Regents Exam Questions S.ID.C.8: Correlation Coefficient 1 Name: ________________________
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S.ID.C.8: Correlation Coefficient 1
1 Bella recorded data and used her graphing calculator to find the equation for the line of best fit. She then used the
correlation coefficient to determine the strength of the linear fit. Which correlation coefficient represents the
strongest linear relationship?
1) 0.9 3) -0.3
2) 0.5 4) -0.8
2 Analysis of data from a statistical study shows a linear relationship in the data with a correlation coefficient of
-0.524. Which statement best summarizes this result?
1) There is a strong positive correlation
between the variables.
3) There is a moderate positive correlation
between the variables.
2) There is a strong negative correlation
between the variables.
4) There is a moderate negative correlation
between the variables.
3 The results of a linear regression are shown below.
y = ax + b
a = −1.15785
b = 139.3171772
r = −0.896557832
r
2
= 0.8038159461
Which phrase best describes the relationship between x and y?
1) strong negative correlation 3) weak negative correlation
2) strong positive correlation 4) weak positive correlation
4 What is the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth?
1) 1.00 3)
−
0
.
9
3
2) 0.93 4)
−
1
.
0
0
Regents Exam Questions S.ID.C.8: Correlation Coefficient 1 Name: ________________________
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5 The scatterplot below compares the number of bags of popcorn and the number of sodas sold at each performance
of the circus over one week.
Which conclusion can be drawn from the scatterplot?
1) There is a negative correlation between
popcorn sales and soda sales.
3) There is no correlation between popcorn
sales and soda sales.
2) There is a positive correlation between
popcorn sales and soda sales.
4) Buying popcorn causes people to buy
soda.
6 The table below shows the time, in hours, spent by students on electronic devices and their math test scores. The
data collected model a linear regression.
Time Spent on an
Electronic Device (hours)
Math Test Score
3 85
1 99
4 81
0 98
3 90
7 65
5 78
2 90
What is the correlation coefficient, to the nearest hundredth, for these data?
1)
−
0
.
9
8
3) 0.98
2)
−
0
.
9
5
4) 0.95
Regents Exam Questions S.ID.C.8: Correlation Coefficient 1 Name: ________________________
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7 The table below shows 6 students' overall averages and their averages in their math class.
Overall Student
Average
92 98 84 80 75 82
Math Class
Average
91 95 85 85 75 78
If a linear model is applied to these data, which statement best describes the correlation coefficient?
1) It is close to
−
1
. 3) It is close to 0.
2) It is close to 1. 4) It is close to 0.5.
8 At Mountain Lakes High School, the mathematics and physics scores of nine students were compared as shown in
the table below.
Mathematics
55 93 89 60 90 45 64 76 89
Physics
66 89 94 52 84 56 66 73 92
State the correlation coefficient, to the nearest hundredth, for the line of best fit for these data. Explain what the
correlation coefficient means with regard to the context of this situation.
9 A nutritionist collected information about different brands of beef hot dogs. She made a table showing the number
of Calories and the amount of sodium in each hot dog.
Calories per
Beef Hot Dog
Milligrams of Sodium
per Beef Hot Dog
186 495
181 477
176 425
149 322
184 482
190 587
158 370
139 322
a) Write the correlation coefficient for the line of best fit. Round your answer to the nearest hundredth.
b) Explain what the correlation coefficient suggests in the context of this problem.
ID: A
1
S.ID.C.8: Correlation Coefficient 1
Answer Section
1 ANS: 1 REF: 061714ai
2 ANS: 4 REF: 011703ai
3 ANS: 1 REF: 081722ai
4 ANS: 3 REF: 061411ai
5 ANS: 2 REF: 061604ai
6 ANS: 1
r = −0.98
REF: 082223ai
7 ANS: 2
r = 0.92
REF: 081606ai
8 ANS:
r ≈ 0.92
. The correlation coefficient suggests a strong positive correlation between a student’s mathematics and
physics scores.
REF: 011831ai
9 ANS:
r ≈ 0.94
. The correlation coefficient suggests that as calories increase, so does sodium.
REF: 011535ai
