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Question: The following data on sale price, size,

The following data on sale price, size, and land-to-building ratio for 10 large industrial properties appeared in the paper “Using Multiple regression analysis in real estate appraisal” (Appraisal Journal [2002]: 424–430):
The following data on sale price, size, and land-to-building ratio for 10 large industrial properties appeared in the paper “Using Multiple regression analysis in real estate appraisal” (Appraisal Journal [2002]: 424–430):


a. If you wanted to predict sale price and you could use either size or land-to-building ratio as the basis for making predictions, which would you use? Explain. 
b. Based on your choice in Part (a), find the equation of the least squares regression line for predicting sale price.

a. If you wanted to predict sale price and you could use either size or land-to-building ratio as the basis for making predictions, which would you use? Explain. b. Based on your choice in Part (a), find the equation of the least squares regression line for predicting sale price.





Transcribed Image Text:

Sale Price (millions of dollars) Size Land-to- (thousands of sq. ft.) Building Property Ratio 1 10.6 2,166 2.0 2.6 751 3.5 3 30.5 2,422 3.6 4 1.8 224 4.7 5 20.0 3,917 1.7 8.0 2,866 2.3 7 10.0 1,698 3.1 6.7 1,046 4.8 9 5.8 1,108 7.6 10 4.5 405 17.2 00


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> The report “Seat Belt Use in 2014” (National Highway Traffic Safety Administration) included the estimated percentages of drivers who wear seat belts for the 50 states and the District of Columbia. In the accompanying

> The following data on violent crime on Florida college campuses during 2014 are from the FBI web site. a. Construct adotplot using the 15 observations on number of violent crimes reported. Which schools stand out from the rest? b. One of the Florida sc

> An exam is given to students in an introductory statistics course. Comment on the expected shape of the histogram of scores if: a. the exam is very easy b. the exam is very difficult c. half the students in the class have had calculus, the other half

> The following two relative frequency distributions were constructed from data in the report “Undergraduate Students and Credit Cards in 2004” (Nellie Mae, May 2005). One distribution summarizes credit bureau data for a

> A report from Texas Transportation Institute (Texas A&M University System, 2005) titled “Congestion Reduction Strategies” included the following data on extra travel time during rush hour for very large and for lar

> USA TODAY (June 11, 2010) gave the following data on median age for each of the 50 U.S. states and the District of Columbia (DC). Construct a stem-and-leaf display using stems 28, 29,…,42. Comment on shape, center, and variability of

> Box Office Mojo (www.boxofficemojo.com) tracks movie ticket sales. Ticket sales (in millions of dollars) for each of the top 20 movies in 2014 and 2015 are shown in the accompanying tables. Continue to next pages… Construct com

> An article in the San Luis Obispo New Times (February 4, 2016) reported the accompanying concussion rates for different high school sports. The given data are concussion rates per 10,000 athletes participating in high school sports in 2012. a. Construct

> The 2015 urban Mobility Scorecard (texas a&M transportation institute, mobility.tamu.edu/ums/report/, rerieved april 19, 2017) included data on the estimated cost (in millions of dollars) resulting from traffic congestion for different urban areas. T

> In the United States, movies are rated by the Motion Picture Association of America (MPAA). The accompanying table gives the MPAA rating of the 25 top moneymaking movies of 2015 (data from www.boxofficemojo .com, retrieved October 10, 2016). Use the give

> The report “2013 International Bedroom Poll: Summary of Findings” describes a survey of 251 adult Americans conducted by the National Sleep Foundation (www.sleep foundation.org/sites/default/files/RPT495a.pdf, retrieved April 15, 2017). Participants in t

> The report “Findings from the 2014 College Senior Survey” (Higher Education Research Institute, December 2014) summarizes data collected from more than 13,000 college seniors across the United States. One question in t

> Heal the Bay is an environmental organization that releases an annual beach report card based on water quality (Heal the Bay Beach Report Card, www.beachreportcard.org, retrieved May 7, 2016). The grades for 20 beaches in three counties in Washington (Wh

> Each year, The Princeton Review conducts surveys of high school students who are applying to college and of parents of college applicants. The report “2016 College Hopes & Worries Survey Findings” (www.princetonre

> The report “Trends in Education 2010: Community Colleges” (www.collegeboard.com/trends) included the accompanying information on student debt for students graduating with an AA degree from a public community college in

> The report referenced in the previous exercise also gave responses to the question “What do you think is the best long-term investment?” by gender. Relative frequencies for the six response categories for men and for w

> The Gallup report “More Americans Say Real Estate Is Best Long-Term Investment” (www.gallup.com, April 20, 2016, retrieved April 15, 2017) included data from a poll of 1015 adults. The responses to the question â

> To learn about TV viewing habits of high school students, each person in a sample of students was asked how many hours he or she spent watching TV during the previous week. Required: 1. How many variables are in the data set? 2. Are the variables in th

> To learn if there is a relationship between water consumption and headache frequency, people in a sample of young adults were asked how much water (in ounces) they drink in a typical day and how many days per month they experience a headache. Required:

> The insurance institute for highway Safety (www.iihs .org, June 11, 2009) published data on repair costs for cars involved in different types of accidents. In one study, seven different 2009 models of mini- and micro-cars were driven at 6 mph straight in

> To compare the number of hours spent studying in a typical week for male and female students, data were collected from each person in a random sample of 50 female students and each person in a random sample of 50 male students. Required: 1. How many var

> To learn about what super power middle school students would most like to have, each person in a sample of middle school students was asked to choose among invisibility, extreme strength, the ability to freeze time, and the ability to fly. Required: 1.

> Classify each of the following variables as either categorical or numerical. a. Number of text messages sent by a college student in a typical day b. Amount of time a high school senior spends playing computer or video games in a typical day c. Number

> For the numerical variables in the previous exercise, which are discrete and which are continuous?

> Classify each of the following variables as either categorical or numerical. a. Color of an M&M candy selected at random from a bag of M&M’s b. N umber of green M&M’s in a bag of M&M’s c. Weight (in grams) of a bag of M&M’s d. G ender of the next per

> For the numerical variables in the previous exercise, which are discrete and which are continuous?

> Classify each of the following variables as either categorical or numerical. a. W eight (in ounces) of a bag of potato chips b. Number of items purchased by a grocery store customer c. Brand of cola purchased by a convenience store customer d. A moun

> To learn about political affiliation (Democrat, Republican, Independent, and Other) of students at a particular college, each student in a random sample of 200 students was asked to indicate his or her political affiliation. Required: 1. How many variab

> To learn how the amount of money spent on a fast-food meal might differ for men and women, the amount spent on lunch at a particular fast-food restaurant was determined for each person in a sample of 50 women and each person in a sample of 50 men. Requi

> To learn how GPA at the end of the freshman year in college is related to high school GPA, both high school GPA and freshman year GPA were determined for each student in a sample of 100 students who had just completed their freshman year at a particular

> Data on tipping percent for 20 restaurant tables, consistent with summary statistics given in the paper “racial and ethnic Differences in tipping: the role of Perceived Descriptive and injunctive tipping norms” (Restau

> To see if there is a difference in car color preferences of men and women, each person in a sample of 100 males and each person in a sample of 100 females was shown pictures of a new model car in five different colors and asked to select which color they

> To learn about the heights of five-year-old children, the height of each child in a sample of 40 five-year-old children was measured. Required: 1. How many variables are in the data set? 2. Are the variables in the data set categorical or numerical? 3

> For the following numerical variables, state whether each is discrete or continuous. a. The length of a 1-year-old rattlesnake b. The altitude of a location in California selected randomly by throwing a dart at a map of the state c. The distance from

> Classify each of the following variables as either categorical or numerical. For those that are numerical, determine whether they are discrete or continuous. a. Brand of computer purchased by a customer b. State of birth for someone born in the United

> To learn about how much money students at a particular college spend on textbooks, each student in a random sample of 200 students was asked how much he or she spent on textbooks for the current semester.

> To see if there is a difference between faculty and students at a particular college with respect to how they commute to campus (drive, walk, bike, and so on), each person in a random sample of 50 faculty members and each person in a random sample of 100

> To learn about how number of years of education and income are related, each person in a random sample of 500 residents of a particular city was asked how many years of education he or she had completed and what his or her annual income was. Required: 1

> To compare commute distances for full-time and part-time students at a large college, commute distance (in miles) was determined for each student in a random sample of 50 full-time students and for each student in a random sample of 50 part-time students

> The accompanying data on x = Average energy density (calories per 100 grams) and y = Average cost (in dollars) for eight different food groups are from the paper “the Cost of U.S. Foods as related to their nutritional valueâ€

> The article “$115K! the 13 best Paying U.s. Companies” (USA TODAY, august 11, 2015) gave the following data on median worker pay (in thousands of dollars) and the 1-year percent change in stock price for the 13 highest

> the accompanying data on total amount of time per day (in minutes) spent using a cell phone are consistent with summary statistics in the paper “the relationship between cell Phone use and academic Performance in a Sample of u.S. colleg

> Can you tell how old a lobster is by its size? This question was investigated by the authors of a paper that appeared in the Biological Bulletin (august 2007). Researchers measured carapace (the exterior shell) length of 27 laboratory-raised lobsters of

> The following table gives the number of heart transplants performed in the United States each year from 2006 to 2015 (U.s. Department of health and human services, optn.transplant.hrsa.gov/data/view-data-reports/national -data/, retrieved april 22, 2017

> Does it pay to stay in school? The report Trends in Higher Education (the College board, 2010) looked at the median hourly wage gain per additional year of schooling. The report states that workers with a high school diploma had a median hourly wage that

> Is living in a large high-rise apartment building a disadvantage in a medical emergency? This question was investigated in the paper “impact of building height and volume on Cardiac arrest response time” (Prehospital E

> Explain why it can be misleading to use the least squares regression line to obtain predictions for x values that are substantially larger or smaller than the x values in the data set.

> For a given data set, the sum of squared deviations from the line y = 40 + 6x is 529.5. For this same data set, which of the following could be the sum of squared deviations from the least squares regression line? Explain your choice. i. 308.6 ii. 529

> The relationship between hospital patient-to-nurse ratio and various characteristics of job satisfaction and patient care has been the focus of a number of research studies. Suppose x = Patient-to-nurse ratio is the predictor variable. For each of the fo

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> For each of the four scatterplots shown, answer the following questions: i. Does there appear to be a relationship between x and y? ii. If so, does the relationship appear to be linear? iii. If so, would you describe the linear relationship as positiv

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> Briefly explain why it is important to consider the value of se in addition to the value of r2 when evaluating the usefulness of the least squares regression line.

> Briefly explain why a large value of r2 is desirable in a regression setting.

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> Briefly explain why it is important to consider the value of r2 in addition to the value of se when evaluating the usefulness of the least squares regression line.

> For the data of Exercise 3.22, multiply each data value by 10, then calculate the standard deviation. How does this value compare to s for the original data? More generally, what happens to s if each observation is multiplied by the same positive constan

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> Briefly explain why a small value of se is desirable in a regression setting.

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> Use the data given in Exercise 4.33 to construct two scatterplots—one of number of cell phone calls versus age and the other of number of text messages sent versus age. Based on the scatterplots, do you think age is a better predictor o

> Use the data given in the previous exercise to find the equation of the least squares regression line for predicting y = Number of text messages sent using x = Age as a predictor

> The following table gives data on age, number of cell phone calls made in a typical day, and number of text messages sent in a typical day for a random sample of 10 people selected from those enrolled in adult education classes offered by a school distri

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> For the data in Exercise 3.22, subtract 10 from each sample observation. For the new set of values, calculate the mean and all the deviations from the mean. How do these deviations compare to the deviations from the mean for the original sample? How will

> The authors of the paper “evaluating existing Movement hypotheses in linear systems Using larval stream salamanders” (Canadian Journal of Zoology [2009]: 292–298) investigated whether water temperatur

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> What does it mean when we say that the regression line is the least squares regression line?

> Two scatterplots follow. Explain why it makes sense to use the least squares regression line to summarize the relationship between x and y for one of these data sets but not the other. Scatterplot 1 Scatterplot 2 110 100 90 + 80 y 70 60 50 + 40 + 3

> The authors of the paper “statistical Methods for assessing agreement between two Methods of Clinical Measurement” (International Journal of Nursing Studies [2010]: 931–936) compared two different ins

> Acrylamide is a chemical that is sometimes found in cooked starchy foods and which is thought to increase the risk of certain kinds of cancer. The paper “a statistical regression Model for the estimation of acrylamide Concentrations in

> Medical researchers have noted that adolescent females are much more likely to deliver lowbirth-weight babies than are adult females. Because low-birth-weight babies have a higher mortality rate, a number of studies have examined the relationship between

> Data on x = Size of a house (in square feet) and y = Amount of natural gas used (therms) during a specified period were used to fit the least squares regression line. The slope was 0.017 and the intercept was -5.0. Houses in this data set ranged in size

> Data on y = Time to complete a task (in minutes) and x = Number of hours of sleep on the previous night were used to find the least squares regression line. The equation of the line was ˆ y = 12 - 0.36x. For this data set, would the sum of squa

> Two scatterplots are shown below. Explain why it makes sense to use the least squares regression line to summarize the relationship between x and y for one of these data sets but not the other. Scatterplot 1 Scatterplot 2 110 100 90 80 y 70 60 + 5

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