Deck 3: Correlation and Regression

Question 1

The observation that Y decreases as X increases suggests

A) a positive correlation.
B) no correlation.
C) a negative correlation.
D) a curvilinear correlation.

Answer 1

C

Question 2

A scatter diagram is

A) a bivariate plot of individual data points.
B) a univariate plot of individual data points.
C) a form of the stem and leaf display.
D) a method for calculating variance.

Answer 2

A

Question 3

What is the point of least squares for the numbers 4,6,8,and 10?

A) indeterminate
B) 4
C) 7
D) 10

Answer 3

C

Question 4

Given the following ordered pairs,the correlation is 8 7
7 6
3 2
1 2
1 2

A) positive.
B) negative.
C) zero.
D) perfect.

Question 5

If the scores on X give us no information about the scores on Y,this indicates

A) a positive correlation.
B) a negative correlation.
C) no correlation.
D) curvilinear correlation.

Question 6

In a negative correlation,

A) individuals tend to maintain the same or a similar relative performance.
B) scores on one variable tell us nothing about scores on a second.
C) individuals who score low on one variable tend to score low on a second.
D) high scores on the X variable are associated with low scores on the Y variable.

Question 7

Correlation coefficients describe the

A) degree of linearity of relation between X and Y.
B) mean of X and Y.
C) direction and magnitude of relationship between X and Y.
D) causality of relationships between X and Y.

Question 8

Which of the following correlations represents the strongest relationship between two variables?

A) -.85
B) .01
C) .50
D) .80

Question 9

If the line that comes closest to all points in a scatter diagram is perfectly straight,the correlation between the two variables is

A) linear.
B) curvilinear.
C) positive.
D) unknown.

Question 10

What do scatter diagrams do?

A) Allow visualization of the relationship between two variables
B) Create an objective measure of reliability
C) Relate univariate observations to bivariate distributions
D) Demonstrate the statistical validity of measures

Question 11

The correlation equals +1 for which of the following four pairs of numbers?

A) (2,4), (4,8), (0,0), (-2,-4)
B) (0,0), (1,1), (2,4), (3,9)
C) (4,3), (2,-1), (-2,-9), (0,-5)
D) (4,-9), (2,-1), (-2,-2), (0,-5)

Question 12

Which of the following four pairs of numbers describes a nonlinear relation?

A) (2,4), (4,8), (0,0), (-2,-4)
B) (0,0), (1,1), (2,4), (3,9)
C) (4,3), (2,-1), (-2,-9), (0,-5)
D) (4,-9), (2,-1), (-2,-2), (0,-5)

Question 13

Each point on a scatter diagram represents

A) the variance of a set of scores.
B) the standard deviation of a set of scores.
C) where an individual scored compared to the mean.
D) where an individual scored on both x and y.

Question 14

Graphs that show pairs of individual values are called ____ plots.

A) validity
B) regression
C) scatter
D) normality

Question 15

Which of the following is true of correlations?

A) They cannot be used to determine statistical significance.
B) They provide the basis for transforming observations to scales.
C) They are particularly useful with nominal scales.
D) They describe the direction and magnitude of relationships between two variables.

Question 16

The best-fitting straight line through a set of points in a scatter diagram is known as the

A) regression line.
B) linear line.
C) correlation line.
D) perfect correlation.

Question 17

What is the point of least squares for the numbers 2,7,8,and 11?

A) indeterminate
B) 4
C) 7
D) 10

Question 18

Which of the following four pairs of numbers describes a correlation that is very close to .0?

A) (2,4), (4,8), (0,0), (-2,-4)
B) (0,0), (1,1), (2,4), (3,9)
C) (4,3), (2,-1), (-2,-9), (0,-5)
D) (4,-9), (2,-1), (-2,-2), (0,-5)

Question 19

The correlation equals -1 for which of the following four pairs of numbers?

A) (2,4), (4,8), (0,0), (-2,-4)
B) (0,0), (1,1), (2,4), (3,9)
C) (4,3), (2,-1), (-2,-9), (0,-5)
D) (4,-9), (2,-1), (-2,-2), (0,-5)

Question 20

People who drink caffeinated beverages tend to experience increased alertness and psychomotor activity.This demonstrates a(n)

A) positive correlation.
B) negative correlation.
C) zero correlation.
D) unknown.

Question 21

The correlation coefficient can take any value from

A) -1.0 to 1.0.
B) 0 to 1.0.
C) -1.0 to 0.
D) 1.0 to 10.0.

Question 22

The point at which the regression line crosses the Y axis is the

A) slope.
B) regression coefficient.
C) predicted value of X.
D) intercept.

Question 23

Assume that X and Y correlate .6,are in Z score form,and that a particular value of X is 1.What is the predicted value of Y?

A) 0
B) .4
C) .6
D) 1

Question 24

If the regression between X and Y is less than perfect,

A) predicted values of Y are relatively further from the mean of Y than observed values of X are to the mean of X.
B) predicted values of Y are relatively closer to the mean of Y than observed values of X are to the mean of X.
C) values of Y cannot be predicted from observations of X.
D) observed values of X are relatively closer to the mean of X than predicted values of Y are to the mean of Y.

Question 25

Suppose that X is used to predict Y and that both are in Z-score form.Which of the following is always true regarding the predicted Y score?

A) It is larger than the obtained X score.
B) It is smaller than the X score.
C) It is closer to 0 than the obtained Y score.
D) It is closer to 0 than the X score.

Question 26

In the formula Y´ = a + bX,Y´ is the

A) regression coefficient.
B) raw score of Y.
C) predicted value of Y.
D) intercept.

Question 27

Suppose that we find a regression relating X to Y by the following equation: Y´ = 12 + .80X.If we observe an X score of 2,what score on Y would we expect?

A) 8
B) 10.4
C) 13.6
D) 16.4

Question 28

If the correlation between X and Y is 0 and we observe a score (in Z units)of 1.5 on X,what score would be predicted for Y?

A) -1.5
B) -.75
C) 0
D) 1.5

Question 29

In the linear equation Y´ = a + bX,"b" is called

A) the slope.
B) the intercept.
C) the actual score.
D) the predicted score.

Question 30

The intercept is the

A) value obtained using the equation to predict scores.
B) slope of the regression line.
C) value of Y when X is zero.
D) standard deviation of a test score.

Question 31

If the correlation between X and Y is .60 and we observe a score of 1.0 (Z units)on X,what score would be predicted for Y?

A) -1.2
B) 0
C) 0.6
D) 1.6

Question 32

Correlation coefficients can be tested for significance using the

A) Z distribution.
B) t distribution.
C) principle of least squares.
D) regression distribution.

Question 33

What is the difference between correlation and regression?

A) Regression requires standardized units,while correlation does not.
B) Correlation is the same thing as regression except that the scores are in standardized units.
C) In regression,scores on the Y axis regress toward the mean,while in correlation they do not.
D) In correlation,scores on the Y axis regress toward the mean,while in regression they do not.

Question 34

In the linear equation Y´ = a + bX,"a" is called

A) the regression coefficient.
B) the intercept.
C) the actual score.
D) the predicted score.

Question 35

Assumed that X and Y correlate .3 in a sample of 102.What is the approximate t-value used to test the significance of this relationship?

A) 0
B) 1
C) 2
D) 3

Question 36

The difference between the observed and predicted score is

A) the residual.
B) the intercept.
C) the Z score.
D) correlation coefficient.

Question 37

A correlation of .80 suggests that

A) the scores on X and Y are not related.
B) standardized scores on the Y axis are expected to be .8 times the corresponding scores on the X axis.
C) scores on Y will be 80% larger than corresponding scores on X.
D) the differences between X and Y are statistically non-significant.

Question 38

When you know nothing about a person's academic ability,the best estimate of his or her academic ability should be based on the

A) mean.
B) Z score.
C) criterion.
D) correlation.

Question 39

A common use of correlation is to determine evidence for

A) criterion validity.
B) face validity.
C) a normative sample.
D) a scatter plot.

Question 40

Assume that X and Y correlate .4,are in Z score form,and that a particular value of X is 1.What is the predicted value of Y?

A) 0
B) .4
C) .6
D) 1

Question 41

One formula for the correlation between two dichotomous variables is

A) Spearman's rank order formula.
B) the point biserial correlation.
C) the phi coefficient.
D) the biserial correlation.

Question 42

An appropriate correlation coefficient describing the relationship between two artificially dichotomous variables is

A) biserial correlation.
B) phi coefficient.
C) tetrachoric correlation.
D) point biserial correlation.

Question 43

What does regression do?

A) It ensures the statistical significance of correlations.
B) It converts raw scores to t scores.
C) It makes predictions about scores based on other scores.
D) It creates linear relationships for transforms.

Question 44

Which of the following is the slope of the regression line?

A) The regression coefficient
B) The intercept
C) The relative covariance
D) The best fit

Question 45

The difference between the predicted value of Y and the observed value is called the

A) standard deviation.
B) standard error of the mean.
C) residual.
D) factor score.

Question 46

What type of prediction uses information gained from representative groups?

A) normative
B) regressive
C) correlational
D) transformative

Question 47

To assess the relationship between intelligence and passing or failing this exam,you would use the

A) point biserial.
B) Pearson r.
C) biserial correlation.
D) tetrachoric correlation.

Question 48

Which of the following is a true dichotomous variable?

A) football players' numbers
B) weight
C) time
D) gender

Question 49

The type of correlation coefficient used to find the association between two sets of ranks is called

A) Spearman's rho.
B) the point biserial correlation.
C) the phi coefficient.
D) factor loading.

Question 50

Which of the following describes the relationship between a true dichotomous variable and a continuous variable?

A) Spearman's rho
B) point biserial correlation
C) Pearson product-moment
D) the phi coefficient

Question 51

The formula Y - Y´ represents

A) the true score.
B) the residual.
C) the standard error of estimate.
D) shrinkage.

Question 52

One formula for the correlation between a continuous variable and an artificially dichotomized variable is

A) Spearman's rank order formula.
B) the point biserial correlation.
C) the phi coefficient.
D) the biserial correlation.

Question 53

Which of the following is used to test the statistical significance of correlations?

A) The regression line
B) The t distribution
C) The coefficient of relatedness
D) The slope and intercept

Question 54

The type of correlation coefficient used to correlate a dichotomous variable (two categories)and a continuous variable is called

A) Spearman's rho.
B) the point biserial correlation.
C) the phi coefficient.
D) multivariate analysis.

Question 55

Which of the following is true of the best-fitting line?

A) It establishes statistical significance.
B) It increases as the correlation decreases.
C) It is rarely useful for prediction.
D) It minimizes residuals.

Question 56

In regression plots,a perfect forecaster of the criterion is at a(n)

A) 45 degree angle.
B) 90 degree angle.
C) 0 degree angle.
D) 100 degree angle.

Question 57

Which of the following is an artificially dichotomous variable?

A) gender
B) weight
C) passing/failing a final exam
D) GPA

Question 58

In order to determine the relationship between sex of subject and income level,one would use the

A) phi coefficient.
B) point biserial correlation.
C) Spearman's rho.
D) Pearson r.

Question 59

Which of the following is used to describe the relationship between two dichotomous variables,at least one of which is a true dichotomy?

A) tetrachoric correlation
B) phi coefficient
C) point biserial correlation
D) Spearman's rho

Question 60

Which of the following describes the relationship between two artificially dichotomous variables?

A) tetrachoric correlation
B) factor analysis
C) discriminant analysis
D) multiple regression

Question 61

It is difficult to observe significant correlation between the GRE score and graduate school GPA among elite graduate students because of

A) range restriction.
B) the elite syndrome.
C) unreliability in the GRE.
D) shrinkage.

Question 62

Suppose we wanted to predict success in graduate school on the basis of undergraduate G.P.A. ,IQ,and professor ratings.The statistical method that would be most useful is

A) bivariate correlation.
B) Spearman's rho.
C) multiple regression.
D) factor analysis.

Question 63

If the coefficient of determination is 0.49,what is the correlation coefficient?

A) 0.24
B) 0.51
C) 0.70
D) 0.89

Question 64

X and Y correlate .2.What is the coefficient of determination of this relation?

A) 0
B) .04
C) .45
D) .75

Question 65

Assume that X and Y correlate .6,are in Z-score form,and that a particular value of X is 1.What is the value of the Y residual?

A) 0
B) .4
C) .6
D) 1

Question 66

The standard deviation of the residuals is called the

A) coefficient of alienation.
B) shrinkage.
C) coefficient of determination.
D) standard error of estimate.

Question 67

X and Y correlate .8.What is the coefficient of alienation of this relation?

A) 0
B) .20
C) .60
D) .80

Question 68

How is discriminant analysis different from multiple regression?

A) In discriminant analysis,the criterion variable is a set of categories rather than a continuous variable.
B) The criterion variable is continuous in discriminant analysis but not in multiple regression.
C) Discriminant analysis is a form of factor analysis,while multiple regression is not.
D) Discriminant analysis and multiple regression involve exactly the same process.

Question 69

An appropriate statistical technique that one might use to see how Scholastic Aptitude Test Scores and High School Grades jointly relate to Freshman grades is

A) linear regression.
B) multiple regression.
C) discriminant analysis.
D) factor analysis.

Question 70

The relationship between TV viewing and aggressive behavior might be influenced by poor social adjustment.Social adjustment here is regarded as a(n)____ problem.

A) restricted range
B) shrinkage
C) third variable
D) lack of linearity

Question 71

The observation that the preference for watching TV shows depicting violence is correlated -.86 with altruism suggests

A) TV violence causes altruistic behavior.
B) altruistic behavior causes a preference for TV violence.
C) increases in altruism are associated with decreases in preference for violent programs.
D) there is no relationship between TV preference and altruism.

Question 72

What is the sum of the predicted value of Y and its residual?

A) the coefficient of determination
B) the obtained Y
C) the alienation coefficient
D) the sum of squares

Question 73

X and Y correlate .5.What is the coefficient of determination of this relation?

A) 0
B) .25
C) .50
D) .75

Question 74

Suppose you had a series of eight measures of anxiety that you administered to a sample.You would use the statistical technique referred to as ____ in order to test the hypothesis that they are all measuring the same thing (anxiety).

A) linear regression
B) multiple regression
C) discriminant analysis
D) factor analysis

Question 75

X and Y correlate .6.What is the coefficient of alienation of this relation?

A) 0
B) .36
C) .60
D) .80

Question 76

An appropriate statistical technique that one might use to see how Scholastic Aptitude Test Scores and High School Grades explain differences among majors in Psychology,Sociology,and Political Science is

A) linear regression.
B) multiple regression.
C) discriminant analysis.
D) factor analysis.

Question 77

The coefficient of alienation is the

A) squared correlation coefficient.
B) index of variation in Y not explained by its relationship to X.
C) standard deviation of the residuals.
D) square root of the standard deviation.

Question 78

A study demonstrates that the number of cigarettes smoked per day is significantly correlated with the number of respiratory infections experienced by young adults.This observation suggests that

A) cigarette smoking causes respiratory infections.
B) cigarette smoking does not cause respiratory infections.
C) cigarette smoking causes some respiratory infections but not others.
D) the data do not allow inferences about causation.

Question 79

The coefficient of determination is the

A) number of degrees of freedom.
B) difference between predicted and observed values of Y.
C) mean.
D) squared correlation coefficient.

Question 80

The amount of decrease observed when a regression equation is created for one population and applied to another is called

A) the true score.
B) the standard deviation.
C) a residual.
D) shrinkage.