Concept explainers
In each of the next two problems, two linear models are given for the data. For each model,
(a) Find the residuals and their sum;
(b) Find the sum of the squares of the residuals;
(c) Decide which model is the better fit. (See Example 2.)
International Trade The following table shows the South Koreas’s petrochemical exports to China (in billions of dollars) for several years.
Year | 2010 | 2011 | 2012 | 2013 | 2014 |
Petrochemical | 16 | 21 | 21 | 23 | 21.4 |
Let x=10 correspond to the year 2010. Two equations that model these data are
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Finite Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
- LIFE SCIENCE APPLICATIONS HIV Infection The time interval between a persons initial infection with HIV and that persons eventual development of AIDS symptoms is an important issue. The method of infection with HIV affects the time interval before AIDS develops. One study of HIV patients who were infected by intravenous drug use found that 17 of the patients had AIDS after 4 years and 33 had developed the disease after 7 years. The relationship between the time interval and the percentage of patients with AIDS can be modeled accurately with a linear equation. Source: Epidemiologic Review. a. Write a linear equation y=mt+b that models these data, using the ordered pairs (4,0.17) and (7,0.33). b. Use your equation from part a to predict the number of years before half of these patients will have AIDS.arrow_forwardHOW DO YOU SEE IT? Discuss how well a linear model approximates the data shown in each scatter plot.arrow_forwardDemand for Candy Bars In this problem you will determine a linear demand equation that describes the demand for candy bars in your class. Survey your classmates to determine what price they would be willing to pay for a candy bar. Your survey form might look like the sample to the left. a Make a table of the number of respondents who answered yes at each price level. b Make a scatter plot of your data. c Find and graph the regression line y=mp+b, which gives the number of respondents y who would buy a candy bar if the price were p cents. This is the demand equation. Why is the slope m negative? d What is the p-intercept of the demand equation? What does this intercept tell you about pricing candy bars? Would you buy a candy bar from the vending machine in the hallway if the price is as indicated. Price Yes or No 50 75 1.00 1.25 1.50 1.75 2.00arrow_forward
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