5.6 - Test Yourself!

Question 1

Which of the following is not appropriate for studying the relationship (association) between two measurement variables?

Scatterplot
The answer is Bar Graph - because a bar graph can only be used with categorical data.
Bar Graph
Correct. Bar Graph - because a bar graph can only be used with categorical data.
Correlation
The answer is Bar Graph - because a bar graph can only be used with categorical data.
Regression
The answer is Bar Graph - because a bar graph can only be used with categorical data.

Question 2

Which of the following is the range of possible values that a correlation can assume?

0 to 1
The answer is -1 to 1 because a perfect linear relationship either has a correlation of -1 or +1, these two numbers form the boundaries for possible values for a correlation.
-1 to 0
The answer is -1 to 1 because a perfect linear relationship either has a correlation of -1 or +1, these two numbers form the boundaries for possible values for a correlation.
-1 to 1
Correct. -1 to 1 because a perfect linear relationship either has a correlation of -1 or +1, these two numbers form the boundaries for possible values for a correlation.
0 and above
The answer is -1 to 1 because a perfect linear relationship either has a correlation of -1 or +1, these two numbers form the boundaries for possible values for a correlation.

Question 3

The regression line for a set of points is given by \(y = -10 + 6 x\). What is the slope of the line?

-10

The answer is 6 because the slope is the b value in the formula in the textbook (page 189) and the sign is important. In this case, for each additional unit of x, the y value is predicted to increase (since the sign is positive) by 6 units.
10

The answer is 6 because the slope is the b value in the formula in the textbook (page 189) and the sign is important. In this case, for each additional unit of x, the y value is predicted to increase (since the sign is positive) by 6 units.
-6

The answer is 6 because the slope is the b value in the formula in the textbook (page 189) and the sign is important. In this case, for each additional unit of x, the y value is predicted to increase (since the sign is positive) by 6 units.
6

Correct. 6 because the slope is the b value in the formula in the textbook (page 189) and the sign is important. In this case, for each additional unit of x, the y value is predicted to increase (since the sign is positive) by 6 units.

Question 4

Describe the association found in the graph above.

positive linear association
The answer is negative linear association - because the y value decreases as the x value increases which is a negative association. Anytime one variable decreases as the other variable increases you have a negative association.
negative linear association
Correct. Negative linear association - because the y value decreases as the x value increases which is a negative association. Anytime one variable decreases as the other variable increases you have a negative association.
neither positive nor negative linear association
The answer is negative linear association - because the y value decreases as the x value increases which is a negative association. Anytime one variable decreases as the other variable increases you have a negative association.

Question 5

Suppose a correlation -.65 is obtained from two measurement variables. Which of the following might represent the slope that would be found if a regression equation were calculated?

5.4
The answer is -2.8 because the slope and the correlation must always have the same sign.
-2.8
Correct. -2.8 because the slope and the correlation must always have the same sign.
0
The answer is -2.8 because the slope and the correlation must always have the same sign.

Question 6

If you make a scatterplot of the miles of highways versus the number of infant deaths for the fifty states you will find a moderate positive correlation. An obvious problem with viewing this as important evidence that building highways causes infant deaths is that:

bigger states with more miles of highways like California and Texas are also the most populous states so more infant deaths are expected.
Correct. More populous states like California and Texas are expected to have more infant deaths. Watch out for variables that are both strongly related to population size. Often using rates (like infant deaths per 1000 births) is more valid.
many infant deaths do not happen as part of car accidents.
The answer is that more populous states like California and Texas are expected to have more infant deaths. Watch out for variables that are both strongly related to population size. Often using rates (like infant deaths per 1000 births) is more valid.
laws about car seats for children vary from state-to-state.
The answer is that more populous states like California and Texas are expected to have more infant deaths. Watch out for variables that are both strongly related to population size. Often using rates (like infant deaths per 1000 births) is more valid.
the sample size of 50 is too small to determine if there is a relationship.
The answer is that more populous states like California and Texas are expected to have more infant deaths. Watch out for variables that are both strongly related to population size. Often using rates (like infant deaths per 1000 births) is more valid.

Question 7

The correlation between the heights and weights of the people in a small room was 0.6 until former basketball star Shaquille O’Neal (7 ft 1 in and 335 lb) entered the room. At that point the correlation:

was lower than 0.6.
The answer is: higher than 0.6. Shaquille O’Neal would be an outlier in both height and weight (falling in the far upper right of the scatterplot) and would increase the correlation.
was still 0.6
The answer is: higher than 0.6. Shaquille O’Neal would be an outlier in both height and weight (falling in the far upper right of the scatterplot) and would increase the correlation.
was higher than 0.6.
Correct. Higher than 0.6. Shaquille O’Neal would be an outlier in both height and weight (falling in the far upper right of the scatterplot) and would increase the correlation.

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5.6 - Test Yourself!

Think About It!