StatTutor Lesson - Measuring linear association: correlation

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Measuring linear association-correlation (1)
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      Question 1

      37

      Question 1.

      Which scattterplot displays data with the strongest relationship?

      A.
      B.
      C.

      Correct. The cloud of data in the scatterplot on the left is skinnier than the cloud of data in the plot on the right. Note that the labeling on the x- and y-axes are the same for both scatterplots.
      Incorrect. The cloud of data in the scatterplot on the left is skinnier than the cloud of data in the plot on the right. Note that the labeling on the x- and y-axes are the same for both scatterplots.
      2
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      Question 2

      60

      Question 2.

      Which scattterplot displays data with the strongest relationship?

      A.
      B.
      C.

      Correct. If you note the labeling on the x- and y-axes, you will see that the same data is plotted in both scatterplots.
      Incorrect. If you note the labeling on the x- and y-axes, you will see that the same data is plotted in both scatterplots.
      2
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      Question 3

      93

      Question 3.

      Which scatterplot displays data with the strongest relationship?

      A.
      B.
      C.

      Correct. This is a hard question as the cloud of data in the plot on the right is much skinnier than the cloud of data in the plot on the left. However, both clouds are parallel to the x-axis. The line drawn through both clouds would have zero slope—indicating no relationship between X and Y.
      Incorrect. This is a hard question as the cloud of data in the plot on the right is much skinnier than the cloud of data in the plot on the left. However, both clouds are parallel to the x-axis. The line drawn through both clouds would have zero slope—indicating no relationship between X and Y.
      2
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      Question 4

      157

      Question 4.

      On the basis of this formula, what type of variables are required for X and Y?

      A.
      B.
      C.

      Correct. Computing correlation, r, requires both X and Y to be quantitative.
      Incorrect. Computing correlation, r, requires both X and Y to be quantitative.
      2
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      Question 5

      181

      Question 5.

      Why is plotting the data so important before computing r?

      A.
      B.
      C.

      Correct. Correlation should only be computed for X and Y when their relationship is linear.
      Incorrect. Correlation should only be computed for X and Y when their relationship is linear.
      2
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      Question 6

      228

      Question 6.

      True or false: The formula for computing r includes z-scores for both X and Y.

      A.
      B.

      Correct. This is a correct statement.
      Incorrect. This is a correct statement.
      2
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      Question 7

      327

      Question 7.

      Is the direction of the relationship displayed in the scatterplot positive or negative or no relationship?

      A.
      B.
      C.

      Correct. While not strong, the direction of a line drawn through the cloud of data would have negative slope.
      Incorrect. While not strong, the direction of a line drawn through the cloud of data would have negative slope.
      2
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      Question 8

      400

      Question 8.

      True or false: Multiplying the z-score for X by the z-score for Y always gives positive products.

      A.
      B.

      Correct. z-scores can be negative or positive. A positive z-score multiplied by a negative z-score gives a negative product.
      Incorrect. z-scores can be negative or positive. A positive z-score multiplied by a negative z-score gives a negative product.
      2
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      Question 9

      443

      Question 9.

      True or false: Because the value for r is negative, we can say that the direction of the relationship is negative.

      A.
      B.

      Correct. This is a correct statement.
      Incorrect. This is a correct statement.
      2
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      Question 10

      467

      Question 10.

      Since r = –0.54, how should we describe the strength of the relationship?

      A.
      B.
      C.

      Correct. On a scale from zero to one, 0.54 is near the middle so it tells us that the strength is “moderate.”
      Incorrect. On a scale from zero to one, 0.54 is near the middle so it tells us that the strength is “moderate.”
      2
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      Question 11

      550

      Question 11.

      True or false: For these data, all of the products are positive.

      A.
      B.

      Correct. This is a correct statement. All rectangles have red or pink colors.
      Incorrect. This is a correct statement. All rectangles have red or pink colors.
      2
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      Question 12

      587

      Question 12.

      How would you describe these products?

      A.
      B.
      C.
      D.
      E.

      Correct. Since most of the rectangles have pink or red colors rather than blue colors, most of the products are positive.
      Incorrect. Since most of the rectangles have pink or red colors rather than blue colors, most of the products are positive.
      2
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      Question 13

      599

      Question 13.

      How would you describe these products?

      A.
      B.
      C.
      D.
      E.

      Correct. The number of rectangles with pink and red colors is about the same as the number of rectangles with blue colors.
      Incorrect. The number of rectangles with pink and red colors is about the same as the number of rectangles with blue colors.
      2
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      Question 14

      608

      Question 14.

      How would you describe these products?

      A.
      B.
      C.
      D.
      E.

      Correct. The number of rectangles with red and pink colors is less than the number of rectangles with blue colors.
      Incorrect. The number of rectangles with red and pink colors is less than the number of rectangles with blue colors.
      2
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      Question 15

      627

      Question 15.

      How would you describe these products?

      A.
      B.
      C.
      D.
      E.

      Correct. All rectangles have blue colors.
      Incorrect. All rectangles have blue colors.
      2
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      Question 16

      686

      Question 16.

      True or false: The closer the data points are to the line, the closer r is to either –1.0 or +1.0.

      A.
      B.

      Correct. This is a correct statement.
      Incorrect. This is a correct statement.
      2
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      Questions 17-18

      720

      Question 17.

      With r = 0.941, is direction positive or negative?

      A.
      B.

      Correct. Since the sign on “r” is positive, direction is positive.
      Incorrect. Since the sign on “r” is positive, direction is positive.
      2
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      Questions 19-20

      755

      Question 19.

      With r = –0.553, is direction positive or negative?

      A.
      B.

      Correct. Since the sign on “r” is negative, direction is negative.
      Incorrect. Since the sign on “r” is negative, direction is negative.
      2
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      Question 21

      829

      Question 21.

      With r = –0.226, is direction positive or negative?

      A.
      B.

      Correct. Since the sign on “r” is negative, direction is negative.
      Incorrect. Since the sign on “r” is negative, direction is negative.
      2
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      Questions 22-23

      845

      Question 22.

      With r = –0.226, how should we describe strength?

      A.
      B.
      C.

      Correct. On a scale from zero to one, 0.226 is close to zero, so strength is weak.
      Incorrect. On a scale from zero to one, 0.226 is close to zero, so strength is weak.
      2
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