Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305115347
Author: Roxy Peck; Chris Olsen; Jay L. Devore
Publisher: Brooks Cole
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 5.3, Problem 32E
a.
To determine
Create a
b.
To determine
Obtain an equation for the least-squares line.
c.
To determine
Find the predicted value of nitrogen retention for 0.06 gram of nitrogen intake.
d.
To determine
Obtain the residual for the observation (0.06, 0.01).
e.
To determine
Identify the potentially influential observation in the data set from the scatterplot in Part a.
Explain the reason the observation is potentially influential.
f.
To determine
Find the predicted value of nitrogen retention for 0.06 gram of nitrogen intake.
Compare this with the prediction in Part c.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The article "Estimating Population Abundance in Plant Species with Dormant Life-Stages:
Fire and the Endangered Plant Grevillea caleye R Br." (T. Auld and J. Scott, Ecological
Management and Restoration, 2004:125-129) presents estimates of population sizes of a
certain rare shrub in areas burnt by fire. The following table presents population counts and
areas (in m?) for several patches containing the plant.
Агеа
3739
Population
3015
5277
1847
400
17
345
392
142
40
7000
2521
213
11958
1200
2878
707
113
1392
157
12000
10880
711
74
2259
223
81
15
33
18
1254
1320
229
351
1000
92
841
1720
1500
300
228
31
228
17
10
Compute the least-squares line for predicting population (y) from area (x).
Б.
a.
Plot the residuals versus the fitted values. Does the model seem appropriate?
Compute the least-squares line for predicting In y from In x.
Plot the residuals versus the fitted values. Does the model seem appropriate?
Using the more appropriate model, construct a 95% prediction interval for the…
1. (Prob. 11-12, p. 438) An article in the Journal of Environmental Engineering (1989, Vol. 115(3), pp.
608–619) reported the results of a study on the occurrence of sodium and chloride in surface
streams in central Rhode Island. The following data are chloride concentration y (in milligrams per
liter) and roadway area in the watershed x (in percentage).
y
4.4
6.6
9.7
10.6
10.8
10.9
0.19
0.15
0.57
0.70
0.67
0.63
y
11.8
12.1
14.3
14.7
15.0
17.3
0.47
0.70
0.60
0.78
0.81
0.78
y
19.2
23.1
27.4
27.7
31.8
39.5
0.69
1.30
1.05
1.06
1.74
1.62
a.
Draw a scatter diagram of the data. Does a simple linear regression model seem appropriate
here?
b. Fit the simple linear regression model using the method of least squares. Find an estimate of
o?.
C.
Estimate the mean chloride concentration for a watershed that has 1% roadway area.
d. Find the fitted value corresponding to x = 0.47 and the associated residual.
The article "Effect of Environmental Factors on Steel Plate CoIrosion Under Marine
Immersion Conditions" (C. Soares, Y. Garbatov, and A. Zayed, Corrosion Engineering,
Science and Technology, 2011:524-541) descrībes an experiment in which nine steel
specimens were submerged in seawater at various temperatures, and the corrosion rates
were measured. The results are presented in the following table (obtained by digitizing a
graph).
Temperature (*C)
Corrosion (mnm/yr)
26.6
1.58
26.0
1.45
27.4
1.13
21.7
0.96
14.9
0.99
11.3
1.05
15.0
0.82
8.7
0.68
8.2
0.56
Construct a scatterplot of corosion (y) versus temperature (x). Verify that a linear
model is appropriate.
Compute the least-squares line for predicting corrosion from temperature.
Two steel specimens whose temperatures differ by 10°C are submerged in seawater.
By how much would you predict their corrosion rates to differ?
Predict the corrosion rate for steel submerged in seawater at a temperature of 20°C.
Compute the fitted values.…
Chapter 5 Solutions
Introduction to Statistics and Data Analysis
Ch. 5.1 - For each of the scatterplots shown, answer the...Ch. 5.1 - For each of the following pairs of variables,...Ch. 5.1 - Is the following statement correct? Explain why or...Ch. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - The accompanying data are x = Cost (cents per...Ch. 5.1 - The authors of the paper Flat-footedness Is Not a...Ch. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - The accompanying data were read from graphs that...
Ch. 5.1 - It may seem odd, but one of the ways biologists...Ch. 5.1 - An auction house released a list of 25 recently...Ch. 5.1 - A sample of automobiles traversing a certain...Ch. 5.2 - Two scatterplots are shown below. Explain why it...Ch. 5.2 - The authors of the paper Statistical Methods for...Ch. 5.2 - Prob. 16ECh. 5.2 - A sample of 548 ethnically diverse students from...Ch. 5.2 - The relationship between hospital patient-to-nurse...Ch. 5.2 - Prob. 19ECh. 5.2 - Prob. 20ECh. 5.2 - Studies have shown that people who suffer sudden...Ch. 5.2 - The data given in the previous exercise on x =...Ch. 5.2 - An article on the cost of housing in Califomia...Ch. 5.2 - The following data on sale price, size, and...Ch. 5.2 - Explain why it can be dangerous to use the...Ch. 5.2 - The sales manager of a large company selected a...Ch. 5.2 - Explain why the slope b of the least-squares line...Ch. 5.2 - Prob. 28ECh. 5.3 - Does it pay to stay in school? The report Trends...Ch. 5.3 - The data in the accompanying table is from the...Ch. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Some types of algae have the potential to cause...Ch. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - The article Examined Life: What Stanley H. Kaplan...Ch. 5.3 - Prob. 38ECh. 5.3 - The article California State Parks Closure List...Ch. 5.3 - The article referenced in the previous exercise...Ch. 5.3 - A study was carried out to investigate the...Ch. 5.3 - Both r2 and se are used to assess the fit of a...Ch. 5.3 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - The paper Aspects of Food Finding by Wintering...Ch. 5.4 - Food intake of grazing animals is limited by the...Ch. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - The paper Population Pressure and Agricultural...Ch. 5.4 - Determining the age of an animal can sometimes be...Ch. 5.5 - The paper How Lead Exposure Relates to Temporal...Ch. 5.5 - The following quote is from the paper Evaluation...Ch. 5 - The accompanying data represent x = Amount of...Ch. 5 - The paper A Cross-National Relationship Between...Ch. 5 - The following data on x = Score on a measure of...Ch. 5 - Prob. 58CRCh. 5 - Prob. 59CRCh. 5 - Prob. 60CRCh. 5 - The paper Effects of Canine Parvovirus (CPV) on...Ch. 5 - The paper Aspects of Food Finding by Wintering...Ch. 5 - Data on salmon availability (x) and the percentage...Ch. 5 - No tortilla chip lover likes soggy chips, so it is...Ch. 5 - The article Reduction is Soluble Protein and...Ch. 5 - An accurate assessment of oxygen consumption...Ch. 5 - Consider the four (x, y) pairs (0, 0), (1, 1), 1,...Ch. 5 - Prob. 1CRECh. 5 - Data from a survey of 1046 adults age 50 and older...Ch. 5 - Prob. 3CRECh. 5 - Prob. 4CRECh. 5 - Prob. 5CRECh. 5 - In August 2009, Harris Interactive released the...Ch. 5 - Prob. 7CRECh. 5 - Prob. 8CRECh. 5 - Prob. 9CRECh. 5 - Prob. 10CRECh. 5 - Prob. 11CRECh. 5 - Prob. 12CRECh. 5 - Prob. 13CRECh. 5 - Cost-to-charge ratios (the percentage of the...Ch. 5 - Prob. 15CRECh. 5 - In the article Reproductive Biology of the Aquatic...Ch. 5 - Prob. 17CRECh. 5 - Prob. 18CRECh. 5 - The paper “Population Pressure and Agricultural...Ch. 5 - Anabolic steroid abuse has been increasing despite...Ch. 5 - Prob. 69ECh. 5 - Prob. 70ECh. 5 - Prob. 71ECh. 5 - Prob. 72ECh. 5 - Suppose the hypothetical data below are from a...Ch. 5 - Prob. 74E
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
- Urban Travel Times Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, sent by residents driving to work. City Population N Driving time T Los Angeles 6489 16.8 Pittsburgh 1804 12.6 Washington 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. a Construct a power model of driving time in minutes as a function of population measured in thousands b Is average driving time in Pittsburgh more or less than would be expected from its population? c If you wish to move to a smaller city to reduce your average driving time to work by 25, how much smaller should the city be?arrow_forwardIn a study, the effects of the mane of a male lion as a signal of quality to mates and rivals was explored. Four life-sized dummies of male lions provided a tool for testing female response to the unfamiliar lions whose manes varied by length (long or short) and color (blonde or dark). The female lions were observed to see whether they approached each of the four life-sized dummies. Complete parts (a) through (e) below. a. Identify the experimental units. Choose the correct answer below. The female lions The male dummies The mane colors The mane lengths Part 2 b. Identify the response variable. Choose the correct answer below. A. Whether or not (yes or no) the mane length affected how the female lions reacted to a male dummy. B. Whether or not (yes or no) the female lions approached the same dummies. C. Whether or not (yes or no) the female lions approached a male dummy. D. Whether or not…arrow_forward(2.16) Table 2.12 comes from one of the first studies of the link between lung cancer and smoking, by Richard Doll and A. Bradford Hill. In 20 hospitals in London, UK, patients admitted with lung cancer in the previous year were queried about their smoking behavior. For each patient admitted, researchers studied the smoking behavior of a noncancer control patient at the same hospital of the same sex and within the same 5-year grouping on age. A smoker was defined as a person who had smoked at least one cigarette a day for at least a year. Table 2.12. Data for Problem 2.16 Cases 688 21 709 Lung Cancer Have Smoked Yes No Total Based on data reported in Table IV, R. Doll and A. B. Hill, Br. Med. J., 739-748, September 30, 1950. Controls 650 59 709 a) Identify the response variable and the explanatory variable. b) Identify the type of study this was. c) Can you use these data to compare smokers with nonsmokers in terms of the proportion who suffered lung cancer? Why or why not? d)…arrow_forward
- Here is the data and scenario for the above questions: An ornithologist is studying the role of color in flower selection for a particular species of hummingbird. He places 3 lilac bushes with similar size, flower yield, and scent profile near a known hummingbird habitat--one with white flowers, one with pink flowers, and one with purple flowers. He then uses surveillance cameras to count hummingbird visits to each of the 3 bushes for 30 days. The daily visit count data for each lilac color bush is summarized below: White Pink Purple Mean: 17.2 17.8 18.5 S.Dev: 1.9 1.4 2.6 (Hint for calculations: What is n here, and why? What are the actual data sets corresponding to each mean?) What does the ornithologist conclude? Do you have a recommendation for further study?arrow_forwardGrey-Seal Nursing. The average lactation (nursing) period of all earless seals is 23 days. Grey seals are one of several types of earless seals. The length of time that a female grey seal nurses her pup is studied by S. Twiss et al. in the article “Variation in Female Grey Seal (Halichoerus grypus) Reproductive Performance Corre- lates to Proactive-Reactive Behavioural Types” (PLOS ONE 7(11): e49598. doi:10.1371/journal.pone.0049598). A sample of 14 female grey seals had the following lactation periods, in days. At the 5% significance level, do the data provide sufficient evidence to conclude that the mean lactation period of grey seals differs from 23 days? Assume that the population standard deviation is 3.0 days. (Note: The sum of the data is 274.9 days.)arrow_forwardThe Journal of Engineering in Industry (Aug. 1993) reported on an automated system designed to replace the cutting tool of a drilling machine at optimum times. To test the system, data were collected over a broad range of materials, drill sizes, drill speeds, and feed rates – called machining conditions. Although a total of 168 different machining conditions were possible, only eight were employed in this study. These are described below: Experiment Workpiece Drill Size (in.) 25 25 Drill Speed (грт) 1250 1800 Feed Rate Material (ipr) .011 .005 1 Cast Iron Cast Iron Steel Steel 25 25 3750 2500 .003 .003 .008 4 Steel 25 .125 .125 2500 Steel Steel 4000 4000 3000 .0065 .009 .010 Steel .125 a. Suppose one (and only one) of the 168 possible machining conditions will detect a flaw in the system. What is the probability that the experiment conducted in the study will detect the system flaw? b. Suppose the system flaw occurs when drilling steel material with a 25-inch drill size at a speed of…arrow_forward
- ) Which model is the better predictor based on the MSEarrow_forward2 The table shows the total number of trade apprenticeships in Canada each year from 1991 to 1997 a) Consider the year 1991 as year #0. Create a scatter plot of the data on the next page using the DESMOS graphing calculator. Year apprenticeships 1991 1992,945 1992 180,965 1993 168,985 1994 163,750 163,370 165,325 1995 1996 1997 171,180 b) From the scatter plot, which model appears most appropriate: linear, quadratic, exponential. Give reason for your answer c) Generate a model for the data (line/curve of best fit) using regression. Write the equation of the model that best fits the data. d) Use the model to predict when apprenticeships will return to 1991 levels. 2.arrow_forwardWing Length. D. Cristol et al. published results of their studies of two subspecies of dark-eyed juncos in the paper “Migratory Dark-Eyed Juncos, Junco hyemalis, Have Better Spatial Memory and Denser Hippocampal Neurons Than Nonmigratory Conspecifics” (Animal Behaviour, Vol. 66, Issue 2, pp. 317–328). One of the subspecies migrates each year, and the other does not migrate. A hypothesis test is to be performed to decide whether the mean wing lengths for the two subspecies (migratory and nonmigratory) are different. a. identify the variable. b. identify the two populations. c. determine the null and alternative hypotheses. d. classify the hypothesis test as two tailed, left tailed, or right tailed.arrow_forward
- The following table shows the typical depth (rounded to the nearest foot) for nonfailed wells in geological formations in Baltimore County (The Journal of Data Science, 2009, Vol. 7, pp. 111-127). Geological Formation Group Number of Nonfailed Wells Nonfailed Well Depth Gneiss 1,515 255 Granite 26 218 Loch Raven Schist 3,290 317 Mafic 349 231 Marble 280 267 Prettyboy Schist 1,343 255 Other schists 887 267 Serpentine 36 217 Total 7,726 2,027 Let the random variable X denote the depth (rounded to the nearest foot) for nonfailed wells. Detemine the cumulative distribution function for X. Round your answers to four decimal places (e.g. 98.7654). x < 217 217arrow_forwardThe stated goal of a chain of service stores is to provide a lube and oil change for anyone's automobile in 15 minutes. The manager at one store thinks that there is a growing disparity among his workers in the time it takes to lube and change the oil of an automobile. To monitor this, the manager has selected a sample of 20 days and has recorded the time it took to service 100 automobiles each day. Data about the number of times the service was performed in 15 minutes or less (515) are found below. Complete parts a through c Click the icon to view the data. a. Compute p and sp p-(Round to four decimal places as needed.) Sp (Round to four decimal places as needed) b. Construct a p-chart and determine if the process of the time required for oil and lube jobs is in control Which graph below shows a p-chart for the data? O A. OB. Am 0.05 -ww Is the process in control? OA. Since 10 points in a row are below the centerline, followed by 10 points above, conclude that the process is out of…arrow_forwardTable 2.12 comes from one of the first studies of the link between lung cancer and smoking, by Richard Doll and A. Bradford Hill. In 20 hospitals in London, UK, patients admitted with lung cancer in the previous year were queried about their smoking behavior. For each patient admitted, researchers studied the smoking behavior of a noncancer control patient at the same hospital of the same sex and within the same 5-year grouping on age. A smoker was defined as a person who had smoked at least one cigarette a day for at least a year. a) Identify the response variable, the explanatory variable and identify the type of study this was. B) Can you use these data to compare smokers with nonsmokers in terms of the proportion who suffered lung cancer? Why or why not? c)Summarize the association and explain how to interpret it.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Sampling Methods and Bias with Surveys: Crash Course Statistics #10; Author: CrashCourse;https://www.youtube.com/watch?v=Rf-fIpB4D50;License: Standard YouTube License, CC-BY
Statistics: Sampling Methods; Author: Mathispower4u;https://www.youtube.com/watch?v=s6ApdTvgvOs;License: Standard YouTube License, CC-BY