Question 1

In the following correlation matrix, which two exams correlate the highest, and which two correlate the lowest? $\begin{array}{lcccc} 
& \text { Exam 1 } & \text { Exam 2 } & \text { Exam 3 } & \text { Exam } \
\text { Exam 1 } & 1.00 & -.025 & -.740 & -.36 \
\text { Exam 2 } & -.025 & 1.00 & .425 & .011 \
\text { Exam 3 } & -.740 & .425 & 1.00 & .682 \
\text { Exam 4 } & -.366 & .011 & .682 & 1.00
\end{array}$
A) Highest: Exam 1 & Exam 3; lowest: Exam 2 & Exam 4
B) Highest: Exam 3 & Exam 4; lowest: Exam 1 & Exam 2
C) Highest: Exam 1 & Exam 3; lowest: Exam 1 & Exam 2
D) Highest: Exam 3 & Exam 4; lowest: Exam 1 & Exam 3

Accepted Answer

Exam 1 and Exam 3 have the highest correlation of -.740, and Exam 2 and Exam 4 have the lowest correlation of .011.

Question 2

What does a correlation coefficient describe about the relationship between two variables?
A) The variability and strength
B) The variability and direction
C) The mean and variability
D) The direction and strength

Accepted Answer

The correlation coefficient describes the direction (positive or negative) and strength (weak, moderate, strong) of the relationship between two variables.

Question 3

If there is a negative correlation between leg strength scores and the time to run a 50-yard dash, what run times are associated with high leg strength scores?
A) Slow times
B) Fast times
C) Either fast or slow times
D) It depends on the variability of the scores

Accepted Answer

A negative correlation means that as one variable (leg strength scores) increases, the other variable (run time) decreases. Therefore, high leg strength scores would be associated with fast run times.

Question 4

If the correlation coefficient between the length of marriage and marital happiness is +.82, what can we conclude?
A) Happiness declines as the number of years married increases
B) Short marriages are happy marriages
C) Happy marriages cause long marriages
D) Long marriages tend to be happy ones

Accepted Answer

The correlation coefficient of +.82 indicates a strong positive correlation between length of marriage and marital happiness. Therefore, long marriages tend to be happy ones. However, it does not necessarily mean that short marriages are not happy.

Question 5

How much of the variance in final exam scores is accounted for by the variance in Exam 1's scores, if the coefficient between the two exams is .45?
A) .20
B) .45
C) .67
D) Depends on sample size

Accepted Answer

To find how much of the variance in final exam scores is accounted for by the variance in Exam 1's scores, you square the correlation coefficient (.45^2), which equals .2025, or approximately .20 when rounded. This is because the square of the correlation coefficient (r^2) represents the proportion of variance in one variable that is predictable from the other variable.

Question 6

What pattern of correlations would produce the best multiple regression equation?
 $\begin{array}{|l|l|l|}
\hline & \text { Criterion with Predictors } & \begin{array}{l}
\text { Predictors with } \
\text { Predictors }
\end{array} \
\hline \text { a. } & \text { Low } & \text { Low } \
\hline \text { b. } & \text { Low } & \text { High } \
\hline \text { c. } & \text { High } & \text { Low } \
\hline \text { d. } & \text { High } & \text { High } \
\hline
\end{array}$

Accepted Answer

The answer of What pattern of correlations would produce the...

Question 7

A simple regression formula for predicting weight in pounds from height in inches is Ŷ= 1.6X + 60. What is the slope of the regression line to predict weight from height?
A) 60
B) 61.6
C) 37.5
D) Positive

Accepted Answer

The slope of the regression line is the coefficient of the independent variable (in this case, height in inches), which is 1.6. This indicates the amount of change in the dependent variable (weight) for a one-unit change in the independent variable (height). Since 1.6 is a positive number, the slope is positive.

Question 8

Given that the regression equation is Ŷ = .5X + 25 and the standard error of estimate is 3, what is the range of scores that would capture a person's true Y score 68% of the time, if that person had an X score of 30?
A) 27-33
B) 37-43
C) 37-53
D) 34-46

Accepted Answer

Given the regression equation Ŷ = .5X + 25, for an X score of 30, the predicted Y (Ŷ) would be (.5*30) + 25 = 15 + 25 = 40. For 68% of the time (which corresponds to roughly one standard deviation on either side of the mean in a normal distribution), the range would be Ŷ ± the standard error of estimate. Therefore, the range is 40 ± 3, which gives us 37 to 43.

Question 9

What is the standard deviation of the residuals resulting from predicting Y scores from X scores?
A) Zero
B) One
C) SEM
D) SEE

Accepted Answer

The standard deviation of residuals resulting from predicting Y scores from X scores is the standard error of estimate (SEE), which measures the average amount by which the observed values deviate from the predicted values. Therefore, the best choice is D, SEE. Choices A and B are incorrect because the residuals are not always equal to zero or one. Choice C, SEM (standard error of the mean), is not relevant in this context since we are interested in the variability of Y scores, not their mean.

Question 10

If the regression equation Ŷ= .25X + 12 was plotted, what shape would it take, and where would it cross the Y axis?
A) Curvilinear, at Y=.25
B) Curvilinear, at Y=12
C) Linear, at Y=.25
D) Linear, at Y=12

Accepted Answer

The equation Ŷ= .25X + 12 is a linear equation, as it follows the general form of Y = MX + B (where M is the slope and B is the Y-intercept). The slope is .25 and the Y-intercept is 12, which means the line will cross the Y-axis at Y=12 and will have a positive slope. Therefore, the correct answer is D, Linear, at Y=12.

Question 11

If two predictor variables to be used in developing a multiple regression equation both correlate with the criterion variable at .75, what correlation coefficient between the two predictor variables would lead to the most efficient regression equation?
A) .00
B) .25
C) .75
D) .95

Accepted Answer

The most efficient regression equation would have predictor variables that are highly correlated with the criterion variable, but not highly correlated with each other. Therefore, the correlation coefficient between the two predictor variables should be as close to 0 as possible.

Question 12

Which of the following is the primary purpose of correlational research?
A) To study individual situations in depth
B) To study disease rates in the population
C) To combine and quantify past research reports
D) To study the relationships among variables

Accepted Answer

correlational research is designed to study the relationships between variables, typically examining how they are related or associated with each other. This type of research does not involve manipulating variables, but rather observing and measuring them to identify possible patterns or connections.

Question 13

Which of the following statistics is a measure of the amount of variance accounted for between two variables? A) Standard deviation B) r² C) r D) SEE

Accepted Answer

r² is the coefficient of determination, which measures the proportion of variance in the dependent variable that is explained by the independent variable.

Question 14

Which symbol is commonly used to indicate a Pearson product-moment correlation coefficient?
A) r
B) s
C) P
D) C

Accepted Answer

The symbol "r" is commonly used to represent Pearson product-moment correlation coefficient. This measure of correlation is used to indicate the strength and direction of the linear relationship between two variables.

Question 15

What does a negative value of r mean?
A) There is no relationship between two variables
B) High scores on one variable are associated with low scores on a second variable
C) High scores on one variable are associated with high scores on a second variable
D) There is a mistake in the calculation of the coefficient

Accepted Answer

A negative value of r indicates an inverse relationship between two variables, where high scores on one variable are associated with low scores on the second variable. Option A is incorrect as a negative value of r still indicates a relationship, just an inverse one. Option C is incorrect as it refers to a positive value of r. Option D is unlikely, as long as the calculation was done correctly.

Question 16

What conclusion should be drawn if the correlation coefficient between a physical fitness test and a rating of basketball playing ability is .90?
A) People who are physically fit will be successful in playing basketball.
B) Playing basketball develops physical fitness.
C) Physical fitness is necessary to be successful in playing basketball.
D) Basketball playing ability and physical fitness are strongly associated.

Accepted Answer

The correlation coefficient value of .90 indicates a strong positive association between physical fitness and basketball playing ability. It does not necessarily imply causation or direction of the relationship, but it does suggest that as physical fitness increases, basketball playing ability tends to increase as well.

Question 17

What does a correlation coefficient of +.91 mean?
A) No relationship exists between two variables.
B) Those who did better on the first test did worst on the second test.
C) Those who did better on the first test were average on the second test.
D) Those who did better on the first test also did better on the second test.

Accepted Answer

A correlation coefficient of +.91 indicates a strong positive correlation between the two variables, meaning that those who did better on the first test also did better on the second test.

Question 18

Of the following, which correlation coefficient best describes the relationship between height and weight in healthy adults?
A) -.87
B) .00
C) +.10
D) +.45

Accepted Answer

A positive correlation coefficient indicates that as one variable increases, the other variable also increases. In the case of height and weight in healthy adults, it can be assumed that as height increases, weight also increases. Therefore, a positive correlation coefficient would be appropriate, and D (+.45) is the closest to representing a moderate positive correlation. Choices A, B, and C are not appropriate because they either indicate a strong negative correlation, no correlation, or a weak positive correlation.

Question 19

If a test of athletic ability has a .12 correlation coefficient with batting average in baseball, how well does the test predict batting success?
A) Extremely well
B) Very well
C) Moderately well
D) Not very well

Accepted Answer

A correlation coefficient of .12 indicates a very weak relationship between the test of athletic ability and batting average, suggesting the test does not predict batting success very well.

Question 20

Which correlation method is used when both variables are measured on an ordinal level?
A) Pearson's r
B) Spearman's rho
C) Rank biserial
D) Point biserial

Accepted Answer

When both variables are measured on an ordinal level, Spearman's rho is the best correlation method to use. This is because it considers the ranked values of both variables rather than their raw scores, which may not accurately represent the underlying relationship between the two variables.

Quiz 5: Correlation and Regression

What does a correlation coefficient describe about the relationship between two variables?

If there is a negative correlation between leg strength scores and the time to run a 50-yard dash, what run times are associated with high leg strength scores?

If the correlation coefficient between the length of marriage and marital happiness is +.82, what can we conclude?

How much of the variance in final exam scores is accounted for by the variance in Exam 1's scores, if the coefficient between the two exams is .45?

A simple regression formula for predicting weight in pounds from height in inches is Ŷ= 1.6X + 60. What is the slope of the regression line to predict weight from height?

Given that the regression equation is Ŷ = .5X + 25 and the standard error of estimate is 3, what is the range of scores that would capture a person's true Y score 68% of the time, if that person had an X score of 30?

What is the standard deviation of the residuals resulting from predicting Y scores from X scores?

If the regression equation Ŷ= .25X + 12 was plotted, what shape would it take, and where would it cross the Y axis?

If two predictor variables to be used in developing a multiple regression equation both correlate with the criterion variable at .75, what correlation coefficient between the two predictor variables would lead to the most efficient regression equation?

Which of the following is the primary purpose of correlational research?

Which of the following statistics is a measure of the amount of variance accounted for between two variables?

Which symbol is commonly used to indicate a Pearson product-moment correlation coefficient?

What does a negative value of r mean?

What conclusion should be drawn if the correlation coefficient between a physical fitness test and a rating of basketball playing ability is .90?

What does a correlation coefficient of +.91 mean?

Of the following, which correlation coefficient best describes the relationship between height and weight in healthy adults?

If a test of athletic ability has a .12 correlation coefficient with batting average in baseball, how well does the test predict batting success?

Which correlation method is used when both variables are measured on an ordinal level?