For a data set consisting of two data points: a. Identify the regression line. b. What is the sum of squared errors for the regression line? Explain your answer.
> The ability to estimate the volume of a tree based on a simple measurement, such as the tree’s diameter, is important to the lumber industry, ecologists, and conservationists. Data on volume, in cubic feet, and diameter at breast height, in inches, for 7
> y = −8 − 4x a. find the y-intercept and slope. b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation. c. use two points to graph the equation.
> An issue of BARRON’S presented information on top wealth managers in the United States, based on individual clients with accounts of $1 million or more. Data were given for various variables, two of which were number of private client managers and privat
> Apply the empirical rule to solve each exercise. The data set has mean 25 and standard deviation 5. Fill in the following blanks: a. Approximately 68% of the observations lie. b. Approximately 95% of the observations lie. c. Approximately 99.7% of the ob
> The magazine Consumer Reports publishes information on automobile gas mileage and variables that affect gas mileage. In one issue, data on gas mileage (in miles per gallon) and engine displacement (in liters) were published for 121 vehicles. Those data a
> Does a higher state per capita income equate to a higher per capita beer consumption? From the document Survey of Current Business, published by the U.S. Bureau of Economic Analysis, and from the Brewer’s Almanac, published by the Beer Institute, we obta
> Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be carcinogens and a great danger to natural ecosystems. As a result of several studies, PCB production was banned in the United States in 1979 and by the Stockholm Convention on Persi
> The National Oceanic and Atmospheric Administration publishes temperature information of cities around the world in Climates of the World. A random sample of 50 cities gave the data on average high and low temperatures in January shown on the WeissStats
> In the article, “Ghost of Speciation Past” (Nature, Vol. 435, pp. 29–31), T. Kocher looked at the origins of a diverse flock of cichlid fishes in the lakes of southeast Africa. Suppose that you wanted to select a sample from the hundreds of species of ci
> On the WeissStats site are data on home size (in square feet) and assessed value (in thousands of dollars) for the same homes. a. Obtain a scatterplot for the data. b. Decide whether finding a regression line for the data is reasonable. If so, then also
> The document Arizona Residential Property Valuation System, published by the Arizona Department of Revenue, describes how county assessors use computerized systems to value single-family residential properties for property tax purposes. On the WeissStats
> Box Office Mojo collects and posts data on movie grosses. For a random sample of 50 movies, we obtained both the domestic (U.S.) and overseas grosses, in millions of dollars. The data are presented on the WeissStats site. a. Obtain a scatterplot for the
> The Information Please Almanac provides data on the ages at inauguration and of death for the presidents of the United States. We give those data on the WeissStats site for those presidents who are not still living at the time of this writing. a. Obtain
> How important are birdies (a score of one under par on a given golf hole) in determining the final total score of a woman golfer? From the U.S. Women’s Open website, we obtained data on number of birdies during a tournament and final score for 63 women g
> Apply the empirical rule to solve each exercise. The data set has mean 10 and standard deviation 3. Fill in the following blanks: a. Approximately 68% of the observations lie between ___ and ____. b. Approximately 95% of the observations lie between___ a
> y = 6 − 7x a. find the y-intercept and slope. b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation. c. use two points to graph the equation.
> In the paper “Mating System and Sex Allocation in the Gregarious Parasitoid Cotesia glomerata” (Animal Behaviour, Vol. 66, pp. 259–264), H. Gu and S. Dorn reported on various aspects of the mating system and sex allocation strategy of the wasp C. glomera
> We provided data on age and price for a sample of 11 Orions between 2 and 7 years old. On the WeissStats site, we have given the ages and prices for a sample of 31 Orions between 1 and 11 years old. a. Obtain a scatterplot for the data. b. Is it reasonab
> The negative relation between study time and test score found in Exercise 4.63 has been discovered by many investigators. Provide a possible explanation for it. Data from Exercise 4.63: An instructor at Arizona State University asked a random sample of
> In the article “Graphs in Statistical Analysis” (American Statistician, Vol. 27, Issue 1, pp 17–21), F. Anscombe presented four sets of data points with almost identical basic statistical properties (means, standard deviations, regression lines, etc.) bu
> The members of a population have been numbered 1–500. A sample of size 10 is to be taken from the population, using stratified random sampling with proportional allocation. The strata are of sizes 200, 150, and 150, where stratum #1 consists of the membe
> In Exercise 4.59, you determined a regression equation that can be used to predict the price of a Corvette, given its age. a. Should that regression equation be used to predict the price of a 4-year-old Corvette? a 10-year-old Corvette? Explain your answ
> In Exercise 4.58, you determined a regression equation that relates the variables percentage of investments in energy securities and tax efficiency for mutual fund portfolios. a. Should that regression equation be used to predict the tax efficiency of a
> An instructor at Arizona State University asked a random sample of eight students to record their study times in a beginning calculus course. She then made a table for total hours studied (x) over 2 weeks and test score ( y) at the end of the 2 weeks. He
> In the article “The Human Vomeronasal Organ. Part II: Prenatal Development” (Journal of Anatomy, Vol. 197, Issue 3, pp. 421–436), T. Smith and K. Bhatnagar examined the controversial issue of the human vomeronasal organ, regarding its structure, function
> We have provided simple data sets for you to practice the basics of finding measures of center. 2, 5, 0, −1 a. mean. b. median. c. mode(s).
> Identify two statistical methods other than a census for obtaining information.
> Plants emit gases that trigger the ripening of fruit, attract pollinators, and cue other physiological responses. N. Agelopolous et al. examined factors that affect the emission of volatile compounds by the potato plant Solanum tuberosum and published th
> Hanna Properties specializes in customhome resales in the Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. A random sample of nine custom homes currently listed for sale provided the following information on size and price. Here, x denot
> y = −1 + 2x a. find the y-intercept and slope. b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation. c. use two points to graph the equation.
> The Kelley Blue Book provides information on wholesale and retail prices of cars. Following are age and price data for 10 randomly selected Corvettes between 1 and 6 years old. Here, x denotes age, in years, and y denotes price, in hundreds of dollars. F
> Tax efficiency is a measure, ranging from 0 to 100, of how much tax due to capital gains stock or mutual funds investors pay on their investments each year; the higher the tax efficiency, the lower is the tax. In the article “At the Mercy of the Manager”
> The data points in Exercise 4.45. a. find the regression equation for the data points. Use the defining formulas in Definition 4.4 to obtain Sxx and Sxy . b. graph the regression equation and the data points. Data from Exercise 4.45: Line A: y = 3 − 0.6
> The members of a population have been numbered 1–1000. A sample of size 20 is to be taken from the population, using stratified random sampling with proportional allocation. The strata are of sizes 300, 200, 400, and 100, where stratum #1 consists of the
> The data points in Exercise 4.44. a. find the regression equation for the data points. Use the defining formulas in Definition 4.4 to obtain Sxx and Sxy . b. graph the regression equation and the data points. Data from Exercise 4.44: Line A: y = 1.5 + 0
> The data points in Exercise 4.43. a. find the regression equation for the data points. Use the defining formulas in Definition 4.4 to obtain Sxx and Sxy . b. graph the regression equation and the data points. Data from Exercise 4.43: Line A: y = −1 + 3x
> The data points in Exercise 4.42. a. find the regression equation for the data points. Use the defining formulas in Definition 4.4 to obtain Sxx and Sxy . b. graph the regression equation and the data points. Data from Exercise 4.42: Line A: y = 9 − 2x,
> A quantitative data set of size 150 has mean 35 and standard deviation 4. At least how many observations lie between 23 and 47?
> a. find the regression equation for the data points. Use the defining formulas in Definition 4.4 to obtain Sxx and Sxy . b. graph the regression equation and the data points.
> a. find the regression equation for the data points. Use the defining formulas in Definition 4.4 to obtain Sxx and Sxy . b. graph the regression equation and the data points.
> a. find the regression equation for the data points. Use the defining formulas in Definition 4.4 to obtain Sxx and Sxy . b. graph the regression equation and the data points.
> a. find the regression equation for the data points. Use the defining formulas in Definition 4.4 to obtain Sxx and Sxy . b. graph the regression equation and the data points.
> y = 3 + 4x a. find the y-intercept and slope. b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation. c. use two points to graph the equation.
> a. find the regression equation for the data points. Use the defining formulas in Definition 4.4 to obtain Sxx and Sxy. b. graph the regression equation and the data points.
> a. find the regression equation for the data points. Use the defining formulas in Definition 4.4 to obtain Sxx and Sxy . b. graph the regression equation and the data points.
> The members of a population have been numbered 1–100. A sample of size 30 is to be taken from the population, using cluster sampling. The clusters are of equal size 10, where cluster #1 consists of the members of the population numbered 1–10, cluster #2
> We presented summary statistics for data on bank robberies for five variables: amount stolen, number of bank staff present, number of customers present, number of bank raiders, and travel time from the bank to the nearest police station. These summary st
> For each of the following sets of data points, determine the regression equation both without and with the use of Formula.
> A quantitative data set of size 200 has mean 20 and standard deviation 4. At least how many observations lie between 8 and 32?
> Line A: y = 3 − 0.6x, Line B: y = 4 – x Data points: a. plot the data points and the first linear equation on one graph and the data points and the second linear equation on another. b. construct tables for x, y, y, e, and eˆ2. c. determine which line fi
> Line A: y = 1.5 + 0.5x, Line B: y = 1.125 + 0.375x Data points: a. plot the data points and the first linear equation on one graph and the data points and the second linear equation on another. b. construct tables for x, y, y, e, and eˆ2. c. determine wh
> Line A: y = −1 + 3x, Line B: y = 1 + 2x Data points: a. plot the data points and the first linear equation on one graph and the data points and the second linear equation on another. b. construct tables for x, y, y, e, and eˆ2. c. determine which line f
> Line A: y = 9 − 2x, Line B: y = 6 – x Data points: a. plot the data points and the first linear equation on one graph and the data points and the second linear equation on another. b. construct tables for x, y, y, e, and eˆ2. c. determine which line fits
> For which of the following sets of data points can you reasonably determine a regression line? Explain your answer.
> For which of the following sets of data points can you reasonably determine a regression line? Explain your answer.
> Answer true or false to each statement, and explain your Answers. a. The graph of a linear equation slopes upward unless the slope is 0. b. The value of the y-intercept has no effect on the direction that the graph of a linear equation slopes.
> Fill in the blanks. a. In the context of regression, an ____ is a data point that lies far from the regression line, relative to the other data points. b. In regression analysis, an ____ is a data point whose removal causes the regression equation to cha
> The members of a population have been numbered 1–50. A sample of size 20 is to be taken from the population, using cluster sampling. The clusters are of equal size 10, where cluster #1 consists of the members of the population numbered 1–10, cluster #2 c
> Regarding probability sampling: a. What is it? b. Does probability sampling always yield a representative sample? Explain your answer. c. Identify some advantages of probability sampling.
> Using the regression equation to make predictions for values of the predictor variable outside the range of the observed values of the predictor variable is called ___ .
> Regarding the two variables under consideration in a regression analysis, a. what is the dependent variable called? b. what is the independent variable called?
> Regarding the line that best fits a set of data points, a. what is that line called? b. what is the equation of that line called?
> Regarding the criterion used to decide on the line that best fits a set of data points, a. what is that criterion called? b. specifically, what is the criterion?
> Regarding a scatterplot, a. identify one of its uses. b. what property should it have to obtain a regression line for the data?
> In this section, we stated that any no vertical line can be described by an equation of the form y = b0 + b1x. a. Explain in detail why a vertical line can’t be expressed in this form. b. What is the form of the equation of a vertical line? c. Does a ver
> The grade of a road is defined as the distance it rises (or falls) to the distance it runs horizontally, usually expressed as a percentage. Consider a road with positive grade, g. Suppose that you begin driving on that road at an altitude a0. a. Find the
> According to Hooke’s law for springs, developed by Robert Hooke (1635–1703), the force exerted by a spring that has been compressed to a length x is given by the formula F = −k(x − x0), where x0 is the natural length of the spring and k is a constant, ca
> Refer to Exercise 4.26. The linear equation is y = 64 − 32x. a. find the y-intercept and slope of the specified linear equation. b. explain what the y-intercept and slope represent in terms of the graph of the equation. c. explain what the y-intercept an
> Consider the linear equation y = b0 + b1x. a. Identify and give the geometric interpretation of b0. b. Identify and give the geometric interpretation of b1.
> A quantitative data set of size 60 has mean 100 and standard deviation 16. At least how many observations lie between 68 and 132?
> The members of a population have been numbered 1–500. A sample of size 9 is to be taken from the population, using systematic random sampling. a. Apply Procedure 1.1 to determine the sample (i.e., the numbers corresponding to the members of the populatio
> Refer to Exercise 4.25. The linear equation is y = 32 + 1.8x. a. find the y-intercept and slope of the specified linear equation. b. explain what the y-intercept and slope represent in terms of the graph of the equation. c. explain what the y-intercept a
> Refer to Exercise 4.24. The linear equation is y = 30 + 55x. a. find the y-intercept and slope of the specified linear equation. b. explain what the y-intercept and slope represent in terms of the graph of the equation. c. explain what the y-intercept an
> Refer to Exercise 4.23. The linear equation is y = 68.22 + 0.25x. a. find the y-intercept and slope of the specified linear equation. b. explain what the y-intercept and slope represent in terms of the graph of the equation. c. explain what the y-interce
> A ball is thrown straight up in the air with an initial velocity of 64 feet per second (ft/sec). According to the laws of physics, if you let y denote the velocity of the ball after x seconds, y = 64 − 32x. a. Determine b0 and b1 for this linear equation
> The two most commonly used scales for measuring temperature are the Fahrenheit and Celsius scales. If you let y denote Fahrenheit temperature and x denote Celsius temperature, you can express the relationship between those two scales with the linear equa
> Richard’s Heating and Cooling in Prescott, Arizona, charges $55 per hour plus a $30 service charge. Let x denote the number of hours required for a job, and let y denote the total cost to the customer. a. Find the equation that expresses y in terms of x.
> During one month, the Avis Rent-A-Car rate for renting a Buick LeSabre in Mobile, Alabama, was $68.22 per day plus 25c/ per mile. For a 1-day rental, let x denote the number of miles driven and let y denote the total cost, in dollars. a. Find the equatio
> 0 and 3 a. determine whether it slopes upward, slopes downward, or is horizontal, without graphing the equation. b. find its equation. c. use two points to graph the equation.
> 3 and 0 a. determine whether it slopes upward, slopes downward, or is horizontal, without graphing the equation. b. find its equation. c. use two points to graph the equation.
> A quantitative data set of size 80 has mean 30 and standard deviation 5. At least how many observations lie between 20 and 40?
> −1.5 and 0 a. determine whether it slopes upward, slopes downward, or is horizontal, without graphing the equation. b. find its equation. c. use two points to graph the equation.
> The members of a population have been numbered 1–372. A sample of size 5 is to be taken from the population, using systematic random sampling. a. Apply Procedure 1.1 to determine the sample (i.e., the numbers corresponding to the members of the populatio
> Fill in the blank. The graph of a linear equation with one independent variable is a ____.
> 0 and −0.5 a. determine whether it slopes upward, slopes downward, or is horizontal, without graphing the equation. b. find its equation. c. use two points to graph the equation.
> 0.4 and 1 a. determine whether it slopes upward, slopes downward, or is horizontal, without graphing the equation. b. find its equation. c. use two points to graph the equation.
> Exercise 4.163 a. construct a scatterplot for the data. b. decide whether using the rank correlation coefficient is reasonable. c. decide whether using the linear correlation coefficient is reasonable. d. find and interpret the rank correlation coefficie
> −2 and −3 a. determine whether it slopes upward, slopes downward, or is horizontal, without graphing the equation. b. find its equation. c. use two points to graph the equation.
> Exercise 4.14 a. construct a scatterplot for the data. b. decide whether using the rank correlation coefficient is reasonable. c. decide whether using the linear correlation coefficient is reasonable. d. find and interpret the rank correlation coefficien
> A Knight-Ridder News Service article in an issue of the Wichita Eagle discussed a study on the relationship between country music and suicide. The results of the study, coauthored by S. Stack and J. Gundlach, appeared as the paper “The Effect of Country
> The coefficient of determination of a set of data points is 0.716. a. Can you determine the linear correlation coefficient? If yes, obtain it. If no, why not? b. Can you determine whether the slope of the regression line is positive or negative? Why or w
> A quantitative data set has size 50. At least how many observations lie within three standard deviations to either side of the mean?
> In the article “Comparison of Fiber Counting by TV Screen and Eyepieces of Phase Contrast Microscopy” (American Industrial Hygiene Association Journal, Vol. 63, pp. 756–761), I. Moa et al. reported on determining fiber density by two different methods. T
> The data for estriol levels of pregnant women and birth weights on the WeissStats site. Use the technology of your choice to a. decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate. If so, then als
> Surveys that combine one or more of simple random sampling, systematic random sampling, cluster sampling, and stratified sampling employ what is called sampling.
> The data for age and percentage of body fat for 18 randomly selected adults are on the WeissStats site. Use the technology of your choice to a. decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate.
> The data for volume, in cubic feet, and diameter at breast height, in inches, for 70 shortleaf pines are on the WeissStats site. Use the technology of your choice to a. decide whether use of the linear correlation coefficient as a descriptive measure for
> The data for gas mileage and engine displacement for 121 vehicles are provided on the WeissStats site. Use the technology of your choice to a. decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate.
> The data for per capita income and per capita beer consumption for the 50 states and Washington, D.C.. are on the WeissStats site. Use the technology of your choice to a. decide whether use of the linear correlation coefficient as a descriptive measure f
> The data on shell thickness and concentration of PCBs for 60 Anacapa pelican eggs are on the WeissStats site. Use the technology of your choice to a. decide whether use of the linear correlation coefficient as a descriptive measure for the data is approp
