Question 1

A researcher records the odometer reading and price for a group of used Hondas.What kind of correlation is likely to be obtained for these two variables?
A)A positive correlation
B)A negative correlation
C)A correlation near zero
D)A correlation near one

Accepted Answer

Typically, as the odometer reading (mileage) increases on a used car, the price decreases, resulting in a negative correlation between the two variables.

Question 2

A set of n = 10 pairs of scores has ΣX = 20,ΣY = 30,and ΣXY = 74.What is the value of SP for these data?
A)74
B)24
C)14
D)-14

Accepted Answer

C

Question 3

A set of n = 5 pairs of X and Y scores has ΣX = 15,ΣY = 5,and ΣXY = 10.For these data,what is the value of SP?
A)-5
B)5
C)10
D)25

Accepted Answer

SP (Sum of Products) is calculated using the formula SP = ΣXY - (ΣX)(ΣY)/n. Substituting the given values, SP = 10 - (15*5)/5 = 10 - 15 = -5.

Question 4

The scatter plot for a set of X and Y values shows the data points clustered in a nearly perfect circle.For these data,what is the most likely value for the Pearson correlation?
A)A positive correlation near 0
B)A negative correlation near 0
C)Either positive or negative near 0
D)A value near +1.00 or -100

Accepted Answer

The Pearson correlation measures the linear relationship between two variables. If the scatter plot shows data points clustered in a nearly perfect circle, it indicates that there is no clear linear relationship between X and Y. Therefore, the Pearson correlation would be near 0, but it does not specify whether it would be slightly positive or slightly negative, hence either positive or negative near 0 is correct.

Question 5

The Pearson correlation is calculated for a sample of n = 20 individuals.If a hypothesis test is used to determine whether the correlation is significant,what df value would be used for the t statistic?
A)18
B)19
C)20
D)21

Accepted Answer

The degrees of freedom (df) for a Pearson correlation coefficient test is calculated as n - 2, where n is the sample size. Here, n = 20, so df = 20 - 2 = 18.

Question 6

A set of n = 15 pairs of scores (X and Y values)produces a correlation of r = 0.40.If each of the X values is multiplied by 2 and the correlation is computed for the new scores,what value will be obtained for the new correlation?
A)r = 0.20
B)r = 0.40
C)r = 0.80
D)Cannot be determined without knowing all the X and Y scores

Accepted Answer

When each X value is multiplied by 2, it only changes the scale of the X values, not the relationship between X and Y. Therefore, the correlation coefficient will remain the same.

Question 7

The results from a research study indicate that adolescents who watch more violent content on television also tend to engage in more violent behavior than their peers.The correlation between amount of TV violent content and amount of violent behavior is an example of _______.
A)a positive correlation
B)a negative correlation
C)a correlation near zero
D)a correlation near one

Accepted Answer

A positive correlation means that as one variable increases, so does the other variable. In this case, as the amount of TV violent content increases, so does the amount of violent behavior.

Question 8

A set of n = 15 pairs of scores (X and Y values)has SS_X = 4,SS_Y = 25,and SP = 6.What is the Pearson correlation for these data? A)6/100 B)6/10 C)6/(100/15) D)6/(10/?0v15)

Accepted Answer

The answer of A set of n = 15 pairs...

Question 9

What would the scatter plot show for data that produce a Pearson correlation of r = +0.88?
A)Points clustered close to a line that slopes up to the right
B)Points clustered close to a line that slopes down to the right
C)Points widely scattered around a line that slopes up to the right
D)Points widely scattered around a line that slopes down to the right

Accepted Answer

A Pearson correlation of +0.88 indicates a strong positive correlation, meaning that as one variable increases, the other tends to increase as well. A scatter plot for this data would show points clustered close to a line that slopes up to the right, indicating a clear positive linear relationship between the two variables.

Question 10

What is indicated by a positive value for a correlation?
A)Increases in X tend to be accompanied by increases in Y
B)Increases in X tend to be accompanied by decreases in Y
C)A much stronger relationship than if the correlation were negative
D)A much weaker relationship than if the correlation were negative

Accepted Answer

A positive value for a correlation indicates that there is a positive relationship between the two variables being studied, meaning that as one variable increases, the other variable is likely to increase as well.

Question 11

A researcher measures IQ and weight for a group of college students.What kind of correlation is likely to be obtained for these two variables?
A)A positive correlation
B)A negative correlation
C)A correlation near zero
D)A correlation near one

Accepted Answer

The variables IQ and weight are not directly related in a way that would suggest either a positive or negative correlation. Therefore, it is most likely that any correlation between these two variables would be near zero, indicating no strong relationship.

Question 12

A set of n = 5 pairs of X and Y values has SS_X = 16,SS_Y = 4 and SP = 2.For these data,what is the Pearson correlation ? A)r = 2/64 B)r = 2/8 C)r = $\surd$2/8 D)r = 64/64

Accepted Answer

The formula for Pearson correlation is: 
r = (SSxy / √(SSxx * SSyy))
where SSxy is the sum of squares of the differences between each X and Y value, SSxx is the sum of squares of the differences between each X value and the mean of X, and SSyy is the sum of squares of the differences between each Y value and the mean of Y.

Using the given values:
SSxy = SSS1U1B1XS1U1B0 - ((SP * SSS1U1B1YS1U1B0)/n) = 16 - ((2 * 4)/5) = 14.2
SSxx = SSS1U1B0XS1U1B0 - ((SP * SP)/n) = 16 - ((2*2)/5) = 15.2
SSyy = SSS1U1B0YS1U1B0 - ((SP * SP)/n) = 4 - ((2*2)/5) = 3.2

Plugging in these values:
r = (14.2 / √(15.2 * 3.2)) = 2/8

Thus, the answer is B.

Question 13

As the sample size gets larger,what happens to the size of the correlation that is needed for significance?
A)It also gets larger
B)It gets smaller
C)It stays constant
D)There is no consistent relationship between sample size and the critical value for a significant correlation.

Accepted Answer

As the sample size increases, the size of the correlation needed to achieve statistical significance actually gets smaller. This is because with larger sample sizes, the statistical tests have more power to detect a true effect, allowing even smaller correlations to be considered statistically significant.

Question 14

For a two-tailed hypothesis test evaluating a Pearson correlation,what is stated by the null hypothesis?
A)There is a non-zero correlation for the general population
B)The population correlation is zero
C)There is a non-zero correlation for the sample
D)The sample correlation is zero

Accepted Answer

The null hypothesis for a two-tailed hypothesis test evaluating a Pearson correlation states that the population correlation is zero.

Question 15

Which of the following Pearson correlations shows the greatest strength or consistency of relationship?
A)-0.90
B)+0.74
C)+0.85
D)-0.33

Accepted Answer

A correlation of -0.90 indicates a very strong negative relationship, stronger than the positive relationships indicated by +0.74 and +0.85, and significantly stronger than the weak negative relationship indicated by -0.33. The strength of a correlation is indicated by its absolute value, regardless of the sign.

Question 16

Suppose the correlation between height and weight for adults is +0.40.What proportion (or percent)of the variability in weight can be explained by the relationship with height?
A)40%
B)60%
C)16%
D)84%

Accepted Answer

The proportion of variability in weight that can be explained by the relationship with height is found by squaring the correlation coefficient (r^2). So, 0.40^2 = 0.16, or 16%.

Question 17

What is indicated by a Pearson correlation of r = +1.00 between X and Y?
A)Each time X increases,there is a perfectly predictable increase in Y
B)Every change in X causes a change in Y
C)Every increase in X causes an increase in Y
D)All of the other 3 choices occur with a correlation of +1.00.

Accepted Answer

A Pearson correlation of +1.00 indicates a perfect positive correlation, meaning that every time X increases, there is a perfectly predictable increase in Y.

Question 18

A researcher obtains a Pearson correlation of r = 0.60 for a sample of n = 6 pairs of X and Y scores.If the researcher tests the significance of the correlation,what value will be obtained for the t statistic?
A)0.6/0.16 = 3.75
B)0.6/0.4 = 1.50
C)0/6/0.8 = 0.77
D)0.6/1.0 = 0.6

Accepted Answer

To calculate the t statistic for a correlation coefficient, we use the formula t = r*sqrt(n-2)/sqrt(1-r^2). Substituting in the values, we get t = 0.60*sqrt(6-2)/sqrt(1-0.60^2) = 1.50. Therefore, the correct option is B.

Question 19

For which of the following Pearson correlations would the data points be clustered most closely around a straight line?
A)r = -0.10
B)r = +0.40
C)r = -0.70
D)There is no relationship between the correlation and how close the points are to a straight line.

Accepted Answer

The closer the absolute value of the correlation coefficient is to 1, the more closely the data points will be clustered around a straight line. In this case, a correlation coefficient of -0.70 indicates a strong negative relationship, which would result in a tightly clustered group of data points around a straight line.

Question 20

A researcher measures driving distance from college and weekly cost of gas for a group of commuting college students.What kind of correlation is likely to be obtained for these two variables?
A)A positive correlation
B)A negative correlation
C)A correlation near zero
D)A correlation near one

Accepted Answer

It is likely that as the driving distance from college increases, the weekly cost of gas will increase as well, resulting in a positive correlation.

Quiz 14: Correlation and Regression

A researcher records the odometer reading and price for a group of used Hondas.What kind of correlation is likely to be obtained for these two variables?

A set of n = 10 pairs of scores has ΣX = 20,ΣY = 30,and ΣXY = 74.What is the value of SP for these data?

A set of n = 5 pairs of X and Y scores has ΣX = 15,ΣY = 5,and ΣXY = 10.For these data,what is the value of SP?

The scatter plot for a set of X and Y values shows the data points clustered in a nearly perfect circle.For these data,what is the most likely value for the Pearson correlation?

The Pearson correlation is calculated for a sample of n = 20 individuals.If a hypothesis test is used to determine whether the correlation is significant,what df value would be used for the t statistic?

A set of n = 15 pairs of scores (X and Y values) produces a correlation of r = 0.40.If each of the X values is multiplied by 2 and the correlation is computed for the new scores,what value will be obtained for the new correlation?

The results from a research study indicate that adolescents who watch more violent content on television also tend to engage in more violent behavior than their peers.The correlation between amount of TV violent content and amount of violent behavior is an example of _______.

A set of n = 15 pairs of scores (X and Y values) has SS_X = 4,SS_Y = 25,and SP = 6.What is the Pearson correlation for these data?

What would the scatter plot show for data that produce a Pearson correlation of r = +0.88?

What is indicated by a positive value for a correlation?

A researcher measures IQ and weight for a group of college students.What kind of correlation is likely to be obtained for these two variables?

A set of n = 5 pairs of X and Y values has SS_X = 16,SS_Y = 4 and SP = 2.For these data,what is the Pearson correlation ?

As the sample size gets larger,what happens to the size of the correlation that is needed for significance?

For a two-tailed hypothesis test evaluating a Pearson correlation,what is stated by the null hypothesis?

Which of the following Pearson correlations shows the greatest strength or consistency of relationship?

Suppose the correlation between height and weight for adults is +0.40.What proportion (or percent) of the variability in weight can be explained by the relationship with height?

What is indicated by a Pearson correlation of r = +1.00 between X and Y?

A researcher obtains a Pearson correlation of r = 0.60 for a sample of n = 6 pairs of X and Y scores.If the researcher tests the significance of the correlation,what value will be obtained for the t statistic?

For which of the following Pearson correlations would the data points be clustered most closely around a straight line?

A researcher measures driving distance from college and weekly cost of gas for a group of commuting college students.What kind of correlation is likely to be obtained for these two variables?