Deck 3: Correlation and Regression

Question 1

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)

Answer 1

C

Question 2

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

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

Answer 2

C

Question 3

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)

Answer 3

A

Question 4

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

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

Question 5

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 6

The observation that Y decreases as X increases suggests

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

Question 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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 16

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 17

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 18

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

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

Question 19

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

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

Question 20

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.

Question 21

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 22

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 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

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 25

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 26

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 27

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 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,"a" is called

A) the regression coefficient.
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

The difference between the observed and predicted score is

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

Question 32

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 33

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 34

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 35

Suppose that X and Y are uncorrelated. X has a mean of 15 and Y has a mean of 19. Given a score of 14 on a particular X observation, the best prediction of Y is

A) 0.
B) 15.
C) 19.
D) indeterminate.

Question 36

Correlation coefficients can be tested for significance using the

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

Question 37

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 38

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 39

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 40

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 41

Which of the following is a true dichotomous variable?

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

Question 42

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 43

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 44

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 45

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 46

What type of prediction uses information gained from representative groups?

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

Question 47

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 48

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 49

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 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

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 52

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 53

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 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

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 56

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 57

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 58

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 59

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 60

Which of the following is an artificially dichotomous variable?

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

Question 61

A regression equation was derived from a small sample in which X and Y correlated .6. The equation is Y´ = 6X + 15. Suppose this equation were applied to a second sample. It is likely that the correlation between the scores predicted from this equation and the observed scores will be

A) 0.
B) less than 0.6.
C) approximately 0.6.
D) greater than 0.6.

Question 62

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 63

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 64

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 65

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 66

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 67

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

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

Question 68

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 69

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 70

The formula Y - Y´ represents

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

Question 71

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 72

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 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

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 75

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 76

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

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

Question 77

b. less than .6.
C) approximately .6.
D) greater than .6.

Question 78

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.

Question 79

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

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

Question 80

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.