2.4E: Fitting Linear Models to Data (Exercises)
 Page ID
 13900
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The following is data for the first and second quiz scores for 8 students in a class. Plot the points, then sketch a line that fits the data.
First Quiz  11  20  24  25  33  42  46  49 

Second Quiz  10  16  23  28  30  39  40  49 

Eight students were asked to estimate their score on a 10 point quiz. Their estimated and actual scores are given. Plot the points, then sketch a line that fits the data.
Predicted  5  7  6  8  10  9  10  7 

Actual  6  6  7  8  9  9  10  6 
Based on each set of data given, calculate the regression line using your calculator or other technology tool, and determine the correlation coefficient.
3.  x y 5 4 7 12 10 17 12 22 15 24  4.  x y 8 23 15 41 26 53 31 72 56 103  5.  x y 3 21.9 4 22.22 5 22.74 6 22.26 7 20.78 8 17.6 9 16.52 10 18.54 11 15.76 12 13.68 13 14.1 14 14.02 15 11.94 16 12.76 17 11.28 18 9.1  6.  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 14 24.7 15 22 16 20.1 17 19.8 18 16.8 


A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression are given below. Use this to predict the number of situps a person who watches 11 hours of TV can do.
y=ax+b
a=1.341
b=32.234
r\({}^{2}\)=0.803
r=0.896

A regression was run to determine if 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.
y=ax+b
a=6.301
b=1.044
r\({}^{2}\)=0.940
r=0.970
Match each scatterplot shown below with one of the four specified correlations.
9. r = 0.95 10. r = 0.89 11. r = 0.26 12. r = 0.39
A B C D

The US census tracks the percentage of persons 25 years or older who are college graduates. That data for several years is given below. Determine if the trend appears linear. If so and the trend continues, in what year will the percentage exceed 35%?
Year  1990  1992  1994  1996  1998  2000  2002  2004  2006  2008 

Percent Graduates  21.3  21.4  22.2  23.6  24.4  25.6  26.7  27.7  28  29.4 

The US import of wine (in hectoliters) for several years is given below. Determine if the trend appears linear. If so and the trend continues, in what year will imports exceed 12,000 hectoliters?
Year  1992  1994  1996  1998  2000  2002  2004  2006  2008  2009 

Imports  2665  2688  3565  4129  4584  5655  6549  7950  8487  9462 
Section 2.5 Absolute Value Functions 159