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A regression was run to determine whether there is a relationship between the diameter of a tree ( $x,$ in inches) and the tree’s age ( $y,$ 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 $60\xb0\text{F}.$
For the following exercises, match each scatterplot with one of the four specified correlations in [link] and [link] .
$r=0.\text{95}$
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 $r=0.\text{985}$ 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.
$x$ | 8 | 15 | 26 | 31 | 56 |
$y$ | 23 | 41 | 53 | 72 | 103 |
$y=\text{1}.\text{64}0x+\text{13}.\text{8}00$ , $r=0.\text{987}$
$x$ | 5 | 7 | 10 | 12 | 15 |
$y$ | 4 | 12 | 17 | 22 | 24 |
$x$ | $y$ | $x$ | $y$ |
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 |
$$y=-0.962x+26.86,r=-0.965$$
$x$ | $y$ |
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 |
$x$ | $y$ |
21 | 17 |
25 | 11 |
30 | 2 |
31 | −1 |
40 | −18 |
50 | −40 |
$y=-\text{1}.\text{981}x+\text{6}0.\text{197}$ ; $r=-0.\text{998}$
$x$ | $y$ |
100 | 2000 |
80 | 1798 |
60 | 1589 |
55 | 1580 |
40 | 1390 |
20 | 1202 |
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