Solved: You Explain It! Video Games and GPAsA student at

The difference between the observed and predicted value of y is the error, or ________.

Problem 2AYU If the linear correlation between two variables is negative, what can be said about the slope of the regression line?

Problem 3AYU True or False: The least-squares regression line always travels through the point (x, y).

Problem 4AYU If the linear correlation coefficient is 0, what is the equation of the least-squares regression line?

Problem 5AYU For the data set x 0 2 3 5 6 6 y 5.8 5.7 5.2 2.8 1.9 2.2 (a)Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. ________________ (b)Given that sx= 2.4221, sy = 1.8239, and r = –0.9477,determine the least-squares regression line. ________________ (c)Graph the least-squares regression line on the scatter diagram drawn in part (a)

Problem 6AYU For the data set x 2 4 8 8 9 y 1.4 1.8 2.1 2.3 2.6 (a)Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. ________________ (b)Given that sx = 3.03315, sy = 0.461519, and r = 0.957241, ________________ (c)Graph the least-squares regression line on the scatter diagram drawn in part (a).

Problem 7AYU In Problems (a)By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable. (b)Select two points from the scatter diagram and find the equation of the line containing the points selected. (c)Graph the line found in part (b) on the scatter diagram. (d)By hand, determine the least-squares regression line. (e)Graph the least-squares regression line on the scatter diagram. (f )Compute the sum of the squared residuals for the line found in part (b). (g)Compute the sum of the squared residuals for the least-squares regression line found in part (d). (h)Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d). x 3 4 5 7 8 y 4 6 7 12 14

In Problems 7-12: (a) By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) By hand, determine the least-squares regression line. (e) Graph the least-squares regression line on the scatter diagram. (f ) Compute the sum of the squared residuals for the line found in part (b). (g) Compute the sum of the squared residuals for the least-squares regression line found in part (d). (h) Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d).

Problem 9AYU In Problems (a).By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable (b)Select two points from the scatter diagram and find the equation of the line containing the points selected. (c)Graph the line found in part (b) on the scatter diagram. (d)By hand, determine the least-squares regression line. (e)Graph the least-squares regression line on the scatter diagram. (f )Compute the sum of the squared residuals for the line found in part (b). (g)Compute the sum of the squared residuals for the least-squares regression line found in part (d). (h)Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d). x -2 -1 0 1 2 y -4 0 1 4 5

Problem 10AYU In Problems (a)By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable. (b)Select two points from the scatter diagram and find the equation of the line containing the points selected. (c)Graph the line found in part (b) on the scatter diagram. (d)By hand, determine the least-squares regression line. (e)Graph the least-squares regression line on the scatter diagram. (f )Compute the sum of the squared residuals for the line found in part (b). (g)Compute the sum of the squared residuals for the least-squares regression line found in part (d). (h)Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d) x -2 -1 0 1 2 y 7 6 3 2 0

Problem 11AYU In Problems (a)By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable. (b)Select two points from the scatter diagram and find the equation of the line containing the points selected. (c)Graph the line found in part (b) on the scatter diagram. (d)By hand, determine the least-squares regression line. (e)Graph the least-squares regression line on the scatter diagram. (f )Compute the sum of the squared residuals for the line found in part (b). (g)Compute the sum of the squared residuals for the least-squares regression line found in part (d). (h)Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d). x 20 30 40 50 60 y 100 95 91 83 70

Problem 12AYU In Problems (a)By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable. (b)Select two points from the scatter diagram and find the equation of the line containing the points selected. (c)Graph the line found in part (b) on the scatter diagram. (d)By hand, determine the least-squares regression line. (e)Graph the least-squares regression line on the scatter diagram. (f )Compute the sum of the squared residuals for the line found in part (b). (g)Compute the sum of the squared residuals for the least-squares regression line found in part (d). (h)Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d). x 5 10 15 20 25 y 2 4 7 11 18

Problem 13AYU You Explain It! Video Games and GPAsA student at Joliet Junior College conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week, x, and grade-point average, y. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is ? = –0.0526 x + 2.9342. (a)Predict the grade-point average of a student who plays video games 8 hours per week. ________________ (b)Interpret the slope. ________________ (c)If appropriate, interpret the y-intercept. ________________ (d)A student who plays video games 7 hours per week has a grade-point average of 2.68. Is this student’s grade-point average above or below average among all students who play video games 7 hours per week?

Problem 14AYU You Explain It! Study Time and Exam ScoresAfter the first exam in a statistics course, Professor Katula surveyed 14 randomly selected students to determine the relation between the amount of time they spent studying for the exam and exam score. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is ? = 6.3333 x + 53.0298. (a)Predict the exam score of a student who studied 2 hours. ________________ (b)Interpret the slope. ________________ (c)What is the mean score of students who did not study? ________________ (d)A student who studied 5 hours for the exam scored 81 on the exam. Is this student’s exam score above or below average among all students who studied 5 hours?

You Explain It! Winning Percentage and On-base Percentage In his best-selling book Moneyball, author Michael Lewis discusses how statistics can be used to judge both a baseball player’s potential and a team’s ability to win games. One aspect of this analysis is that a team’s on-base percentage is the best predictor of winning percentage. The on-base percentage is the proportion of time a player reaches a base. For example, an on-base percentage of 0.3 would mean the player safely reaches bases 3 times out of 10, on average. For the 2010 baseball season, winning percentage, y, and on-base percentage, x, are linearly related by the least-squares regression equation \(\hat {y}= 3.4722 x – 0.6294\). (a) Interpret the slope. (b) For 2010, the lowest on-base percentage was 0.298 and the highest on-base percentage was 0.350. Use this information to explain why it does not make sense to interpret the y-intercept. (c) Would it be a good idea to use this model to predict the winning percentage of a team whose on-base percentage was 0.250? Why or why not? (d) The 2010 World Series Champion San Francisco Giants had an on-base percentage of 0.321 and a winning percentage of 0.568. What is the residual for San Francisco? How would you interpret this residual?

Problem 16AYU You Explain It! CO2 and Energy ProductionThe leastsquares regression equation ? = 0.7676 x – 52.6841 relates the carbon dioxide emissions (in hundred thousands of tons), y, and energy produced (hundred thousands of megawatts), x, for all countries in the world in 2010. (www.carma.org) (a)Interpret the slope. ________________ (b)Is the y-intercept of the model reasonable? Why? What would you expect the y-intercept of the model to equal? Why? ________________ (c)For 2010, the lowest energy-producing country was Rwanda, which produced 0.094 hundred thousand megawatts of energy. The highest energy-producing country was the United States, which produced 4190 hundred thousand megawatts of energy in 2010. Would it be reasonable to use this model to predict the CO2 emissions of a country if it produced 6394 hundred thousand megawatts of energy in 2010? Why or why not? ________________ (d)In 2010, China produced 3260 hundred thousand megawatts of energy and emitted 3120 hundred thousand tons of carbon dioxide. What is the residual for China? How would you interpret this residual?

Problem 17AYU An Unhealthy Commute(Refer to Problem An Unhealthy CommuteThe Gallup Organization regularly surveys adult Americans regarding their commute time to work. In addition, they administer a Well-Being Survey. According to the Gallup Organization, “The Gallup-Healthways Well-Being Index Composite Score is comprised of six sub-indices: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment and Basic Access.” A complete description of the index can be found athttp://www.well-beingindex.com/. The data in the following table are based on the results of the survey, which represent commute time to work (in minutes) and well-being index score. Commute Time (in minutes) Gallup-Healthways Well-Being Index Composite Score 5 69.2 15 68.3 25 67.5 35 67.1 50 66.4 72 66.1 105 63.9 The Gallup Organization (a)Which variable do you believe is likely the explanatory variable and which is the response variable? ________________ (b)Draw a scatter diagram of the data. ________________ (c)Determine the linear correlation coefficient between commute time and well-being index score. ________________ (d)Does a linear relation exist between the commute time and well-being index score? Problem Section. The following data represent commute times (in minutes) and score on a well-being survey. Commute Time (minutes), x Gallup-Healthways Well-Being Index Composite Score, y 5 69.2 15 68.3 25 67.5 35 67.1 50 66.4 72 66.1 105 63.9 (a)Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable. ________________ (b)Interpret the slope and y-intercept, if appropriate. ________________ (c)Predict the well-being index of a person whose commute is 30 minutes. ________________ (d)Suppose Barbara has a 20-minute commute and scores 67.3 on the survey. Is Barbara more “well-off” than the typical individual who has a 20-minute commute?

Problem 18AYU Credit Scores(Refer to Problem Credit ScoresYour Fair Isaacs Corporation (FICO) credit score is used to determine your creditworthiness. It is used to help determine whether you qualify for a mortgage or credit and is even used to determine insurance rates. FICO scores have a range of 300 to 850, with a higher score indicating a better credit history. The given data represent the interest rate (in percent) a bank would offer on a 36-month auto loan for various FICO scores. Credit Score Interest Rate (percent) 545 18.982 595 17.967 640 12.218 675 8.612 705 6.680 750 5.150 www.myfico.com (a)Which variable do you believe is likely the explanatory variable and which is the response variable? ________________ (b)Draw a scatter diagram of the data. ________________ (c)Determine the linear correlation coefficient between FICO score and interest rate on a 36-month auto loan. ________________ (d)Does a linear relation exist between the FICO score and interest rate? Problem Section. An economist wants to determine the relation between one’s FICO score, x, and the interest rate of a 36-month auto loan, y. The given data represent the interest rate (in percent) a bank would offer on a 36-month auto loan for various FICO scores. Credit Score, x Interest Rate (percent), y 545 18.982 595 17.967 640 12.218 675 8.612 705 6.680 750 5.150 www.myfico.com (a)Find the least-squares regression line treating the FICO score, x, as the explanatory variable and the interest rate, y, as the response variable. ________________ (b)Interpret the slope and y-intercept, if appropriate. Note: Credit scores have a range of 300 to 850. ________________ (c)Predict the interest rate a person would pay if her FICO scores were the median score of 723. ________________ (d)Suppose Bob has a FICO score of 680 and he is offered an interest rate of 8.3%. Is this a good offer? Why?

Height versus Head Circumference(Refer to Problem Height versus Head Circumference) A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects eleven 3-year-old children from her practice, measures their heights and head circumference, and obtains the data shown in the table on the next page. (a) If the pediatrician wants to use height to predict head circumference, determine which variable is the explanatory variable and which is the response variable. (b) Draw a scatter diagram. (c) Compute the linear correlation coefficient between the height and head circumference of a child. (d) Does a linear relation exist between height and head circumference? (e) Convert the data to centimeters (1 inch=2.54 cm), and recompute the linear correlation coefficient. What effect did the conversion have on the linear correlation coefficient?

Problem 20AYU American Black Bears(Refer to Problem American Black Bears The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the population in the Great Smoky Mountains National Park. One aspect of the study was to develop a model that could be used to predict a bear’s weight (since it is not practical to weigh bears in the field). One variable thought to be related to weight is the length of the bear. The following data represent the lengths and weights of 12 American black bears. Total Length (cm) Weight (kg) 139.0 110 138.0 60 139.0 90 120.5 60 149.0 85 141.0 100 141.0 95 150.0 85 166.0 155 151.5 140 129.5 105 150.0 110 fieldtripearth.org (a)Which variable is the explanatory variable based on the goals of the research? ________________ (b)Draw a scatter diagram of the data. ________________ (c)Determine the linear orrelation coefficient between weight and height. ________________ (d)Does a linear relation exist between the weight of the bear and its height?, Problem Section. The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the population in Great Smoky Mountains National Park. One aspect of the study was to develop a model that could be used to predict a bear’s weight (since it is not practical to weigh bears in the field). One variable thought to be related to weight is the length of the bear. The following data represent the lengths of 12 American black bears. Total Length (cm), x Weight (kg), y 139.0 110 138.0 60 139.0 90 120.5 60 149.0 85 141.0 100 141.0 95 150.0 85 166.0 155 151.5 140 129.5 105 150.0 110 www.fieldtripearth.org (a)Find the least-squares regression line, treating total length as the explanatory variable and weight as the response variable. ________________ (b)Interpret the slope and y-intercept, if appropriate. ________________ (c)Suppose a 149.0-cm bear is captured in the field. Use the least-squares regression line to predict the weight of the bear. ________________ (d)What is the residual of the 149.0-cm bear? Is this bear’s weight above or below average for a bear of this length?

Weight of a Car versus Miles per Gallon (Refer to Problem Weight of a Car versus Miles per Gallon) An engineer wants to determine how the weight of a car, x, affects gas mileage, y. The following data represent the weights of various domestic cars and their miles per gallon in the city for the 2011 model year. (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) A Buick Regal weighs 3600 pounds and gets 18 miles per gallon. Is the miles per gallon of a Regal above average or below average for cars of this weight? (d) Would it be reasonable to use the least-squares regression line to predict the miles per gallon of a Toyota Prius, a hybrid gas and electric car? Why or why not?

Bone Length (Refer to Problem Bone Length) Research performed at NASA and led by Emily R. Morey-Holton measured the lengths of the right humerus and right tibia in 11 rats that were sent to space on Spacelab Life Sciences 2. The following data were collected. (a) Draw a scatter diagram treating the length of the right humerus as the explanatory variable and the length of the right tibia as the response variable. (b) Compute the linear correlation coefficient between the length of the right humerus and the length of the right tibia. (c) Does a linear relation exist between the length of the right humerus and the length of the right tibia? (d) Convert the data to inches (1 mm = 0.03937 inch), and recompute the linear correlation coefficient. What effect did the conversion from millimeters to inches have on the linear correlation coefficient?

Cola Consumption vs. Bone Density Example 5 in Section 4.1 on page 185 discussed the effect of cola consumption on bone mineral density in the femoral neck of women. (a) Find the least-squares regression line treating cola consumption per week as the explanatory variable. (b) Interpret the slope. (c) Interpret the intercept. (d) Predict the bone mineral density of the femoral neck of a woman who consumes four colas per week. (e) The researchers found a woman who consumed four colas per week to have a bone mineral density of 0.873 g/cm2. Is this woman’s bone mineral density above or below average among all women who consume four colas per week? (f) Would you recommend using the model found in part (a) to predict the bone mineral density of a woman who consumes two cans of cola per day? Why?

Problem 24AYU Attending Class The following data represent the number of days absent, x, and the final grade, y, for a sample of college students in a general education course at a large state university. No. of absences, x 0 1 2 3 4 5 6 7 8 9 Final grade, y 89.2 86.4 83.5 81.1 78.2 73.9 64.3 71.8 65.5 66.2 College Teaching, 53(1), 2005. (a)Find the least-squares regression line treating number of absences as the explanatory variable and final grade as the response variable. ________________ (b)Interpret the slope and y-intercept, if appropriate. ________________ (c)Predict the final grade for a student who misses five class periods and compute the residual. Is the final grade above or below average for this number of absences? ________________ (d)Draw the least-squares regression line on the scatter diagram of the data. ________________ (e)Would it be reasonable to use the least-squares regression line to predict the final grade for a student who has missed 15 class periods? Why or why not?

CEO Performance (Refer to Problem CEO Performance) The following data represent the total compensation for 10 randomly selected chief executive officers (CEO) and the company’s stock performance in 2009. (a) One would think that a higher stock return would lead to a higher compensation. Based on this, what would likely be the explanatory variable? (b) Draw a scatter diagram of the data. (c) Determine the linear correlation coefficient between compensation and stock return. (d) Does a linear relation exist between compensation and stock return? Does stock performance appear to play a role in determining the compensation of a CEO?

Does Size Matter? (Refer to Problem Does Size Matter?) Researchers wondered whether the size of a person’s brain was related to the individual’s mental capacity. They selected a sample of right-handed introductory psychology students who had SAT scores higher than 1350. The subjects took the Wechsler Adult Intelligence Scale-Revised to obtain their IQ scores. MRI scans were performed at the same facility for the subjects. The scans consisted of 18 horizontal MR images. The computer counted all pixels with a nonzero gray scale in each of the 18 images, and the total count served as an index for brain size. (a) Draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable. Comment on what you see. (b) Compute the linear correlation coefficient between MRI count and IQ. Are MRI count and IQ linearly related? (c) A lurking variable in the analysis is gender. Draw a scatter diagram treating MRI count as the explanatory variable and IO as the response variable, but use a different plotting symbol for each gender. For example, use a circle for males and a triangle for females. What do you notice? (d) Compute the linear correlation coefficient between MRI count and IQ for females. Compute the linear correlation coefficient between MRI count and IO for males. Are MRI count and IQ linearly related? What is the moral?

Male vs. Female Drivers (Refer to Problem 34, Section 4.1.) The following data represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. \(\begin{array}{|c|c|c|c|c|} \hline \text { Age } & \begin{array}{c} \text { Number of } \\ \text { Male Licensed } \\ \text { Drivers (000s) } \end{array} & \begin{array}{c} \text { Number } \\ \text { of Fatal } \\ \text { Crashes } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Female Licensed } \\ \text { Drivers (000s) } \end{array} & \begin{array}{c} \text { Number } \\ \text { of Fatal } \\ \text { Crashes } \end{array} \\ \hline<16 & 12 & 227 & 12 & 77 \\ \hline 16-20 & 6,424 & 5,180 & 6,139 & 1,113 \\ \hline 21-24 & 6,941 & 5,016 & 6,816 & 2,780 \\ \hline 25-34 & 18,068 & 8,595 & 17,664 & 2,742 \\ \hline 35-44 & 20,406 & 7,990 & 20,063 & 2,285 \\ \hline 45-54 & 19,898 & 7,118 & 19,984 & 1,514 \\ \hline 55-64 & 14,340 & 4,527 & 14,441 & 938 \\ \hline 65-74 & 8,194 & 2,274 & 8,400 & 980 \\ \hline>74 & 4,803 & 2,022 & 5,375 & 936 \\ \hline \end{array} \) (a) Find the least-squares regression line for males treating number of licensed drivers as the explanatory variable, \(x\), and number of fatal crashes, \(y\), as the response variable. Repeat this procedure for females. (b) Interpret the slope of the least-squares regression line for each gender, if appropriate. How might an insurance company use this information? (c) Was the number of fatal accidents for 16- to 20-year-old males above or below average? Was the number of fatal accidents for 21- to 24-year-old-males above or below average? Was the number of fatal accidents for males greater than 74 years old above or below average? How might an insurance company use this information? Does the same relationship hold for females?

Problem 28AYU Putting It Together: Housing PricesOne of the biggest factors in determining the value of a home is the square footage. The following data represent the square footage and asking price (in thousands of dollars) for a random sample of homes for sale in Naples, Florida, in December 2010. Square Footage, x Asking Price ($000s), y 1148 154 1096 159.9 1142 169 1288 169.9 1322 170 1466 179.9 1344 180 1544 189 1494 189.9 realtor.com (a)Which variable is the explanatory variable? ________________ (b)Draw a scatter diagram of the data. ________________ (c)Determine the linear correlation coefficient between square footage and asking price. ________________ (d)Is there a linear relation between the square footage and asking price? ________________ (e)Find the least-squares regression line treating square footage as the explanatory variable. ________________ (f)Interpret the slope. ________________ (g)Is it reasonable to interpret the y-intercept? Why? ________________ (h)One home that is 1092 square feet is listed at $189,900. Is this home’s price above or below average for a home of this size? What might be some reasons for this price?

Problem 29AYU Putting It Together: Smoking and Birth WeightIt is well known that women should not smoke while pregnant, but what is the effect of smoking on a baby’s birth weight? Researchers Ira M. Bernstein and associates “sought to estimate how the pattern of maternal smoking throughout pregnancy influences newborn size.” To conduct this study, 160 pregnant, smoking women were enrolled in a prospective study. During the third trimester of pregnancy, the woman self-reported the number of cigarettes smoked. Urine samples were collected to measure cotinine levels (to assess nicotine levels). Birth weights (in grams) of the babies were obtained upon delivery. (a)The histogram, drawn in MINITAB, shows the birth weight of babies whose mothers did not smoke in the third trimester of pregnancy (but did smoke prior to the third trimester). Describe the shape of the distribution. What is the class width of the histogram? BirthWcight of Babies Whose Mothers Did Not Smoke in I hird I rimcstcr ________________ (b)Is this an observational study or a designed experiment? ________________ (c)What does it mean for the study to be prospective? ________________ (d)Why would the researchers conduct a urinalysis to measure cotinine levels? ________________ (e)What is the explanatory variable in the study? What is the response variable? ________________ (f)The scatter diagram of the data drawn using MINITAB is shown on the next page. What type of relation appears to exist between cigarette consumption in the third trimester and birth weight? ________________ (g)Use the regression output from MINITAB to report the least-squares regression line between cigarette consumption and birth weight. BirthWcight vs Cigarettes Consumed IXring third Irimcstcr Regression Analysis: BirthWeight versus Cigarettes ________________ (h)Interpret the slope. ________________ (i)Interpret the y-intercept. ________________ (j)Would you recommend using this model to predict the birth weight of a baby whose mother smoked 10 cigarettes per day during the third trimester? Why? ________________ (k)Does this study demonstrate that smoking during the third trimester causes lower-birth-weight babies? ________________ (l)Cite some lurking variables that may confound the results ofthe study.

Problem 30AYU What is a residual? What does it mean when a residual is positive?

Problem 31AYU Explain the phrase outside the scope of the model. Why is it dangerous to make predictions outside the scope of the model?

Explain the meaning of Legendre’s quote given on page 197.

Problem 33AYU Explain what each point on the least-squares regression line represents.

Mark Twain, in his book Life on the Mississippi (1884),makes the following observation: Therefore, the Mississippi between Cairo and New Orleans was twelve hundred and fifteen miles long one hundred and seventy-six years ago. It was eleven hundred and eighty after the cut-off of 1722. It was one thousand and forty after the American Bend cut-off. It has lost sixty-seven miles since. Consequently its length is only nine hundred and seventy-three miles at present. Now, if I wanted to be one of those ponderous scientific people, and “let on” to prove what had occurred in the remote past by what had occurred in a given time in the recent past, or what will occur in the far future by what has occurred in late years, what an opportunity is here! Geology never had such a chance, nor such exact data to argue from! Nor “development of species,” either! Glacial epochs are great things,but they are vague—vague. Please observe: In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oolitic Silurian Period, just a million years ago next November, the Lower Mississippi River was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about Science. One gets such wholesale returns of conjecture out of such a trifling investment of fact. Discuss how Twain’s observation relates to the material presented in this section.