Chapter 13, Problem 13.57CRP

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?

Professional basketball has truly become a sport that generates interest among fans around the world. More and more players come from outside the United States to play in the National Basketball Association (NBA). You want to develop a regression model to predict the number of wins achieved by each NBA team, based on field goal (shots made) percentage and three-point field goal percentage. The data are stored in NBA.xlsx . TEAM Wins Field Goal % Three-Point Field Goal % Points Per Game Rebound Freedraw Turnover Houston Rockets 65 46 36.2 112.4 43.5 19.6 13.8 Toronto Raptors 59 47.2 35.8 111.7 44 17.3 13.4 Golden State Warriors 58 50.3 39.1 113.5 43.5 16.6 15.4 Boston Celtics 55 45 37.7 104 44.5 16 14 Philadelphia 76ers 52 47.2 36.9 109.8 47.4 17.1 16.5 Cleveland Cavaliers 50 47.6 37.2 110.9 42.1 18.1 13.7 Portland Trail Blazers 49 45.2 36.6 105.6 45.5 16.7 13.5 Indiana Pacers 48 47.2 36.9 105.6 42.3 14.9 13.3 New Orleans Pelicans 48 48.3 36.2 111.7 44.3 16.1 14.9…

Professional basketball has truly become a sport that generates interest among fans around the world. More and more players come from outside the United States to play in the National Basketball Association (NBA). You want to develop a regression model to predict the number of wins achieved by each NBA team, based on field goal (shots made) percentage and three-point field goal percentage. The data are stored in NBA.xlsx .   TEAM Wins Field Goal % Three-Point Field Goal % Points Per Game Rebound Freedraw Turnover Houston Rockets 65 46 36.2 112.4 43.5 19.6 13.8 Toronto Raptors 59 47.2 35.8 111.7 44 17.3 13.4 Golden State Warriors 58 50.3 39.1 113.5 43.5 16.6 15.4 Boston Celtics 55 45 37.7 104 44.5 16 14 Philadelphia 76ers 52 47.2 36.9 109.8 47.4 17.1 16.5 Cleveland Cavaliers 50 47.6 37.2 110.9 42.1 18.1 13.7 Portland Trail Blazers 49 45.2 36.6 105.6 45.5 16.7 13.5 Indiana Pacers 48 47.2 36.9 105.6 42.3 14.9 13.3 New Orleans Pelicans 48 48.3 36.2 111.7 44.3 16.1 14.9…

please use this situation: A small theater company has a linear regression model to estimate y = the concession stand sales in dollars, based on knowing x = the number of people in attendance.  The regression equation is:   = 6.72x + 11.50  and the correlation coefficient was r = 0.781.  The data set saw the number of people in attendance ranging from a minimum of 18 people to a maximum of 170 people. 1) How reliable would it be to make a prediction for the concession sales amount if there were 500 people in attendance? Explain.

Write out the full linear model including all dummy variables below. Don’t worry about estimating regression coefficients just yet. Feel free to abbreviate variable names so long as they are clearly distinguishable.

The number of megapixels in a digital camera is one of the most important factors in determining picture quality. But, do digital cameras with more megapixels cost more? The following data show the number of megapixels and the price ($) for 10 digital cameras(Consumer Reports, March 2009). The Kodak Easy Share Z1012 IS digital camera has 10 megapixels. Predict the price of this camera using the estimated regression equation developed. Brand and Model Megapixels Price (S) Canon PowerShot SD1100 IS Casio Exilim Card EX-510 180 200 230 8 10 Sony Cyber-shot DSC-T70 Pentax Optio M50 Canon PowerShot G10 Canon PowerShot A590 IS Canon PowerShot El 8 120 470 15 140 180 310 250 10 Fujifilm FinePix FO0FD Sony Cyber-shot DSC-W170 Canon PowerShot A470 12 10 110

A researcher is analyzing the relationship between various variables in housing data for 32 cities: median list prices of single family homes, condominium or co-ops, all homes, median household income, unemployment rate, and population. What is the regression equation for the model that predicts the list price of all homes using population as an explanatory variable?What is the interpretation of the slope? What is the interpretation of the intercept?

Explain why it is not a good idea to exclude an intercept, b0 , from any linear regression model?

After interviewing salespersons at Harley Davidson dealerships, a researcher has created a linear regression line to explain the relationship between a Harley Davidson motorcycle's age (x) and price (y). The regression has an  = 87.7%. Write a sentence summarizing what  says about this regression.         The age of the motorcycle explains 12.3% of the variation in price.   The age of the motorcycle explains 9.36% of the variation in price.   The age of the motorcycle explains 87.7% of the variation in price.   The price of the motorcycle explains 12.3% of the variation in age.   The price of the motorcycle explains 87.7% of the variation in age.