Practice Questions 9.2

What is a scatterplot used for in the field of statistics?

A) To visually see the pattern of the relationship between two variables.
B) To measure the linear relationship between two variables.
C) To visually see where the data values are over a real number line.
D) To check to see that the coordinates of the dots are correct.

Select the two parts done when analyzing a scatterplot.

A) Look at the overall pattern.
B) Look for any exceptions to the overall pattern.
C) Use the Rubber Band method.
D) Check for the number of populations.

Select the overall patterns looked for in analyzing a scatterplot.

A) A linear relationship.
B) A curvi-linear relationship.
C) A bi-linear relationship.
D) No relationship.

What method is used to visually estimate the linear component in a scatterplot?

A) The Origin-Radius method.
B) The Straight-Edge method.
C) The Angle method.
D)  The Rubber-Band method.

Two separate scatterplots are shown below, though they have different directions of relationship, which scatterplot shows a higher linear relationship?

A) Plot A, because the points are closer to horizontal.
B) Plot A, because it has more points so it has more units of information (degrees of freedom).
C) Plot B, because a positive direction is more linear.
D)  Plot B, because its points are closer to a line.

What type of variable relationship is shown in the scatterplot below?


A) A linear relationship.
B) No relationship.
C) A minimal relationship.
D)  A curvi-linear relationship.

Which of the two scatterplots below show no relationship between two variables?


A) Neither scatterplot show no relationship.
B) Scatterplot A shows no relationship.
C)  Both scatterplots show no relationship.
D) Scatterplot B shows no relationship.

Select the exceptions to the overall patterns looked for when analyzing a scatterplot.

A) Pattern of any events.
B) A change in the slope of the mid-line.
C) The presence of extreme values.
D) More than one cluster (group).

How many possible extreme values can be seen in the scatterplot below?


A)  One possible extreme value at coordinates (66, 200).
B) Two possible extreme value at coordinates (66, 200) and (68, 120).
C) One possible extreme value at coordinates (62, 100).
D) Two possible extreme value at coordinates (66, 200) and (70, 200).

Is there an event shown in the scatterplot below?


A) Yes, there appears to be an event of some kind at x=6.
B) The entire scatterplot indicates one event.
C) Yes, there appears to be an event of some kind from x=3 to x=9.
D) Yes, there appears to be an event of some kind from x=5 to x=7.

How many clusters are seen in the scatterplot below?


A) Two definite clusters, perhaps three.
B) Only two definite clusters.
C) One large cluster.
D) Most definitely three clusters.

If scatterplots are so useful to see variable relationships, why is a statistical method using mathematics needed?

A) Some scatterplots are so amorphous that it can be hard to see any pattern.
B) Scatterplots can give erroneous information
C) A scatterplot does not quantify any relationship.
D) Statisticians trust mathematical methods over visual methods.

What type of relationship does linear correlation measure?

A)  Only a linear relationship.
B) Only a dependent relationship.
C) Both linear and curvi-linear relationships.
D) Only if there is any relationship or no relationship.

What calculation provides the foundation for the method of linear correlation?

A) Dividing two variances by each other.
B)  Multiplying two z-scores together.
C) Multiplying two x-values together.
D) Dividing by the degrees of freedom.

In the table used to calculate the linear correlation coefficient by hand, in the last column titled (Zx × Zy) , how many plus (+) and minus (-) signs would you expect for a correlation coefficient near zero (0).

A) There should not be any minus (-) signs in the last column.
B) Many pairs of (+'s) and (-'s).
C)  Equal number of (+'s) and (-'s).
D) Almost all (+'s) and few (-'s).

What two characteristics of linear relationship are expressed in a correlation coefficient?

A) The change in the linear relationship expressed in the distance from zero (0).
B) The lack of a linear relationship expressed as a more negative value.
C) The direction of the linear relationship expressed in the mathematical sign.
D) The strength of the linear relationship expressed in the magnitude of the value.

Match each linear relationship with the movement of the variable data values.

A. No linear relationship.
B. A positive linear relationship.
C. A negative linear relationship.

__ Variable data values move in the same direction.
__ Variable data values move in opposite directions.
__ Variable data values move independently of each other.

Select the values of a correlation coefficient that indicate a strong linear relationship.

A) r = (-1)
B) r = (0)
C) r = (+1)
D) r = (+2)

Match each scatterplot with its correlation coefficient.


A) r= -0.3
B) r= +0.5
C) r= +0.9
D) r= -0.99

How does the Rubber Band method indicate a high linear component?

A) By forming a horseshoe shape.
B)  By forming a narrow oval shape.
C) By forming a rectangular shape.
D) By forming a circular shape.

Two scatterplots are plotted in the graph below, which scatterplot shows the higher linear correlation coefficient?


A)  Plot B, because its points are closer to a line.
B) Plot A, because the points rise faster going left to right.
C) Plot A, because it is above Plot B.
D) Plot B, because the points are closer to horizontal.

How does an extreme value affect the linear correlation coefficient?

A)  All of the other answers.
B) It makes it appear to have a higher linear relationship (+ or -).
C) It gives a large (Zx × Zy) value, which makes a larger (Zx × Zy) sum (+ or -).
D) It creates a situation where the linear correlation coefficient see's only two points, meaning a high linear relationship.