Deck 3: Correlation and Regression

Question 1

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

A)−.85
B).01
C).50
D).80

Answer 1

A

Question 2

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 2

C

Question 3

If the scores on X give us no information about the scores on Y , the sets of scores likely have

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

Answer 3

C

Question 4

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 5

Given the following ordered pairs, you can infer that the correlation is most likely 8 7
7 6
3 2
1 2
1 2

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

Question 6

Correlation measures the magnitude and ____ of a relationship.

A)strength
B)consistency
C)direction
D)regression

Question 7

Each point on a scatter diagram shows

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 8

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 9

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

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

Question 10

What is the point of least squares for the set of scores [2, 7, 8, 11]?

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

Question 11

A scatter diagram is a

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

Question 12

What is the point of least squares for the set of scores [4, 6, 8, 10]?

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

Question 13

In correlation analysis, we ask whether two variables

A)can be measured.
B)experience regression.
C)have a causal relationship.
D)covary.

Question 14

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 15

Diagrams that use a single point to show a person's scores on two measures are called ____ plots.

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

Question 16

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 17

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

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

Question 18

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 19

Suppose that you have two variables, one with a mean of 15 and another with a mean of 19. If you know only that one person's score on the first variable is 14, the best prediction of that person's score on the other is

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

Question 20

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 21

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 22

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 nonsignificant.

Question 23

The principle of least squares minimizes the squared deviation

A)at the intercept.
B)of positive correlations but not negative correlations.
C)of the slope.
D)around the regression line.

Question 24

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 25

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 the set of scores.

Question 26

The Pearson product moment ____ is a ratio to determine the degree of variation in one variable that can be estimated from knowledge about variation in the other variable.

A)residual
B)variable
C)coefficient
D)correlation

Question 27

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 28

Correlation coefficients can be tested for significance using the

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

Question 29

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 30

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 31

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 32

The difference between the observed and predicted score is

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

Question 33

What describes how much change is expected in Y each time X increases by one unit?

A)Intercept
B)Slope
C)Correlation coefficient
D)Covariance

Question 34

In general, a regression line is used to

A)make a prediction about a person's score on one variable, based on the person's score on a different variable.
B)assess the magnitude of the relationship between two variables, based on sets of scores from the same people.
C)assess the direction of the relationship between two variables, based on sets of scores from the same people.
D)determine whether results of a study are statistically significant, based on a sample from the population.

Question 35

Suppose that we are given the regression equation, Y ´ = 12 + .80 X . 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 36

When you know nothing about a person's academic ability and have to make an estimate, the best strategy is to make the prediction based on the

A)mean of a known sample.
B)Z scores of each person in the sample.
C)criterion scores.
D)correlation coefficient.

Question 37

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 38

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

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

Question 39

A common use of correlation is to provide evidence for

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

Question 40

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 41

In order to determine the relationship between a true dichotomous variable and a continuous variable, one would compute

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

Question 42

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 the intercept

Question 43

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 44

Which of the following is a dichotomous variable?

A)Football players' numbers
B)Weight
C)Time
D)Whether you are currently married

Question 45

Which of the following is computed to show the relationship between two artificially dichotomous variables?

A)Tetrachoric correlation
B)Factor analysis
C)Discriminant analysis
D)Multiple regression

Question 46

Regression plots are pictures showing

A)the relationship between variables.
B)cause and effect.
C)the null hypothesis.
D)residuals.

Question 47

To assess the relationship between intelligence and passing or failing this exam, you should compute the

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

Question 48

To see the correlation between two true dichotomous variables, you should compute

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

Question 49

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 50

John is asked to predict Janae's IQ score, but he knows nothing about her. John should predict Janae's IQ is 100 (which is the average IQ score), because he is relying on what kind of data?

A)Normative
B)Regressive
C)Correlational
D)Transformative

Question 51

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 52

What is regression typically used for?

A)The researcher uses it to find the statistical significance of correlations.
B)The researcher uses it to convert raw scores to t scores.
C)The researcher uses it to make predictions about scores based on other scores.
D)The researcher uses it to create linear relationships for transforms.

Question 53

The type of correlation coefficient computed when the data are from a true dichotomous variable and a continuous variable is

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

Question 54

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

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

Question 55

Which of the following is an artificially dichotomous variable?

A)Favorite ice cream flavor
B)Weight
C)Success (pass/fail)on a final exam
D)GPA

Question 56

Which of the following is used to show the relationship between a true dichotomous variable and a continuous variable?

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

Question 57

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

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

Question 58

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 59

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 60

Which of the following is used to show 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 61

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 62

The coefficient of alienation measures what?

A)Shrinkage
B)The coefficient of determination
C)Nonassociation between two variables
D)The standard deviation of residuals

Question 63

A regression equation was derived from a small sample in which X and Y are correlated .6. The equation is Y ´ = .6 X + 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 64

If r = .6, what is the coefficient of alienation ?

A).64
B).36
C).40
D).80

Question 65

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 66

To determine which combination of variables determines whether people are likely to get married or stay single, the appropriate method is

A)linear regression.
B)a two-tailed test.
C)discriminant analysis.
D)factor analysis.

Question 67

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 68

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

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

Question 69

Owning a dog may make people happier. Then again, happier people may be more likely to want a dog. Not knowing whether happiness leads to dog ownership or vice versa, we have

A)restricted range.
B)the correlation-causation problem.
C)cross-validation.
D)shrinkage.

Question 70

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 71

An appropriate statistical technique that one might use to see how Scholastic Aptitude Test (SAT)scores and high school grades jointly relate to college freshman grades is

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

Question 72

A correlation of .6 was obtained from a particular sample. The two measures are then administered to a sample from a more homogeneous population. The expected correlation in this new sample will probably be

A)0
B)less than .6.
C)approximately .6.
D)greater than .6.

Question 73

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 74

The formula Y − Y ´ represents

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

Question 75

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

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

Question 76

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

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

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. We can conclude 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 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 80

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.