Name ________________________________________ Date __________________ Class__________________
Practice B
LESSON
15-2
Line of Best Fit
1. The data in the table are graphed at right along with two
lines of fit.
x
0
2
4
6
y
7
3
4
0
a. Find the sum of the squares of the residuals for
y 3x 9.___________________________
b. Find the sum of the squares of the residuals for
1
y x 5. ___________________________
2
c. Which line is a better fit for the data? ___________________________
2. Use the data in the table to answer the questions that follow.
x
5
6
6.5
7.5
9
y
0
1
3
2
4
a. Find an equation for a line of best fit. ___________________________
b. What is the correlation coefficient? ___________________________
c. How well does the line represent the data? ___________________________
d. Describe the correlation. ___________________________
3. Use the data in the table to answer the questions that follow.
x
10
8
6
4
2
y
1
1.1
1.2
1.3
1.5
a. Find an equation for a line of best fit. ___________________________
b. What is the correlation coefficient? ___________________________
c. How well does the line represent the data? ___________________________
d. Describe the correlation. ___________________________
4. The table shows the number of pickles four students ate during the week versus their
grades on a test. The equation of the least-squares line is y | 2.11x 79.28, and r | 0.97.
Discuss correlation and causation for the data set.
Pickles Eaten
0
2
5
10
Test Score
77
85
92
99
_________________________________________________________________________________________
_________________________________________________________________________________________
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362
Holt McDougal Coordinate Algebra
4. negative correlation
5. C
6. J
7. B
8. F
4. strong pos. correlation; unlikely
cause-and-effect relationship
Practice C
1 a. 26
Reading Strategies
1. number of children in a family; monthly
cost of food; increases; positive
b. 15
2. population of cities in the U.S.; average
February temperature; shows no pattern;
none
c. y
b. 0.53
c. not well
d. weak pos. correlation
15-2 LINE OF BEST FIT
3 a. y
Practice A
c. very well
d. strong pos. correlation
4. strong neg. correlation; likely
cause-and-effect relationship
2 a. y | 0.27 x 3.77
Review for Mastery
1 a. 8, 7, 6, 5
0.13 x 4.28
3 a. y
0.61x 1.05
b. 0.99
1 a. 6
b. 6
c. neither
b. § 0.997
c. very well
d. strong pos. correlation
1
x 4.
3
2 a. y | 0.49 x 4.94
3. number of practice runs; finish time;
decreases; negative
b. 8, 0; 7, –2; 6, –1; 5, –3
b. § –0.997
c. very well
d. strong neg. correlation
c. 0, –2, –1, –3; 0, 4, 1, 9; 14
2. y
x 9
3. 1.51; 12.90
4. strong pos. correlation; likely
cause-and-effect relationship
1.51; 12.90
0.93; strong neg.
Practice B
Challenge
1 a. 134
1.
b. 10
c. y
8
9
1
x 5.
2
2 a. y | 0.78 x 4.54
b. 0.46
c. moderately well
2. 6x – 6
d. weak pos. correlation
2
5. x + 1
3 a. y | 0.06 x 1.58
4. 0.98
7. 1
8. Possible answer: r 0.98 for y 6x 6,
which means there is a strong positive
correlation and that the linear equation is
a very good model of the data; however,
r 1 for y x2 1, which means the
b. 0.99
c. very well
d. strong neg. correlation
© Houghton Mifflin Harcourt Publishing Company
A84
Holt McDougal Coordinate Algebra