Real estate A random sample of records of sales of homes from February 15 to April 30

You go to an open house and find that the house is 1 standard deviation above the mean in size. What would you guess about its price?

You read an ad for a house priced 2 standard deviations below the mean. What would you guess about its size?

A friend tells you about a house whose size in square meters (hes European) is 1.5 standard deviations above the mean. What would you guess about its size in square feet?

What does the slope of 94.454 mean?

What are the units of the slope?

Your house is 2000 sq ft bigger than your neighbors house. How much more do you expect it to be worth?

Is the y-intercept of -3.117 meaningful? Explain.

Would you prefer to find a home with a negative or a positive residual? Explain.

You plan to look for a home of about 3000 square feet. How much should you expect to have to pay?

You find a nice home that size selling for $300,000. Whats the residual?

What does the R2 value mean about the relationship of Price and Size?

Is the correlation of Price and Size positive or negative? How do you know?

If we measure house Size in square meters instead, would R2 change? Would the slope of the line change? Explain.

You find that your house in Saratoga is worth $50,000 more than the regression model predicts. Should you be very surprised (as well as pleased)?

True or false If false, explain briefly. a) We choose the linear model that passes through the most data points on the scatterplot. b) The residuals are the observed y-values minus the y-values predicted by the linear model. c) Least squares means that the square of the largest residual is as small as it could possibly be.

True or false II If false, explain briefly. a) Some of the residuals from a least squares linear model will be positive and some will be negative. b) Least Squares means that some of the squares of the residuals are minimized. c) We write ny to denote the predicted values and y to denote the observed values

Bookstore sales revisited Recall the data we saw in Chapter 6, Exercise 3 for a bookstore. The manager wants to predict Sales from Number of Sales People Working. Here is the regression analysis of Sales vs. Number of Sales People Working. a) Write the regression equation. Define the variables used in your equation. b) What does the slope mean in this context? c) What does the y-intercept mean in this context? Is it meaningful? d) If 18 people are working, what Sales do you predict? e) If sales for the 18 people are actually $25,000, what is the value of the residual? f) Have we overestimated or underestimated the sales?

Disk drives again In Chapter 6, Exercise 4, we saw some data on hard drives. After correcting for an outlier, these data look like this: we want to predict Price from Capacity. Here is the regression analysis of Price vs. Capacity. Variable Coefficient Intercept 8.1006 Num_Workers 0.9134 Dependent variable is Sales R-squared = 93.2, s = 1.477 Dependent variable is Price R-squared = 98.8, s = 17.95 Variable Coefficient Intercept 18.617 Capacity 103.929 a) Write the regression equation. Define the variables used in your equation. b) What does the slope mean in this context? c) What does the y-intercept mean in this context? Is it meaningful? d) What would you predict for the price of a 3.0 TB drive? e) You found a 3.0 TB drive for $300. Is this a good buy? How much would you save compared to what you expected to buy? f) Does the model overestimate or underestimate the price for a 3.0 TB drive?

Bookstore sales once more Here are the residuals for a regression of Sales on Number of Sales People Working for the bookstore Exercise 17: Number of Sales People Working Residual 2 0.07 3 0.16 7 -1.49 9 -2.32 10 0.77 10 2.77 12 0.94 15 0.20 16 -0.72 20 -0.37 Capacity Residual 0.080 3.02 0.120 3.91 0.250 5.35 0.320 18.075 1.0 -23.55 2.0 -21.475 4.0 14.666 a) What are the units of the residuals? b) Which residual contributes the most to the sum that was minimized according to the Least Squares Criterion to find this regression? c) Which residual contributes least to that sum?

Disk drives once more Here are the residuals for a regression of Price on Capacity for the hard drives of Exercise 18. a) Which residual contributes the most to the sum that is minimized by the Least Squares criterion? b) Two of the residuals are negative. What does that mean about those drives? Be specific and use the correct units.

Bookstore sales last time For the regression model for the bookstore of Exercise 17, what is the value of R2 and what does it mean?

Disk drives encore For the hard drive data of Exercise 18, interpret the value of R2

Residual plots Here are residual plots (residuals plotted against predicted values) for three linear regression models. Indicate which condition appears to be violated (linearity, outlier or equal spread) in each case. a) 10 0 10 20 30 40 50 60 70 15 10 5 0 5 10 Fitted Value Residual b) 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 50 40 30 20 10 0 10 Fitted Value Residual c) 100 200 300 400 500 600 700 200 100 0 100 200 Fitted Value

Disk drives last time Here is a scatterplot of the residuals from the regression of the hard drive prices on their sizes from Exercise 18. 220 210 0 100 Predicted Residuals 200 300 400 a) Are any assumptions or conditions violated? If so, which ones? b) What would you recommend about this regression?

Real estate A random sample of records of sales of homes from February 15 to April 30, 1993, from the files maintained by the Albuquerque Board of Realtors gives the Price and Size (in square feet) of 117 homes. A regression to predict Price (in thousands of dollars) from Size has an R-squared of 71.4%. The residuals plot indicated that a linear model is appropriate. a) What are the variables and units in this regression? b) What units does the slope have? c) Do you think the slope is positive or negative? Explain.

Roller coaster The Mitch Hawker poll ranked the Top 10 steel roller coasters in 2011. A table in the previous chapters exercises shows the length of the initial drop (in feet) and the duration of the ride (in seconds). A regression to predict Duration from Drop has R2 = 15.2,. a) What are the variables and units in this regression? b) What units does the slope have? c) Do you think the slope is positive or negative? Explain.

Real estate again The regression of Price on Size of homes in Albuquerque had R2 = 71.4,, as described in Exercise 25. Write a sentence (in context, of course) summarizing what the R2 says about this regression.

Coasters again Exercise 26 examined the association between the Duration of a roller coaster ride and the height of its initial Drop, reporting that R2 = 15.2,. Write a sentence (in context, of course) summarizing what the R2 says about this regression

Real estate redux The regression of Price on Size of homes in Albuquerque had R2 = 71.4,, as described in Exercise 25. a) What is the correlation between Size and Price? Explain why you chose the sign (+ or -) you did. b) What would you predict about the Price of a home 1 standard deviation above average in Size? c) What would you predict about the Price of a home 2 standard deviations below average in Size?

Another ride The regression of Duration of a roller coaster ride on the height of its initial Drop, described in Exercise 26, had R2 = 15.2,. a) What is the correlation between Drop and Duration? b) What would you predict about the Duration of the ride on a coaster whose initial Drop was 1 standard deviation below the mean Drop? c) What would you predict about the Duration of the ride on a coaster whose initial Drop was 3 standard deviations above the mean Drop?

More real estate Consider the Albuquerque home sales from Exercise 25 again. The regression analysis gives the model Price = 47.82 + 0.061 Size. a) Explain what the slope of the line says about housing prices and house size. b) What price would you predict for a 3000-square-foot house in this market? c) A real estate agent shows a potential buyer a 1200-square-foot home, saying that the asking price is $6000 less than what one would expect to pay for a house of this size. What is the asking price, and what is the $6000 called?

Last ride Consider the roller coasters described in Exercise 26 again. The regression analysis gives the model Duration = 64.232 + 0.180 Drop. a) Explain what the slope of the line says about how long a roller coaster ride may last and the height of the coaster. b) A new roller coaster advertises an initial drop of 200 feet. How long would you predict the rides last? c) Another coaster with a 150-foot initial drop advertises a 2-minute ride. Is this longer or shorter than youd expect? By how much? Whats that called?

Misinterpretations A Biology student who created a regression model to use a birds Height when perched for predicting its Wingspan made these two statements. Assuming the calculations were done correctly, explain what is wrong with each interpretation. a) My R2 of 93% shows that this linear model is appropriate. b) A bird 10 inches tall will have a wingspan of 17 inches.

More misinterpretations A Sociology student investigated the association between a countrys Literacy Rate and Life Expectancy, then drew the conclusions listed below. Explain why each statement is incorrect. (Assume that all the calculations were done properly.) a) The Literacy Rate determines 64% of the Life Expectancy for a country. b) The slope of the line shows that an increase of 5% in Literacy Rate will produce a 2-year improvement in Life Expectancy.

ESP People who claim to have ESP participate in a screening test in which they have to guess which of several images someone is thinking of. You and a friend both took the test. You scored 2 standard deviations above the mean, and your friend scored 1 standard deviation below the mean. The researchers offer everyone the opportunity to take a retest. a) Should you choose to take this retest? Explain. b) Now explain to your friend what his decision should be and why.

SI jinx Players in any sport who are having great seasons, turning in performances that are much better than anyone might have anticipated, often are pictured on the cover of Sports Illustrated. Frequently, their performances then falter somewhat, leading some athletes to believe in a Sports Illustrated jinx. Similarly, it is common for phenomenal rookies to have less stellar second seasonsthe so-called sophomore slump. While fans, athletes, and analysts have proposed many theories about what leads to such declines, a statistician might offer a simpler (statistical) explanation. Explain.

Cigarettes Is the nicotine content of a cigarette related to the tars? A collection of data (in milligrams) on 29 cigarettes produced the scatterplot, residuals plot, and regression analysis shown: T Dependent variable is Home Attendance R-squared = 28.4, Variable Coefficient Constant -6760.5 Wins 431.22 Tar (mg) Nicotine (mg) 0.6 0.3 1.2 4 8 12 16 0.9 Predicted Residuals 0.075 0.150 0.075 0.3 0.6 0.9 1.2 0.000 Dependent variable is: nicotine R squared = 92.4, Variable Coefficient Constant 0.154030 Tar 0.065052 a) Do you think a linear model is appropriate here? Explain. b) Explain the meaning of R2 in this context.

Attendance 2010 In the previous chapter, you looked at the relationship between the number of wins by American League baseball teams and the average attendance at their home games for the 2010 season. Here are the scatterplot, the residuals plot, and part of the regression analysis: T Attendance 45,000 40,000 35,000 30,000 25,000 20,000 60 70 80 90 Wins 20,000 210,000 25,000 0 5,000 10,000 25,000 30,000 Fitted Values Residuals 35,000 a) Do you think a linear model is appropriate here? Explain. b) Interpret the meaning of R2 in this context. c) Do the residuals show any pattern worth remarking on? d) The point in the upper right of the plots is the New York Yankees. What can you say about the residual for the Yankees?

Another cigarette Consider again the regression of Nicotine content on Tar (both in milligrams) for the cigarettes examined in Exercise 37. a) What is the correlation between Tar and Nicotine? b) What would you predict about the average Nicotine content of cigarettes that are 2 standard deviations below average in Tar content? c) If a cigarette is 1 standard deviation above average in Nicotine content, what do you suspect is true about its Tar content?

Second inning 2010 Consider again the regression of Average Attendance on Wins for the baseball teams examined in Exercise 38. a) What is the correlation between Wins and Average Attendance? b) What would you predict about the Average Attendance for a team that is 2 standard deviations above average in Wins? c) If a team is 1 standard deviation below average in attendance, what would you predict about the number of games the team has won?

Last cigarette Take another look at the regression analysis of tar and nicotine content of the cigarettes in Exercise 37. a) Write the equation of the regression line. b) Estimate the Nicotine content of cigarettes with 4 milligrams of Tar. c) Interpret the meaning of the slope of the regression line in this context. d) What does the y-intercept mean? e) If a new brand of cigarette contains 7 milligrams of tar T and a nicotine level whose residual is -0.5 mg, what is the nicotine content?

Last inning 2010 Refer again to the regression analysis for average attendance and games won by American League baseball teams, seen in Exercise 38. a) Write the equation of the regression line. b) Estimate the Average Attendance for a team with 50 Wins. c) Interpret the meaning of the slope of the regression line in this context. d) In general, what would a negative residual mean in this context? e) The San Francisco Giants, the 2010 World Champions, are not included in these data because they are a National League team. During the 2010 regular season, the Giants won 92 games and averaged 41,736 fans at their home games. Calculate the residual for this team, and explain what it means.

Income and housing revisited In Chapter 6, Exercise 32, we learned that the Office of Federal Housing Enterprise Oversight (OFHEO) collects data on various aspects of housing costs around the United States. Heres a scatterplot (by state) of the Housing Cost Index (HCI) versus the Median Family Income (MFI) for the 50 states. The correlation is r = 0.65. The mean HCI is 338.2, with a standard deviation of 116.55. The mean MFI is $46,234, with a standard deviation of $7072.47. 700 600 500 400 300 200 Housing Cost Index 35 40 45 50 55 60 70 Median Family Income (thousands of dollars) a) Is a regression analysis appropriate? Explain. b) What is the equation that predicts Housing Cost Index from median family income? c) For a state with MFI = +44,993, what would be the predicted HCI? d) Washington, DC, has an MFI of $44,993 and an HCI of 548.02. How far off is the prediction in c) from the actual HCI? e) If we standardized both variables, what would be the regression equation that predicts standardized HCI from standardized MFI? f) If we standardized both variables, what would be the regression equation that predicts standardized MFI from standardized HCI?

Interest rates and mortgages again In Chapter 6, Exercise 33, we saw a plot of mortgages in the United States (in thousands of dollars) versus the interest rate at various times over the past 26 years. The correlation is r = -0.86. The mean mortgage amount is $121.8 thousand and the mean interest rate is 7.74%. The standard deviations are $47.36 thousand for mortgage amounts and 1.79% for the interest rates. 6 8 200 150 Amount 100 10 Interest 12 a) Is a regression model appropriate for predicting mortgage amount from interest rates? Explain. b) What is the equation that predicts mortgage amount from interest rates? c) What would you predict the mortgage amount would be if the interest rates climbed to 13%? d) Do you have any reservations about your prediction in part c)? e) If we standardized both variables, what would be the regression equation that predicts standardized mortgage amount from standardized interest rates? f) If we standardized both variables, what would be the regression equation that predicts standardized interest rates from standardized mortgage amount?

Online clothes An online clothing retailer keeps track of its customers purchases. For those customers who signed up for the companys credit card, the company also has information on the customers Age and Income. A random sample of 500 of these customers shows the following scatterplot of Total Yearly Purchases by Age: e) If a new brand of cigarette contains 7 milligrams of tar T and a nicotine level whose residual is -0.5 mg, what is the nicotine content? 42. Last inning 2010 Refer again to the regression analysis for average attendance and games won by American League baseball teams, seen in Exercise 38. a) Write the equation of the regression line. b) Estimate the Average Attendance for a team with 50 Wins. c) Interpret the meaning of the slope of the regression line in this context. d) In general, what would a negative residual mean in this context? e) The San Francisco Giants, the 2010 World Champions, are not included in these data because they are a National League team. During the 2010 regular season, the Giants won 92 games and averaged 41,736 fans at their home games. Calculate the residual for this team, and explain what it means. 43. Income and housing revisited In Chapter 6, Exercise 32, we learned that the Office of Federal Housing Enterprise Oversight (OFHEO) collects data on various aspects of housing costs around the United States. Heres a scatterplot (by state) of the Housing Cost Index (HCI) versus the Median Family Income (MFI) for the 50 states. The correlation is r = 0.65. The mean HCI is 338.2, with a standard deviation of 116.55. The mean MFI is $46,234, with a standard deviation of $7072.47. 700 600 500 400 300 200 Housing Cost Index 35 40 45 50 55 60 70 Median Family Income (thousands of dollars) a) Is a regression analysis appropriate? Explain. b) What is the equation that predicts Housing Cost Index from median family income? c) For a state with MFI = +44,993, what would be the predicted HCI? d) Washington, DC, has an MFI of $44,993 and an HCI of 548.02. How far off is the prediction in c) from the actual HCI? e) If we standardized both variables, what would be the regression equation that predicts standardized HCI from standardized MFI? f) If we standardized both variables, what would be the regression equation that predicts standardized MFI from standardized HCI? T T 1400 1200 1000 800 600 400 200 0 Total Yearly Purchases (dollars) 20 30 40 50 60 Age The correlation between Total Yearly Purchases and Age is r = 0.037. Summary statistics for the two variables are: a) What is the linear regression equation for predicting Total Yearly Purchase from Age? b) Do the assumptions and conditions for regression appear to be met? c) What is the predicted average Total Yearly Purchase for an 18-year-old? For a 50-year-old? d) What percent of the variability in Total Yearly Purchases is accounted for by this model? e) Do you think the regression might be a useful one for the company? Explain.

Online clothes II For the online clothing retailer discussed in the previous problem, the scatterplot of Total Yearly Purchases by Income shows The correlation between Total Yearly Purchases and Income is 0.722. Summary statistics for the two variables are: Mean SD Age 29.67 yrs 8.51 yrs Total Yearly Purchase $572.52 $253.62 Mean SD Income $50,343.40 $16,952.50 Total Yearly Purchase $572.52 $253.62 a) What is the linear regression equation for predicting Total Yearly Purchase from Income? b) Do the assumptions and conditions for regression appear to be met? c) What is the predicted average Total Yearly Purchase for someone with a yearly Income of $20,000? For someone with an annual Income of $80,000? d) What percent of the variability in Total Yearly Purchases is accounted for by this model? e) Do you think the regression might be a useful one for the company? Comment

Success in college Colleges use SAT scores in the admissions process because they believe these scores provide some insight into how a high school student will perform at the college level. Regression analysis was computed on using SAT to predict GPA. a) Write the equation of the regression line. b) Explain what the y-intercept of the regression line indicates. c) Interpret the slope of the regression line. d) Predict

SAT scores The SAT is a test often used as part of an application to college. SAT scores are between 200 and 800, but have no units. Tests are given in both Math and Verbal areas. Doing the SAT-Math problems also involves the ability to T a) Describe the relationship. b) Are there any students whose scores do not seem to fit the overall pattern? c) Find the correlation coefficient and interpret this value in context. d) Write the equation of the regression line, defining any variables used in the equation. e) Interpret the slope of this line. f) Predict the math score of a student with a verbal score of 500. g) Every year some student scores a perfect 1600 on these two parts of the test. Based on this model, what would be that students Math score residual?

SAT, take 2 Suppose the AP calculus students complained and insisted that we should use SAT math scores to estimate verbal scores (using the same data from exercise 47). Here is the regression analysis of Math SAT vs. Verbal SAT. Dependent variable is Verbal s = 72.77 Variable Coefficient Intercept 171.333 Math SAT 0.6943 a) What is the correlation? b) Write the equation of the line of regression predicting verbal scores from math scores. c) In general, what would a positive residual mean in this context? d) A person tells you her math score was 500. Predict her verbal score. e) Using that predicted verbal score and the equation you created in Exercise 47, predict her math score. f) Why doesnt the result in part e) come out to 500?

Success, part 2 The standard deviation of the residuals in Exercise 48 is 0.275. Interpret this value in context.

Wildfires 2010 The National Interagency Fire Center (www.nifc.gov) reports statistics about wildfires. Heres an analysis of the number of wildfires between 1985 and 2010. T Dependent variable is Fires R-squared = 1.9, s = 11920 Variable Coefficient Intercept 74487.1 Years since 1985 209.728 a) Is a linear model appropriate for these data? Explain. b) Interpret the slope in this context. c) Can we interpret the intercept? Why or why not? d) What does the value of se say about the size of the residuals? What does it say about the effectiveness of the model? e) What does R2 mean in this context?

Wildfires 2010 The National Interagency Fire Center (www.nifc.gov) reports statistics about wildfires. Heres an analysis of the number of wildfires between 1985 and 2010.

Used cars 2011 Carmax.com lists numerous Toyota Corollas for sale within a 250 mile radius of Redlands, CA. The table below shows the ages of the cars and the advertised prices. a) Make a scatterplot for these data. b) Describe the association between Age and Price of a used Corolla. c) Do you think a linear model is appropriate? d) Computer software says that R2 = 89.1,. What is the correlation between Age and Price? e) Explain the meaning of R2 in this context. f) Why doesnt this model explain 100% of the variability in the price of a used Corolla?

Drug abuse In the exercises of the last chapter you examined results of a survey conducted in the United States and 10 countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. Below is the scatterplot. Summary statistics showed that the mean percent that had used marijuana was 23.9%, with a standard deviation of 15.6%. An average of 11.6% of teens had used other drugs, with a standard deviation of 10.2%. Marijuana (%) Other Drugs (%) 15.0 22.5 7.5 30.0 12.5 25.0 37.5 50.0 a) Do you think a linear model is appropriate? Explain. b) For this regression, R2 is 87.3%. Interpret this statistic in this context. c) Write the equation you would use to estimate the percentage of teens who use other drugs from the percentage who have used marijuana. d) Explain in context what the slope of this line means. e) Do these results confirm that marijuana is a gateway drug, that is, that marijuana use leads to the use of other drugs?

More used cars 2011 Use the advertised prices for Toyota Corollas given in Exercise 53 to create a linear model for the relationship between a cars Age and its Price. a) Find the equation of the regression line. b) Explain the meaning of the slope of the line. c) Explain the meaning of the y-intercept of the line. d) If you want to sell a 7-year-old Corolla, what price seems appropriate? e) You have a chance to buy one of two cars. They are about the same age and appear to be in equally good condition. Would you rather buy the one with a positive residual or the one with a negative residual? Explain. f) You see a For Sale sign on a 10-year-old Corolla stating the asking price as $8,500. What is the residual? g) Would this regression model be useful in establishing a fair price for a 25-year-old car? Explain.

Birthrates 2009 The table shows the number of live births per 1000 women aged 1544 years in the United States, starting in 1965. (National Center for Health Statistics, www.cdc.gov/nchs/) a) Make a scatterplot and describe the general trend in Birthrates. (Enter Year as years since 1900: 65, 70, 75, etc.) b) Find the equation of the regression line. c) Check to see if the line is an appropriate model. Explain. d) Interpret the slope of the line. e) The table gives rates only at 5-year intervals. Estimate what the rate was in 1978. f) In 1978, the birthrate was actually 15.0. How close did your model come? g) Predict what the Birthrate will be in 2010. Comment on your faith in this prediction. h) Predict the Birthrate for 2025. Comment on your faith in this prediction

Burgers In the last chapter, you examined the association between the amounts of Fat and Calories in fast-food hamburgers. Here are the data: Fat (g) 19 31 34 35 39 39 43 Calories 410 580 590 570 640 680 660 a) Create a scatterplot of Calories vs. Fat. b) Interpret the value of R2 in this context. c) Write the equation of the line of regression. d) Use the residuals plot to explain whether your linear model is appropriate. e) Explain the meaning of the y-intercept of the line. f) Explain the meaning of the slope of the line. g) A new burger containing 28 grams of fat is introduced. According to this model, its residual for calories is +33. How many calories does the burger have?

Chicken Chicken sandwiches are often advertised as a healthier alternative to beef because many are lower in fat. Data from tests on 15 different sandwiches randomly selected from the website http:// fast-food-nutrition.findthebest.com/d/a/ChickenSandwich produced the Calories vs. Fat scatterplot and the regression analysis below. 10 200 400 600 800 1000 1200 20 30 40 50 Fat Calories Dependent variable is Calories R-squared = 93.2% s = 63.73 Variable Coefficient SE Intercept 12.7234 43.910 Fat 21.2171 1.5944 a) Do you think a linear model is appropriate in this situation? b) Describe the strength of this association. c) Write the equation of the regression line to estimate calories from the fat content. d) Explain the meaning of the slope. e) Explain the meaning of the y-intercept. f) What does it mean if a certain sandwich has a negative residual?

A second helping of burgers In Exercise 57 you created a model that can estimate the number of Calories in a burger when the Fat content is known. a) Explain why you cannot use that model to estimate the fat content of a burger with 600 calories. b) Make that estimate using an appropriate model.

A second helping of chicken In Exercise 58 you created a model to estimate the number of Calories in a chicken sandwich when you know the Fat. a) Explain why you cannot use that model to estimate the fat content of a 400-calorie sandwich. b) Quiznos large mesquite sandwich stands out on the graph with an impressive 53 fat grams and 1190 calories. What effect do you think this value has on the regression equation?

Body fat It is difficult to determine a persons body fat percentage accurately without immersing him or her in water. Researchers hoping to find ways to make a good estimate immersed 20 male subjects, then measured their waists and recorded their weights.Waist (in.) Weight (lb) Body Fat (%) Waist (in.) Weight (lb) Body Fat (%) 32 175 6 33 188 10 36 181 21 40 240 20 38 200 15 36 175 22 33 159 6 32 168 9 39 196 22 44 246 38 40 192 31 33 160 10 41 205 32 41 215 27 35 173 21 34 159 12 38 187 25 34 146 10 38 188 30 44 219 28 a) Create a model to predict %Body Fat from Weight. b) Do you think a linear model is appropriate? Explain. c) Interpret the slope of your model. d) Is your model likely to make reliable estimates? Explain. e) What is the residual for a person who weighs 190 pounds and has 21% body fat?

Body fat again Would a model that uses the persons Waist size be able to predict the %Body Fat more accurately than one that uses Weight? Using the data in Exercise 61, create and analyze that model.

Heptathlon 2004 We discussed the womens Olympic heptathlon in Chapter 5. The table shows the results from the high jump, 800-meter run, and long jump for the 26 women who successfully completed all three events in the 2004 Olympics. Lets examine the association among these events. Perform a regression to predict high-jump performance from the 800-meter results. a) What is the regression equation? What does the slope mean? b) What percent of the variability in high jumps can be accounted for by differences in 800-m times? c) Do good high jumpers tend to be fast runners? (Be carefullow times are good for running events and high distances are good for jumps.) d) What does the residuals plot reveal about the model? e) Do you think this is a useful model? Would you use it to predict high-jump performance? (Compare the residual standard deviation to the standard deviation of the high jumps.)

Heptathlon 2004 again We saw the data for the womens 2004 Olympic heptathlon in Exercise 63. Are the two jumping events associated? Perform a regression of the long-jump results on the high-jump results. a) What is the regression equation? What does the slope mean? b) What percentage of the variability in long jumps can be accounted for by high-jump performances? c) Do good high jumpers tend to be good long jumpers? d) What does the residuals plot reveal about the model? e) Do you think this is a useful model? Would you use it to predict long-jump performance? (Compare the residual standard deviation to the standard deviation of the long jumps.)

Least squares I Consider the four points (10, 10), (20, 50), (40, 20), and (50,80). The least squares line is yn = 7.0 + 1.1x. Explain what least squares means, using these data as a specific example.

Least squares II Consider the four points (200,1950), (400,1650), (600,1800), and (800,1600). The least squares line is yn = 1975 - 0.45x. Explain what least squares means, using these data as a specific example.