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 and slope represent in terms relating to the application. Data from Exercise 4.24: 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. b. Determine b0 and b1. c. Construct a table similar to Table 4.1 on page 158 for the x-values 0.5, 1, and 2.25 hours. d. Draw the graph of the equation that you determined in part (a) by plotting the points from part (c) and connecting them with a line. e. Apply the graph from part (d) to estimate visually the cost of a job that takes 1.75 hours. Then calculate that cost exactly by using the equation from part (a).
> 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?
> 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.
> 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 4.23. 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
> −3 and 4 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 data for average high and low temperatures in January for a random sample of 50 cities 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
> A quantitative data set has size 60. At least how many observations lie within three standard deviations to either side of the mean?
> The data for home size (in square feet) and assessed value (in thousands of dollars) for the same homes 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
> The data for lot size (in acres) and assessed value (in thousands of dollars) for a sample of homes in a particular area are on the WeissStats site. Use the technology of your choice to a. decide whether use of the linear correlation coefficient as a des
> The data on domestic and overseas grosses for a random sample of 50 movies 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.
> Ideally, in stratified sampling, the members of each stratum should be relative to the characteristic under consideration.
> The data for the ages at inauguration and of death for the presidents of the United States 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
> The data for number of birdies during a tournament and final score for 63 women golfers 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
> Perform the following tasks. a. Compute the linear correlation coefficient, r. b. Can you conclude from your answer in part (a) that the variables x and y are linearly related? Explain your answer. c. Draw a scatterplot for the data. d. Is use of the lin
> Perform the following tasks. a. Compute the linear correlation coefficient, r. b. Can you conclude from your answer in part (a) that the variables x and y are linearly related? Explain your answer. c. Draw a scatterplot for the data. d. Is use of the lin
> Consider the following set of data points. a. Compute the linear correlation coefficient, r. b. Can you conclude from your answer in part (a) that the variables x and y are unrelated? Explain your answer. c. Draw a scatterplot for the data. d. Is use of
> A random sample of 10 students was taken from an introductory statistics class. The following data were obtained, where x denotes height, in inches, and y denotes score on the final exam. a. What sort of value of r would you expect to find for these data
> A quantitative data set has size 80. At least how many observations lie within two standard deviations to either side of the mean
> 5 and 2 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.
> Following are the data on study time and score for calculus students. a. obtain the linear correlation coefficient. b. interpret the value of r in terms of the linear relationship between the two variables in question. c. discuss the graphical interpreta
> Following are the data on age and crown-rump length for fetuses. a. obtain the linear correlation coefficient. b. interpret the value of r in terms of the linear relationship between the two variables in question. c. discuss the graphical interpretation
> Following are the data on plant weight and quantity of volatile emissions. a. obtain the linear correlation coefficient. b. interpret the value of r in terms of the linear relationship between the two variables in question. c. discuss the graphical inter
> Ideally, in cluster sampling, each cluster should the entire population.
> Following are the size and price data for custom homes. a. obtain the linear correlation coefficient. b. interpret the value of r in terms of the linear relationship between the two variables in question. c. discuss the graphical interpretation of the va
> Following are the age and price data for Corvettes. a. obtain the linear correlation coefficient. b. interpret the value of r in terms of the linear relationship between the two variables in question. c. discuss the graphical interpretation of the value
> Following are the data on percentage of investments in energy securities and tax efficiency. a. obtain the linear correlation coefficient. b. interpret the value of r in terms of the linear relationship between the two variables in question. c. discuss t
> Determine the linear correlation coefficient by using a. Definition 4.8. b. Formula 4.3. Compare your answers in parts (a) and (b).
> Determine the linear correlation coefficient by using a. Definition 4.8. b. Formula 4.3. Compare your answers in parts (a) and (b).
