Deck 6: Correlation and Regression

Question 1

A univariate distribution is required to calculate a correlation coefficient.

Answer 1

False

Question 2

Correlation coefficients range from -1.00 to 1.00.

Answer 2

True

Question 3

The numerator of the definitional formula of the correlation coefficient is the product of z scores.

Answer 3

True

Question 4

To find the value of the cross products for a correlation coefficient, multiply the two means.

Question 5

The reliability of a test can be measured using a correlation coefficient.

Question 6

The coefficient of determination is the square of r.

Question 7

The regression equation described in your textbook is based on the largest-squared method.

Question 8

There is only one regression line for a bivariate distribution.

Question 9

There is a strong positive relationship between students' critical reading ability and math ability.

Question 10

Bivariate distributions are required for calculating correlation coefficients.

Question 11

Correlation coefficients can approach 1.00 but never reach that value.

Question 12

The denominator of the z score formula for the correlation coefficient is N.

Question 13

Formulas for r in the textbook use the standard deviation, $\hat { S }$ .

Question 14

Correlation coefficients cannot be used to establish a cause and effect relationship.

Question 15

The regression equation described in your textbook is based on the least-squares method.

Question 16

For a bivariate distribution with 10 pairs of scores, N = 10.

Question 17

The regression coefficient, b, tells where the regression line crosses the Y axis.

Question 18

There is a strong negative correlation between per capita income and violent crime in the U.S.

Question 19

The coefficient of determination is the square root of r.

Question 20

A scatterplot is a graph of a bivariate distribution.

Question 21

The numerator of the definitional formula of the correlation coefficient is the product of the two regression coefficients.

Question 22

Formulas for r in the textbook use the standard deviation, S.

Question 23

Large correlation coefficients indicate a high probability of a cause and effect relationship.

Question 24

Your textbook said that truncating the range of a distribution increases the size of r.

Question 25

If a bivariate distribution is not linear, r will not show the degree of relationship between two variables.

Question 26

The number of regression lines for a bivariate distribution is equal to the number of regression coefficients.

Question 27

The regression coefficient, a, gives the slope of the regression line.

Question 28

Data Set 6-1
The correlation between the number of PhDs and the number of mules in a state used to be approximately -.90. Accept the following simplified summary data.
$\begin{array}{lll}& \underline{\text { PhDs}}& \underline{\text { Mules }}\\\text { Mean } & 40 & 200 \\\text { Standard Deviation } & 15 & 50\end{array}$
In questions based on Data Set 6-1, the task is to predict the number of mules for a state, given the number of PhDs.

-Look at Data Set 6-1. For a state with 60 PhDs the predicted number of mules would be

A) 260
B) 195
C) 140
D) none of the other alternatives are correct.

Question 29

Data Set 6-1
The correlation between the number of PhDs and the number of mules in a state used to be approximately -.90. Accept the following simplified summary data.
$\begin{array}{lll}& \underline{\text { PhDs}}& \underline{\text { Mules }}\\\text { Mean } & 40 & 200 \\\text { Standard Deviation } & 15 & 50\end{array}$
In questions based on Data Set 6-1, the task is to predict the number of mules for a state, given the number of PhDs.

-The b coefficient in Data Set 6-1 is

A) -3.00
B) -0.27
C) 0.27
D) 3.00.

Question 30

Data Set 6-1
The correlation between the number of PhDs and the number of mules in a state used to be approximately -.90. Accept the following simplified summary data.
$\begin{array}{lll}& \underline{\text { PhDs}}& \underline{\text { Mules }}\\\text { Mean } & 40 & 200 \\\text { Standard Deviation } & 15 & 50\end{array}$
In questions based on Data Set 6-1, the task is to predict the number of mules for a state, given the number of PhDs.

-Look at Data Set 6-1. For a state with no PhDs the predicted number of mules is

A) 320
B) 80
C) 20
D) none of the other alternatives are correct.

Question 31

Data Set 6-2
The correlation between a score based on anthropometric measurements (height, strength, reaction time and others) and college GPA is .05. Your task will be to predict GPA, given the anthro measurements. Be sure you set this up properly and work precisely. (Use 3 or 4 decimal places.)
$$\begin{array} { l r c } & \underline{\text { GPA }} & \underline{ \text { Anthro Scores} } \\\text { Mean } & 2.5 & 10 \\\text { Standard Deviation } &0.5 & 2\end{array}$$

-Based on Data Set 6-2, predict a GPA for a person whose anthro data score was 15.

A) 2.81
B) 2.85
C) 2.56
D) none of the other alternatives are correct.

Question 32

Data Set 6-2
The correlation between a score based on anthropometric measurements (height, strength, reaction time and others) and college GPA is .05. Your task will be to predict GPA, given the anthro measurements. Be sure you set this up properly and work precisely. (Use 3 or 4 decimal places.)
$$\begin{array} { l r c } & \underline{\text { GPA }} & \underline{ \text { Anthro Scores} } \\\text { Mean } & 2.5 & 10 \\\text { Standard Deviation } &0.5 & 2\end{array}$$

-See Data Set 6-2. Suppose an excellent statistician used linear regression to predict the GPA for a person whose anthropometric score was 15. How likely is it that such a person would actually get the GPA predicted for her?

A) very
B) moderately
C) hardly.

Question 33

Data Set 6-3
$$\begin{array} { l l } X & Y \\\hline 2 & 3 \\3 & 6 \\5 & 7 \\2 & 4\end{array}$$

-Look at Data Set 6-3. If you were to compute a correlation coefficient, N would be

A) 8
B) 5
C) 4
D) none of the other alternatives are correct.

Question 34

Data Set 6-3
$$\begin{array} { l l } X & Y \\\hline 2 & 3 \\3 & 6 \\5 & 7 \\2 & 4\end{array}$$

-For Data Set 6-3, $\Sigma$ XY is

A) 67
B) 240
C) 16.75
D) 32.

Question 35

Data Set 6-3
$$\begin{array} { l l } X & Y \\\hline 2 & 3 \\3 & 6 \\5 & 7 \\2 & 4\end{array}$$

-The correlation coefficient for Data Set 6-3 is

A) 0.85
B) 1.00
C) -0.90
D) none of the other alternatives are correct.

Question 36

Data Set 6-4
$$\begin{array} { l l } X & Y \\\hline 1 & 4 \\2 & 5 \\3 & 6\end{array}$$

-The correlation coefficient in Data Set 6-4 is

A) positive
B) negative
C) zero
D) not determinable.

Question 37

Data Set 6-4
$$\begin{array} { l l } X & Y \\\hline 1 & 4 \\2 & 5 \\3 & 6\end{array}$$

-In Data Set 6-4, $\Sigma$ XYis

A) 90
B) 16
C) 21
D) none of the other alternatives are correct.

Question 38

Data Set 6-5
Given the regression equation
$\hat { Y }$
= 32 - 2X, where X is the number of complaints each quarter about a service man and Y is the number of months of employment.

-Refer to Data Set 6-5. The number of months of employment of a service man who received 10 complaints would be predicted as

A) 12
B) 22
C) 52
D) none of the other alternatives are correct.

Question 39

Data Set 6-5
Given the regression equation
$\hat { Y }$
= 32 - 2X, where X is the number of complaints each quarter about a service man and Y is the number of months of employment.

-Refer to Data Set 6-5. The correlation coefficient of the data would be

A) positive
B) negative
C) zero
D) cannot tell unless a and b are given, too.

Question 40

Data Set 6-6
$$\begin{array} { l l } X & Y \\\hline 1 & 4 \\2 & 3 \\3 & 2\end{array}$$

-The correlation coefficient in Data Set 6-6 is

A) positive
B) negative
C) zero
D) none of the other alternatives are correct.

Question 41

Data Set 6-6
$$\begin{array} { l l } X & Y \\\hline 1 & 4 \\2 & 3 \\3 & 2\end{array}$$

-In Data Set 6-6, $\Sigma$ XYis

A) 54
B) 16
C) 15
D) none of the other alternatives are correct.

Question 42

Data Set 6-7
$$\begin{array} { l l } X & Y \\\hline 1 & 4 \\2 & 5 \\4 & 6\end{array}$$

-The correlation coefficient in Data Set 6-7 is

A) positive
B) negative
C) zero
D) none of the other alternatives are correct.

Question 43

Data Set 6-7
$$\begin{array} { l l } X & Y \\\hline 1 & 4 \\2 & 5 \\4 & 6\end{array}$$

-In Data Set 6-7, $\Sigma$ XY is

A) 90
B) 98
C) 105
D) 38

Question 44

Data Set 6-7
$$\begin{array} { l l } X & Y \\\hline 1 & 4 \\2 & 5 \\4 & 6\end{array}$$

-In Data Set 6-7, the Pearson correlation coefficient is

A) 1.00
B) 0.98
C) 0.68

Question 45

Data Set 6-8
$$\begin{array} { l l } X & Y \\\hline 1 & 4 \\2 & 3 \\2 & 2\end{array}$$

-The correlation coefficient in Data Set 6-8 is

A) positive
B) negative
C) zero
D) none of the other alternatives are correct.

Question 46

Data Set 6-8
$$\begin{array} { l l } X & Y \\\hline 1 & 4 \\2 & 3 \\2 & 2\end{array}$$

-In Data Set 6-8, $\Sigma$ XY is

A) 54
B) 16
C) 15
D) 14

Question 47

Data Set 6-8
$$\begin{array} { l l } X & Y \\\hline 1 & 4 \\2 & 3 \\2 & 2\end{array}$$

-In Data Set 6-8, the Pearson correlation coefficient is

A) 0.86
B) 0.25
C) -0.25
D) -.87

Question 48

Data Set 6-9
The correlation between high school GPA and college GPA is .50. Given the data that follow, your task is to predict college GPA.
$$\begin{array} { l c c c } & \underline{ \text { College GPA } } & \underline{ \text { High School GPA} } \\\text { Mean } & 2.6 & 3.3 & \\\text { Standard Deviation } & 0.5 & 0.7\end{array}$$

-Look at Data Set 6-9. For a person with a high school GPA of 2.5, the predicted college GPA is

A) 2.04
B) 2.31
C) 2.88

Question 49

Data Set 6-9
The correlation between high school GPA and college GPA is .50. Given the data that follow, your task is to predict college GPA.
$$\begin{array} { l c c c } & \underline{ \text { College GPA } } & \underline{ \text { High School GPA} } \\\text { Mean } & 2.6 & 3.3 & \\\text { Standard Deviation } & 0.5 & 0.7\end{array}$$

-In Data Set 6-9. For a person with a high school GPA of 4.0, the predicted college GPA is

A) 2.85
B) 3.09
C) 4.00

Question 50

Data Set 6-10: The correlation between a score based on anthropometric measurements (height, strength, reaction time and others) and college GPA is .05. Your task will be to predict GPA, given the anthro measurements. Be sure you set this up properly and work precisely (3 or 4 decimal places.).
$$\begin{array} { l c r } & \underline{ \text { GPA }} & \underline{ \text { Anthro }} \\ \text { Mean } & 2.6 & 20 \\\text { Standard Deviation } & 0.7 & 4\end{array}$$

-Based on Data Set 6-10, predict a GPA for a person whose anthro data score was 15.

A) 1.2
B) 2.6
C) 4.0

Question 51

Data Set 6-10: The correlation between a score based on anthropometric measurements (height, strength, reaction time and others) and college GPA is .05. Your task will be to predict GPA, given the anthro measurements. Be sure you set this up properly and work precisely (3 or 4 decimal places.).
$$\begin{array} { l c r } & \underline{ \text { GPA }} & \underline{ \text { Anthro }} \\ \text { Mean } & 2.6 & 20 \\\text { Standard Deviation } & 0.7 & 4\end{array}$$

-The b coefficient in Data Set 6-10 is

A) 5.71
B) 1.75
C) 0.175
D) 0.0088

Question 52

Data Set 6-10: The correlation between a score based on anthropometric measurements (height, strength, reaction time and others) and college GPA is .05. Your task will be to predict GPA, given the anthro measurements. Be sure you set this up properly and work precisely (3 or 4 decimal places.).
$$\begin{array} { l c r } & \underline{ \text { GPA }} & \underline{ \text { Anthro }} \\ \text { Mean } & 2.6 & 20 \\\text { Standard Deviation } & 0.7 & 4\end{array}$$

-Based on the correlation coefficient in Data Set 6-10, the amount of confidence you should place in a prediction about GPA is

A) absolute
B) a high degree
C) a moderate degree
D) almost no confidence.

Question 53

The philosophy that a phenomenon can be better understood if its essential parts are expressed as numbers is called

A) numerical analysis
B) numeralism
C) quantification
D) rational numerology.

Question 54

Quantification is the idea that

A) all things can be counted
B) all physical things can be counted
C) the numerical representation of a phenomenon gives the most important picture
D) a phenomenon can be better understood if its important parts are expressed as numbers.

Question 55

A person who believes in the philosophy of quantification believes

A) only things that be can be counted are real
B) you can understand a phenomenon better by representing it with numbers
C) better understanding comes by measuring smaller and smaller units of a phenomenon
D) numbers are important quality is not.

Question 56

Francis Galton's principal interest was in

A) sociology
B) heredity
C) the psychology of learning
D) the psychology of perception.

Question 57

Galton's effort to find ways to improve the human condition led him to study the field of

A) psychology
B) physics
C) physiology
D) heredity.

Question 58

The credit for working out the mathematics of correlation and regression goes to

A) Francis Galton
B) Charles Darwin
C) Karl Pearson
D) none of the other alternatives are correct.

Question 59

The correlation coefficient was developed just before the year

A) 1600
B) 1700
C) 1800
D) 1900.

Question 60

In a bivariate distribution

A) there is always a pairing of every score in one distribution with another score in the other distribution
B) both distributions use the same units of measurement
C) both descriptive alternative are correct
D) neither of the descriptive alternatives is correct.

Question 61

Suppose you had the exam scores on the first exam for 100 psychology students. A correlation coefficient could be calculated if the scores were divided according to

A) gender-males and females
B) where a person sits in the class-front or back
C) both descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 62

When two distributions can be aligned with paired sets of scores the result is a distribution.

A) bimodal
B) bivariate
C) dual
D) twin.

Question 63

The kind of data required for a Pearson product-moment correlation is

A) qualitative
B) univariate
C) bivariate
D) trivariate.

Question 64

In a bivariate distribution

A) both variables must be measuring the same thing
B) both variables have the same number of scores
C) there are exactly two scores
D) all of the other alternatives are correct.

Question 65

Which of the following statements describes a positive correlation?

A) The more I study the lower my test scores.
B) The greater the cost the better the merchandise.
C) Walnut is more dense than pine.
D) none of the other alternatives are correct.

Question 66

Which of the situations below expresses a positive correlation?

A) The fewer the number of parasites, the fewer the offspring.
B) The larger the size of the building, the more the cost of upkeep.
C) both descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 67

Which of the following statements describes a negative correlation?

A) The more I eat, the less I weigh.
B) The less I eat, the less I weigh.
C) Both The more I eat the less I weigh, and the less I eat the less I weigh
D) The more I exercise, the greater my flexibility.

Question 68

Which of the following statements describes a negative correlation?

A) The more the better.
B) At first practice produces big changes but as time goes on each practice session produces fewer and fewer changes.
C) The more the government gives to you, the lower your ability to think for yourself.
D) None of the other alternatives are correct.

Question 69

Identify the incorrect statement.

A) A negative correlation is obtained when high scores on X go with low scores on Y and low scores on X go with high scores on Y.
B) A positive correlation is obtained when high scores on X go with high scores on Y.
C) A zero correlation is obtained when high scores on X go with both high and low scores on Y and low scores on X go with both high and low scores on Y.
D) None of the other alternatives are correct.

Question 70

"I started with just a little, mild punishment. Over the weeks I punished him more and more frequently. Sure enough, during this time his disruptive behavior has become less and less of a problem." The correlation between punishment and disruptive behavior is

A) positive
B) negative
C) zero.

Question 71

"For the last ten years, I've used smaller and smaller amounts of pesticide, and each year I've had fewer bugs and larger yields."The correlation between amounts of pesticide and number of bugs is

A) positive
B) negative
C) zero
D) not determinable from the information given.

Question 72

Which of the following could not be a correlation coefficient?

A) -.65
B) .00
C) 1.00
D) 1.50

Question 73

The sum of the cross-products is

A) $\Sigma$ X+ $\Sigma$ Y
B) ( $\Sigma$ X) ( $\Sigma$ Y)
C) both descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 74

The techniques in Chapter 6 accurately describe the relationship between two variables when the relationship is that of

A) a straight line
B) a curved line
C) a plane
D) all of the other alternatives are correct.

Question 75

To use the regression equation technique described in your text, you must have

A) a logical pairing of the scores on the two variables
B) a linear relationship between the two variables
C) both descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 76

A Pearson correlation coefficient is appropriate to describe which of the situations below?

A) As X increases, Y decreases by the same amount.
B) As X increases, Y goes up at first slowly and then faster.
C) As X increases, Y goes up at first and then goes down.
D) All of the other alternatives are correct.

Question 77

A linear relationship is described by which of the statements below?

A) The two variables are paired in some logical fashion.
B) For every one-point increase in one variable, there is a four-point increase in the other variable.
C) Both descriptive alternatives are correct.
D) Neither of the descriptive alternatives is correct.

Question 78

According to your textbook, there is acorrelation between critical reading aptitude and mathematics aptitude.

A) positive
B) negative
C) zero.

Question 79

A correlation coefficient of about .7 goes with the relationship between

A) per capita income and violent crime rate in the 50 American states
B) critical reading aptitude and mathematics aptitude
C) number of test takers in a room and motivation

Question 80

A correlation coefficient of about -.7 goes with the relationship between

A) per capita income and violent crime rate in the 50 American states
B) critical reading aptitude and mathematics aptitude
C) number of test takers in a room and motivation.