Practice Page
Directions: Read carefully. These questions pertain to correlations and correlation coefficients.
 
 
 
GA
GB
 
GC
GD
 
GE
GF
 


Choose the scatter plot which could possibly have the given r -value:

  1.
 r = 0.50
A B C D E F
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  2.
 r = 0
A B C D E F
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  3.
 r = -0.85
A B C D E F
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  4.
 r = 0.92
A B C D E F
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  5.
 r = 1
A B C D E F
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  6.
 r = -0.48
A B C D E F
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  7.  What does it mean to say that data has a strong negative correlation? Choose:
There is no relationship at all between the variables.
 
More than half of the variables have a negative value.
 
There is a negative cause and effect relationship.
 
A linear model with a negative slope is appropriate.

 

 

  8.  Which of the following correlation coefficients represents the strongest linear relationship?

Choose:
0.79
0.36
-0.12
-0.87

 

 

  9.  The relationship between the number of widgets packed in a container (x-axis) and the length of the container (y-axis), in inches, is given in the table at the right.
Number of Widgets
Length of Container
3
12 in.
4
15 in.
5
18 in.
6
21 in.
a) Find the linear regression equation for this data.
Choose:
y = 3x + 1
 y = 3x
 
y = 3x + 3
 y = x + 3

b) The linear correlation coefficient for this relationship is:
Choose:
 
1
-1
0.5
0


c) Explain what the correlation coefficient indicates about the linear fit of the data in the context of this problem. Explain the meaning of the slope and the y-intercept.

 

 

   10.  Which calculator output shows the strongest linear relationship between x and y?
Choose:
 
LinReg
y = ax + b
a = 58.135
b = 7.348
r = 0.843
LinReg
y = a + bx
a = 0.702
b = 24.286
r = 0.8145
LinReg
y = ax + b
a = 0.952
b = 3.45
r = 0.633

LinReg
y = ax + b
a = 22.567
b = -4.332
r = 0.894

 

 

  11.  A famous musician is scheduled to perform at a local arena. The cost of a hotel room for the weekend date of the concert, and the distance from the hotel to the arena, as shown in the table at the right.

a) Find the linear regression equation for this data. (Round to nearest hundredths.)
Choose:
y = 152.38x + 493.93
 
y = 152.38x + 493.92
  y = -152.38 + 493.92
  y = -152.38x + 493.93
Distance from Arena
Hotel Room Cost
¼ mi.
$450
½ mi.
$420
¾ mi.
$380
1 mi.
$350
1¼ mi. $310
1½ mi. $250
1¾ mi. $230
2 mi. $190

b) The linear correlation coefficient for this relationship is:
(rounded to three decimal places)
Choose:
 
0.994
0.997
-0.997
-0.994

 

c) Explain what the sign of the correlation coefficient indicates in relation to this problem.

 

 

  12.  The table at the right shows the average target training heart rates, by age, according to the American Heart Association. Which value represents the linear correlation coefficient between a person's age, in years, and that person's average target training heart rate, in beats per minute (bpm)? (Round to four decimal places with Age on x-axis and Heart Rate on y-axis.)
Choose:
 
-0.6652
1.3231
 
-0.9996
0.9993
Age
(years)
Average Target
Heart Rate (bpm)
20
135
30
129
40
122
50
115
60
108
70
102

 

 

  13. A research study finds that fat calories in hamburger have a positive linear association with the amount of sodium found in the hamburger. This finding indicates that:  (choose the best answer)  
Choose:
low amounts of sodium in hamburgers indicates a high number of fat calories in hamburger.
 
high amounts of sodium in hamburgers cause high amounts of fat calories in hamburger.
 
hamburgers with low amounts of fat calories tend to have low amounts of sodium.
 
hamburgers with low amounts of fat calories have high amounts of sodium.



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