Deck 12: Correlation R and Regression Y BX A

Question 1

Correlation is similar to the χ² test of independence in that ______.

A) both require interval or ratio level measurement
B) both examine the relationship between two variables
C) both are non-parametric tests
D) all of these

Answer 1

B

Question 2

Which of these is a name for r?

A) correlation coefficient
B) Pearson's r
C) Pearson's product-moment correlation coefficient
D) all of these

Answer 2

D

Question 3

Pearson's r is ______.

A) an index of linear relationship between two interval or ratio variables
B) an index of curvilinear relationship between two interval or ratio variables
C) an index of linear relationship between two nominal or ordinal variables
D) an index of curvilinear relationship between two nominal or ordinal variables

Answer 3

A

Question 4

A linear relationship is a relationship that ______.

A) follows a straight line
B) follows a curved line
C) follows a straight or curved line
D) none of these

Question 5

To people unfamiliar with statistics, "correlation" most likely is used a synonym for ______.

A) linear relationship
B) relationship
C) curvilinear relationship
D) none of these

Question 6

The value of a correlation reflects ______.

A) one piece of information: magnitude
B) two pieces of information: magnitude and direction
C) three pieces of information: magnitude, direction, and strength
D) none of these

Question 7

A correlation of -1 could be described as ______.

A) perfect relationship
B) imperfect relationship
C) null relationship
D) none of these

Question 8

As compensation increases, turnover decreases. This describes ______.

A) no relationship
B) a positive relationship
C) a negative relationship
D) a perfect relationship

Question 9

Which of these describes the strongest relationship?

A) r = .7
B) r = .6
C) r = -.8
D) These correlations do not differ in strength.

Question 10

A scatterplot depicting a circular cloud of data could be described as ______.

A) a negative relationship
B) a positive relationship
C) a perfect relationship
D) no relationship

Question 11

As CEO compensation decreases, stock price decreases. This describes ______.

A) a negative relationship
B) no relationship
C) a positive relationship
D) a perfect relationship

Question 12

When employees are very relaxed (not at all stressed), they perform poorly. When employees are concerned about meeting deadlines (somewhat stressed), they perform strongly. When employees are overwhelmed (very stressed), they perform poorly. The relationship between stress and performance can be described as ______.

A) positive
B) negative
C) linear
D) curvilinear

Question 13

A correlation is a ______ covariance.

A) curvilinear
B) standardized
C) linear
D) none of these

Question 14

The covariance is different from the variance in that the covariance ______.

A) incorporates information about two variables
B) standardizes the variability in both variables
C) incorporates the sum of the differences between scores and their means
D) none of these; they are the same.

Question 15

Given a dataset where r = .8, adding a new case where the value of x is high and the value of y is high is most likely to ______.

A) increase the magnitude of the correlation
B) decrease the magnitude of the correlation
C) have no effect on the correlation
D) skew the correlation

Question 16

Given a dataset where r = -.9, adding a new case where the value of x is high and the value of y is low is most likely to ______.

A) increase the magnitude of the correlation
B) decrease the magnitude of the correlation
C) have no effect on the correlation
D) skew the correlation

Question 17

The value of correlation over covariance is that correlation ______.

A) better describes linear relationships
B) better describes curvilinear relationships
C) can be used to compare across relationships with dissimilar variables
D) none of these

Question 18

Which of the following is a valid null hypothesis to test a correlation?

A) H₁:  = 0
B) H₁:  = 0
C) H₁:  = 0
D) H₁:  = 0

Question 19

What is the critical value for a correlation where n = 14?

A) t = ±2.160
B) t = ±2.179
C) r = ±2.160
D) r = ±2.179

Question 20

Significance tests for correlation are generally ______.

A) directional
B) linear
C) non-directional
D) curvilinear

Question 21

The conduct a significance test on a correlation, we must ______.

A) consult an r-table
B) convert the correlation to t and consult a t-table
C) convert the correlation to z and consult a z-table
D) none of these

Question 22

You find a correlation of .5. What percentage of variability in your x-variable can be explained by your y-variable?

A) 50%
B) 5%
C) 25%
D) none of these

Question 23

The coefficient of determination is found to be .81. What is the value of r?

A) .81
B) .09
C) .90
D) none of these

Question 24

If the correlation between sales and profit is .7, what percentage of variance in sales is unshared with variance in profit?

A) 70%
B) 30%
C) 49%
D) 51%

Question 25

The Director of Training at our organization wants to provide training to all salespeople across all branches of our organization. If we regressed training scores on instructor quality, ______ would be our x variable, and ______ would be our y variable.

A) Instructor quality, training scores
B) training scores, branch
C) branch, training scores
D) training scores, instructor quality

Question 26

The line of best fit is the best line that can be used to describe ______.

A) the relative directions of the correlations
B) the relationship between two variables
C) the relative magnitudes of correlations
D) none of these

Question 27

Regression can also be called least squares regression because ______.

A) it produces a line minimizing the sum of squared residuals
B) it produces a line minimizing the squared residuals
C) it produces a line minimizing the squares
D) none of these

Question 28

If we find a correlation between training and job performance, we can conclude ______.

A) training causes job performance
B) job performance causes training
C) both a and b
D) none of these

Question 29

We have conducted a regression discovering that y′ = 12x - 10. If the predictor is valued at 1, the value of the criterion is predicted to be ______.

A) 2
B) 0.92
C) 1
D) none of these

Question 30

In this regression formula (y′ = 2x + 1), the "1" is the ______ and the "2" is the ______ .

A) slope, intercept
B) intercept, slope
C) predictor, criterion
D) criterion, predictor

Question 31

Pearson's r is the most common type of correlation.

Question 32

When calculating a correlation, the variable you choose for x and the variable you choose for y is critical to interpretation.

Question 33

A Pearson's product-moment correlation coefficient is often abbreviated as "correlation."

Question 34

A correlation of -.8 is stronger than a correlation of .6.

Question 35

If you can predict y from x with 100% accuracy, you can refer to this as a perfect relationship.

Question 36

As one variable goes down, the other goes down. This describes a positive relationship.

Question 37

The covariance formula differs from the variance formula in that instead of squaring the difference between each score and its mean, we multiply the difference between each x score and its mean with each y score and its mean.

Question 38

If r = -.8, adding a case that is high on x and high on y will result in a stronger correlation.

Question 39

A correlation can be calculated by adding each multiplied pair of z-scores together and dividing by degrees of freedom.

Question 40

H₁:  = 0 is a valid alternative hypothesis for testing the statistical significance of a correlation.

Question 41

Correlation can be tested for statistical significance by converting it to a t-statistic and testing it against a t-distribution with (n - 1) degrees of freedom.

Question 42

If r(8) = 1.2, p > .05, there must have been a sample size of 10.

Question 43

If r = .6, 36% of the variance in each variable is explained by the other.

Question 44

A regression line can be used to predict values outside the range of the original predictor.

Question 45

In regression, the slope can be determined by dividing the rise by the run of the regression line.

Question 46

In regression, we always regress the y variable on the x variable.

Question 47

In the following regression line, the intercept is 5: y′ = 23x - 5

Question 48

In regression, the predictor is also called the dependent variable and the criterion is also called the independent variable.

Question 49

Causation can only be determined by experimental design - not statistics alone.

Question 50

Correlation and the χ² test of independence are similar in purpose with a few key differences. Describe how are these tests are similar. Describe how they are different.

Question 51

When predicting values using a regression line, why can't we use values outside the range of the original x-variable?

Question 52

Correlation is not the same as causation. Why not?

Question 53

How are the coefficient of determination and correlation similar? How are they different?

Question 54

You run a used car dealership and want to know if you are appropriately compensating your sales force, so you collect weekly compensation rates and counts of monthly sales with the intent of comparing them.
1)What is the research question?
2)What are the hypotheses?
3)What are the degrees of freedom for the statistical significance test?
4)What is the critical value for this test?
5)State the formal results of the test.
6)Should you compute a coefficient of determination? How do you know? If so, calculate it.
7)Regress sales on compensation, and report the formula for the regression line here.
8)State all appropriate conclusions.
9)If a salesperson was compensated 450, what would we expect sales to be?