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A regression was run to determine whether there is a relationship between the diameter of a tree ( in inches) and the tree’s age ( in years). The results of the regression are given below. Use this to predict the age of a tree with diameter 10 inches.
61.966 years
For the following exercises, draw a scatter plot for the data provided. Does the data appear to be linearly related?
| 0 | 2 | 4 | 6 | 8 | 10 |
| –22 | –19 | –15 | –11 | –6 | –2 |
| 100 | 250 | 300 | 450 | 600 | 750 |
| 12 | 12.6 | 13.1 | 14 | 14.5 | 15.2 |
For the following data, draw a scatter plot. If we wanted to know when the population would reach 15,000, would the answer involve interpolation or extrapolation? Eyeball the line, and estimate the answer.
| Year | Population |
| 1990 | 11,500 |
| 1995 | 12,100 |
| 2000 | 12,700 |
| 2005 | 13,000 |
| 2010 | 13,750 |
For the following data, draw a scatter plot. If we wanted to know when the temperature would reach 28 °F, would the answer involve interpolation or extrapolation? Eyeball the line and estimate the answer.
| Temperature, °F | 16 | 18 | 20 | 25 | 30 |
| Time, seconds | 46 | 50 | 54 | 55 | 62 |
Interpolation. About
For the following exercises, match each scatterplot with one of the four specified correlations in [link] and [link] .
For the following exercises, draw a best-fit line for the plotted data.
The U.S. Census tracks the percentage of persons 25 years or older who are college graduates. That data for several years is given in [link] http://www.census.gov/hhes/socdemo/education/data/cps/historical/index.html. Accessed 5/1/2014. . Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the percentage exceed 35%?
| Year | Percent Graduates |
| 1990 | 21.3 |
| 1992 | 21.4 |
| 1994 | 22.2 |
| 1996 | 23.6 |
| 1998 | 24.4 |
| 2000 | 25.6 |
| 2002 | 26.7 |
| 2004 | 27.7 |
| 2006 | 28 |
| 2008 | 29.4 |
The U.S. import of wine (in hectoliters) for several years is given in [link] . Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?
| Year | Imports |
| 1992 | 2665 |
| 1994 | 2688 |
| 1996 | 3565 |
| 1998 | 4129 |
| 2000 | 4584 |
| 2002 | 5655 |
| 2004 | 6549 |
| 2006 | 7950 |
| 2008 | 8487 |
| 2009 | 9462 |
Yes, trend appears linear because and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.
[link] shows the year and the number of people unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5?
| Year | Number Unemployed |
| 1990 | 750 |
| 1992 | 670 |
| 1994 | 650 |
| 1996 | 605 |
| 1998 | 550 |
| 2000 | 510 |
| 2002 | 460 |
| 2004 | 420 |
| 2006 | 380 |
| 2008 | 320 |
For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy.
| 5 | 7 | 10 | 12 | 15 | |
| 4 | 12 | 17 | 22 | 24 |
| 3 | 21.9 | 11 | 15.76 |
| 4 | 22.22 | 12 | 13.68 |
| 5 | 22.74 | 13 | 14.1 |
| 6 | 22.26 | 14 | 14.02 |
| 7 | 20.78 | 15 | 11.94 |
| 8 | 17.6 | 16 | 12.76 |
| 9 | 16.52 | 17 | 11.28 |
| 10 | 18.54 | 18 | 9.1 |
| 4 | 44.8 |
| 5 | 43.1 |
| 6 | 38.8 |
| 7 | 39 |
| 8 | 38 |
| 9 | 32.7 |
| 10 | 30.1 |
| 11 | 29.3 |
| 12 | 27 |
| 13 | 25.8 |
| 100 | 2000 |
| 80 | 1798 |
| 60 | 1589 |
| 55 | 1580 |
| 40 | 1390 |
| 20 | 1202 |
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