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Mind On Statistics 4th Edition David D Busch, Jessica M Utts, Robert F Heckard - Solutions

Use the dataset cholesterol on the companion website. For n 5 28 heart attack patients, the variables 2-Day and 4-Day are cholesterol levels measured 2 days and 4 days, respectively, after the attacks.a. Plot 4-Day (y) versus 2-Day (x). Describe the direction and strength of the relationship, and
Use the dataset oldfaithful on the companion website; it gives data for n 5 299 eruptions of the Old Faithful geyser.The variable Duration is the duration (minutes) of an eruption, and the variable TimeNext is the time interval (minutes) until the next eruption.a. Plot TimeNext (y) versus Duration
Use the dataset poverty on the companion website; it includes teenage mother birth rates and poverty rates for the 50 states and the District of Columbia. The variable PovPct is the percent of a state’s population in 2000 living in households with incomes below the federally defined poverty
The following is from Thought Question 3.4 on page 89.Sometimes the main purpose of a regression analysis is to determine the nature of the relationship between two variables, and sometimes the main purpose is to use the equation in the future to predict a y value when the x value is known. Explain
Measure the heights and weights of ten friends of the same sex.a. Draw a scatterplot of the data, with weight on the vertical axis and height on the horizontal axis. Draw a line onto the scatterplot that you believe describes the average pattern. On the basis of two points on this line, estimate
Give an example of a situation not mentioned elsewhere in this chapter in which two variables have no causal connection but are highly correlated because they are both related to a third variable. Explain what the third variable is.
◆ For a statistics class project at a large northeastern university, a student examined the relationship between the following two variables:x 5 body weight (in pounds)y 5 time to chug a 12-ounce beverage (in seconds)We’ll leave it to you to imagine the beverage. The student collected data from
◆ Refer to Exercise 3.90 about the trend in number of persons per household.a. Using statistical software, determine the least squares line for these data. Use the equation of this line to estimate the number of persons per household in the year 2010 (Data source: perhouse dataset on the website
◆ U.S. Census Bureau estimates of the average number of persons per household in the United States for census years between 1850 and 2000 are shown in the following table.(These data are in the file perhouse on the companion website.)
◆ The following table lists the number of pages and the price for 18 books, sorted in order of increasing number of pages. Ten of the books are hardcover and eight are softcover. (These data are in the dataset ProfBooks on the companion website.)a. Draw a scatterplot of y 5 price versus x 5
The winning time in the Olympic men’s 500-meter speed skating race over the years 1924 to 2006 can be described by the following regression equation:Winning time 5 272.63 2 0.1184 1Year2
◆ Refer to Exercise 3.86 about y 5 foot length and x 5 height. (Data source: the heightfoot dataset on the companion website.) If the person who reportedly is 84 inches tall is excluded, the regression equation for the remaining 32 men is y^ 5 0.25 1 0.384x.a. How much does average foot length
◆ The heights (inches) and foot lengths (cm) of 33 college men are shown in the following table. (These data are in the dataset heightfoot on the companion website.)
Refer to Case Study 3.1, in which regression equations are given for males and females relating ideal weight to actual weight. The equations area. Predict the ideal weight for a man who weighs 140 pounds and for a woman who weighs 140 pounds.Compare the results.b. Do the intercepts have logical
The regression line relating verbal SAT scores and college GPA for the data exhibited in Figure 3.12 is Average GPA 5 0.539 1 0.00362 1Verbal SAT2a. Estimate the average GPA for those with verbal SAT scores of 600.b. Explain what the slope of 0.00362 represents in terms of the relationship between
◆ The regression relationship for y 5 student height and x 5 father’s height for the 10 female students listed in the table for Exercise 3.12 and in the dataset UCDchap3 is y^ 5 19.42 1 0.658xa. Give the value of the y-intercept. Does it have a meaningful interpretation in this situation?
◆ Refer to Exercise 3.81 in which the regression relationship between age in years and body temperature in degrees Fahrenheit is given as y^ 5 98.6 2 0.0138x, based on data from 100 blood donors ranging in age from 17 to 84 years old.a. What is the y-intercept for this relationship? Does it have
◆ The dataset bodytemp on the companion website gives age in years and body temperature in degrees Fahrenheit for 100 blood donors ranging in age from 17 to 84 years old. The regression equation is y^ 5 98.6 2 0.0138x.a. In the regression relationship shown, which variable is the response
Using the applet with the target correlation r 5 0, make a plot that has a curvilinear pattern for which the correlation is 0. Sketch an approximate facsimile of your resulting graph.
Using the applet, create a plot for the target correlation r 5 20.8 in which one point is an outlier that inflates the correlation. Make the plot such that if the outlier were removed, the correlation for the remaining points would be between 20.2 and 10.2. Sketch an approximate facsimile of your
Using the applet, create a plot for the target correlation r 5 10.5 in which one point is an outlier that decreases the correlation. Make the plot such that if the outlier were removed, the correlation for the remaining points would be greater than r 5 0.7. Sketch an approximate facsimile of your
Using the applet, create a plot for the target correlation r 5 0. Don’t include any outliers. Sketch an approximate facsimile of your resulting graph.
Using the applet, create a plot for the target correlation r 5 20.8. Don’t include any outliers. Sketch an approximate facsimile of your resulting graph.
Using the applet, create a plot for the target correlation r 5 10.5. Don’t include any outliers. Sketch an approximate facsimile of your resulting graph.
Researchers have shown that there is a positive correlation between average fat intake and the breast cancer rate across countries. In other words, countries with higher fat intake tend to have higher breast cancer rates. Does this correlation prove that dietary fat is a contributing cause of
It is said that a higher proportion of drivers of red cars are given tickets for traffic violations than drivers of any other car color. Does this mean that if you drive a red car rather than a car of some other color, it will cause you to get more tickets for traffic violations? Explain.
Give an example not given elsewhere in this chapter of two variables that are likely to be correlated because they are both changing over time.
Suppose a medical researcher finds a negative correlation between amount of weekly walking and the incidence of heart disease for people over 50 years old; in other words, people who walked more had a lower incidence of heart disease. One possible explanation for this observed association is that
Give an example of a situation in which it would be reasonable to conclude that an explanatory variable causes changes in a response variable.
Suppose that in an observational study, it is observed that the risk of heart disease increases as the amount of dietary fat consumed increases. Write a paragraph discussing why this result does not imply that diets high in fat cause heart disease.
Suppose the indicated relationship has been found between each of the following sets of variables. For each set, discuss possible reasons why the connection may not be causal.Refer to the list of possible reasons for an observed association in Section 3.5.a. A negative relationship between average
Suppose a positive relationship had been found between each of the following sets of variables. For each set, discuss possible reasons why the connection may not be causal.Refer to the list of possible reasons for an observed association in Section 3.5.a. Number of deaths from automobiles and soft
◆ The pennstate2 dataset on the companion website includes heights and the total number of ear pierces for each person in a sample of college students. The correlation be-tween the two variables is 20.495. What third variable may explain this observed correlation? Explain how that third variable
Based on the data for the past 50 years in the United States, there is a strong correlation between yearly beer sales and yearly per capita income. Would you interpret this to mean that increasing a person’s income will cause him or her to drink more beer? Explain.
Explain why a strong correlation would be found between weekly sales of firewood and weekly sales of cough drops over a 1-year period.
◆ The table for Exercise 3.9 gave the average August temperature (y) and geographic latitude (x) for 20 cities in the United States. (The data are part of the temperature dataset on the companion website.) Exercise 3.18 gave the information that the regression equation relating these two
In Exercise 3.21, a regression equation relating x 5 putting distance (feet) to y 5 success rate (in percent) for professional golfers was given as Success rate 5 76.5 2 3.95 (Distance)The equation was based on observations of distances ranging from 5 feet to 15 feet.a. Use the equation to predict
◆ The data in the following table come from a time when the United States had a maximum speed limit of 55 miles per hour in all states. An issue of some concern at that time was whether lower speed limits reduce the highway death rate. (These data are called speedlimit on the companion website.)
Give an example of a prediction that is an extrapolation. Do not give an example that is already in this chapter.
The data in the table for Exercise 3.11 gave the square footage and asking price for nine homes for sale in Orange County, California in February 2010. The house with a square footage of 5500 is an obvious outlier.The value of r 2 for the relationship between y 5 asking price and x 5 square footage
A memorization test is given to ten women and ten men.The researchers find a negative correlation between scores on the test and height. Explain which of the reasons listed at the beginning of Section 3.4 for misleading correlations might explain this finding. Sketch a scatterplot for the
When a correlation value is reported in research journals, there often is not an accompanying scatterplot. Explain why reported correlation values should be supported with either a scatterplot or a description of the scatterplot.
Refer back to Exercise 3.7 about stopping distance and vehicle speed. The least squares line for these data is Average distance 5 244.2 1 5.7 (Speed)a. Use this equation to estimate the average stopping distance when the speed is 80 miles per hour. Do you think this is an accurate estimate?
Sketch a scatterplot in which the correlation without an outlier is negative, but the correlation when the outlier is added is positive. Indicate on your plot which point is the outlier.
Sketch a scatterplot in which the presence of an outlier decreases the observed correlation between the response and explanatory variables. Indicate on your plot which point is the outlier.
◆ The physical dataset on the companion website gives heights (inches) and head circumferences (cm) for a sample of college students. For females only, the correlation between the two variables is 0.05, while for males only, the correlation is 0.19. For the combined sample of males and females,
An article in the Sacramento Bee (May 29, 1998, p. A17)noted, “Americans are just too fat, researchers say, with 54 percent of all adults heavier than is healthy. If the trend continues, experts say that within a few generations virtually every U.S. adult will be overweight.” This prediction is
The average January temperatures (y) and geographic latitudes (x) of 20 cities in the United States were given in the table for Exercise 3.9. The regression equation for these data was given in Exercise 3.24 as y^ 5 1.26 2 2.34x.The value of r 2 for this relationship is 73.3%. What is the
Suppose you know that the slope of a regression line is b1 5 13.5. Based on this value, explain what you know and do not know about the strength and direction of the relationship between the two variables.
◆ The data in the table for Exercise 3.12 show the heights and average of parents’ heights, called “mid-parent height,”for each of 18 college students. The data are also in the file UCDchap3 where the mother’s and father’s heights are provided for each student as well. Student’s
In a regression analysis, the total sum of squares (SSTO) is 800, and the error sum of squares (SSE) is 200. What is the value for r 2?
◆ Refer to Exercise 3.12 and the table for Exercise 3.12 in which heights and mid-parent heights are given for 18 college students (Data source: UCDchap3 dataset on the website for this book). Draw a scatterplot for the data, using different symbols for males and females as instructed in part(b)
Calculate r 2 for Example 3.15 in this chapter (about hours of sleep and hours of study) in which the correlation is 20.36.Write a sentence that interprets this value.
◆ The correlation between latitude and average August temperature is 20.78 for the 20 cities shown in the table for Exercise 3.9. (The data also are in the dataset temperature on the companion website.)a. Calculate r 2 and write a sentence that interprets it in the context of this situation.b. If
◆ The correlation between height and weight is r 5 0.40 for 12th-grade male respondents (n 5 1501) in a survey done in 2003 by the U.S. Centers for Disease Control and Prevention as part of the Youth Risk Behavior Surveillance System. (The raw data are in the dataset YouthRisk03 on the companion
For each pair of variables, identify whether the pair is likely to have a positive correlation, a negative correlation, or no correlation. Briefly indicate your reasoning.a. Verbal skills and age for children under 12 years old.b. Height of husband and height of wife.c. Number of dogs and number of
For each pair of variables, identify whether the pair is likely to have a positive correlation, a negative correlation, or no correlation. Briefly indicate your reasoning.a. Hours of television watched per day and grade point average for college students.b. Number of liquor stores and number of
◆ The dataset bodytemp on the companion website gives age in years and body temperature in degrees Fahrenheit for 100 blood donors ranging in age from 17 to 84 years old.A scatterplot showed a linear relationship with a correlation between age and body temperature of 20.313. Using this value,
In the 1996 General Social Survey, the correlation between respondent age and hours of daily television viewing for n 5 1913 respondents was r 5 10.12. Using this value, characterize the nature of the relationship between age and hours of television watching in 1996.
Refer to the figure for the previous exercises. In scrambled order, correlation values for these four graphs are 20.9, 0, 10.3, and 10.6. Match these correlation values to the graphs.
The figure for this exercise (see next figure) shows four graphs. Assume that all four graphs have the same numerical scales for the two axes. Which graph shows the strongest relationship between the two variables? Which graph shows the weakest?
Sketch a scatterplot showing data for which the correlation is r 5 21.
Suppose two variables have a deterministic linear relationship with a positive association. What is the value of the correlation between them?
Explain how two variables can have a perfect curved relationship yet have zero correlation. Draw a picture of a set of data meeting those criteria.
In Figure 3.11 (p. 84), we observed that the correlation between the left and right handspans of college students was 0.95. The handspans were measured in centimeters. What would be the correlation if the handspans were converted to inches? Explain.
Which implies a stronger linear relationship: a correlation of 10.4 or a correlation of 20.6? Briefly explain.
◆ For 19 female bears, the correlation between x 5 length of the bear (inches) and y 5 chest girth (inches) is r 5 0.82.(Data source: bears-female dataset on the companion website.)a. Describe how chest girth will change when length is increased.b. Assuming that there are no outliers and the
Suppose the value of r 2 is 100% for the relationship between two variables.a. What is indicated about the strength of the relationship?b. What are the two possible values for the correlation coefficient for the two variables?
For n 5 188 students, the correlation between y 5 fastest speed ever driven and x 5 number randomly picked between 1 and 10 is about r 5 0. Describe what this cor relation indicates about the association between the fastest speed driven and picking a number between 1 and 10.
Remember that r 2 can be expressed as a proportion or as a percent. (When written as a percent, the percent sign will always be included.)a. Explain which of the following could not be a value for r 2: 0, 20.25, 0.3, 1.0, 1.7, 25%, 250%, 1200%.b. Refer to the values in part (a). Which one of the
Which of the numbers 0, 0.25, 21.7, 20.5, and 2.5 could not be values of a correlation coefficient? In each case, explain why?
The least squares regression equation for the data in the following table is y^ 5 5 1 2x.x 4 4 7 10 10 y 15 11 19 21 29a. Calculate the value of y^ for each data point.b. Calculate the sum of squared errors for this equation.
The data for this exercise are as follows:x 1234 y 4 10 14 16a. Determine the sum of squared errors (SSE) for each of the following two lines:Line 1: y^ 5 3 1 3x Line 2: y^ 5 1 1 4xb. By the least squares criterion, which of the two lines is better for these data? Why is it better?
◆ The average January temperatures (y) and geographic latitudes (x) of 20 cities in the United States were given in the table for Exercise 3.9. (The data are part of the temperature dataset on the companion website.) The regression equation for these data is y^ 5 1.26 2 2.34xa. What is the slope
◆ Refer to Exercise 3.22.a. Predict the pulse rate after marching for somebody with a resting pulse rate of 70.b. Suppose the pulse rate after marching is 76 for somebody whose resting pulse rate is 70. What is the residual (prediction error) for this individual?
◆ The figure for Exercise 3.8 is a scatterplot of pulse rate after marching in place for 1 minute (y) versus resting pulse rate measured before marching (x) for n 5 63 individuals.(The data are in the pulsemarch dataset on the companion website.) The regression equation for these data is Pulse
Iman (1994) reports that for professional golfers, a regression equation relating x 5 putting distance (in feet) and y 5 success rate (in percent) based on observations of distances ranging from 5 feet to 15 feet is Success rate 5 76.5 2 3.95 (Distance)a. What percentage of success would you expect
Imagine a regression line that relates y 5 average systolic blood pressure to x 5 age. The average blood pressure for people 30 years old is 120, while for those 50 years old the average is 130.a. What is the slope of the regression line?b. What is the estimated average systolic blood pressure for
A regression equation for y 5 handspan (cm) and x 5 height(inches) was discussed in Section 3.2. If the roles of the variables are reversed and only women are considered, the regression equation is Average height 5 51.1 1 0.7 (Handspan).a. Interpret the slope of 0.7 in terms of how height changes
The average August temperatures (y) and geographic latitudes (x) of 20 cities in the United States were given in the table for Exercise 3.9. (The data are part of the temperature dataset on the companion website.) The regression equation for these data is y^ 5 113.6 2 1.01xa. What is the slope of
The equation for converting a temperature from x 5 degrees Celsius to y 5 degrees Fahrenheit is y 5 32 1 1.8x. Does this equation describe a statistical relationship or a deterministic relationship? Briefly explain your answer.
A school cafeteria has a salad bar that is priced based on weight, with salads costing 30 cents an ounce. Students fill a container that weighs 8 ounces when it is empty. Define x to be the weight of the filled container (in ounces) and y to be the price the student is charged (in dollars). The
(Percent took)a. The slope of the equation is 21.11. Interpret this value in the context of how average math SAT changes when the percent of graduates taking the test changes.b. In Missouri, only 8% of graduates took the SAT test. What is the predicted average math SAT score for Missouri?c. In
showing the relationship between the average math SAT score and the percentage of high school graduates taking the test for the 50 states and District of Columbia. (The data are from the sats98 dataset on the companion website.) The regression line for these data is Average math 5 575 2
Refer to the scatterplot for Exercise
in which a regression equation is given that relates average weight and height for men in the 18- to 29-year-old age group.a. Suppose a man in this age group is 72 inches tall. Use the regression equation given in the previous exercise to predict the weight of this man.b. Suppose this man, who is
Refer to Exercise
Suppose that a regression equation for the relationship between y 5 weight (pounds) and x 5 height (inches) for men aged 18 to 29 years old is Average weight 5 2250 1 6 (Height)a. Estimate the average weight for men in this age group who are 70 inches tall.b. What is the slope of the regression
◆ The following table shows sex, height (inches), and midparent height (inches) for a sample of 18 college students.The variable mid-parent height is the average of mother’s height and father’s height. (These data are in the dataset UCDchap3 on the companion website; they are sampled from the
The data in the following table show the square footage and asking price (in thousands of dollars) for nine homes for sale in Orange County, California in February 2010. Orange County has a mixture of residential areas, including suburban neighborhoods and exclusive beachfront properties.a. In the
◆ Refer to the latitude and temperature data in the table presented in Exercise 3.9, which also appear in the temperature dataset on the companion website.a. Draw a scatterplot of y 5 January temperature versus x 5 latitude.b. Is the pattern linear or curved?c. Is the direction of the association
The data in the following table are the geographic latitudes and the average August and January temperatures (Fahrenheit) for 20 cities in the United States. The cities are listed in geographic order from south to north. (These data are part of the temperature dataset on the companion website.)a.
The figure for this exercise is a scatterplot of y 5 pulse rate after marching in place for 1 minute versus x 5 resting pulse rate measured before marching in place. (The data are in the pulsemarch dataset on the companion website.)
The following table shows the relationship between the speed of a car (mph) and the average stopping distance(feet) after the brakes are applied:a. In the relationship between these two variables, which is the response variable (y) and which is the explanatory variable (x)?b. Draw a scatterplot of
Identify whether a scatterplot would or would not be an appropriate visual summary of the relationship between the following variables. In each case, explain your reasoning.a. Verbal SAT score and math SAT score.b. Handspan and sex (male or female).
Identify whether a scatterplot would or would not be an appropriate visual summary of the relationship between the following variables. In each case, explain your reasoning.a. Blood pressure and age.b. Region of country and opinion about stronger gun control laws.
The figure for this exercise is a scatterplot of y 5 head circumference (cm) versus x 5 height (inches) for the 30 females in the physical dataset on the companion website.a. Does the plot show a positive association, a negative association, or no association between the two variables?Explain.b.
◆ The figure for this exercise is a scatterplot of y 5 average math SAT score in 1998 versus x 5 percent of graduating seniors who took the test that year for the 50 states and the District of Columbia. The data are from the sats98 dataset on the companion website.a. Does the plot show a positive
For each of the following pairs of variables, is there likely to be a positive association, a negative association, or no association? Briefly explain your reasoning.a. Miles of running per week and time for a 5-kilometer run.b. Forearm length and foot length.c. Grade level and height for children
For each of the following pairs of variables, is there likely to be a positive association, a negative association, or no association? Briefly explain your reasoning.a. Amount of alcohol consumed and performance on a test of coordination, where a high score represents better coordination.b. Height

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