. Yvette worked 10 hours and slept 8 hours. What is Yvette’s residual? 0.1 1 6 7arrow_forwardThe admissions officer for a certain college developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high school GPA. ŷ = −1.39 + 0.0234x1 + 0.00482x2 where x1 = high-school grade point average x2 = SAT mathematics score y = final college grade point average. (a) Interpret the coefficients in this estimated regression equation. (b) Predict the final college GPA for a student who has a high-school average of 84 and a score of 535 on the SAT mathematics test.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY