Deck 9: Interpretive Aspects of Correlation and Regression

Question 1

What is meant by regression toward the mean? Give several examples.

Answer 1

Consider a group of individuals all with the same X score above (or below) the mean of X; if the correlation is less than perfect, the group will, on the average, be closer to the mean of Y than they were to the mean of X (in standard deviation units). Examples: children who are heaviest at age 6 will, on the average, be somewhat less than the heaviest as adults; the students who perform the poorest in English will, on the average, do somewhat better (relative to the group) in math.

Question 2

In one study, a correlation of +.45 was found between physical strength and ratings of popularity for a group of adolescent boys. What can be said about the degree to which differences in popularity can be "explained" by strength? Give your answer in terms of a percent. Percent of what? Be very precise and complete in your explanation.

Answer 2

(.45)² = 20% of the variance in popularity is associated with variation in physical strength.

Question 3

In a study, the correlation between height of parents and height of adult children was found to be +.61. The summary statistics for the group of children are: in. and S_X = 3.1 in. 
(a) What percent of the children's height variance is associated with variation in parent height, and what percent is associated with other factors? 
(b) Compute the amount of children's height variance associated with variation in parent height and the amount associated with other factors. 
(c) In practice, which results would we normally be more interested in, those from (a) or those from (b) ? Why?

Answer 3

(a)37% and 63% 
(b)associated with variation in parent height: associated with other factors:  
(c)those from (a); the percent of variance explained does not depend on the units of measurement used.

Question 4

Other things being equal, when the range of talent is increased, S_YX will

A) increase
B) decrease
C) remain the same
D) change in an unpredictable manner

Question 5

The amount of regression on the mean is least when r is

A) low
B) high
C) negative
D) positive

Question 6

In which situation does the phenomenon of regression on the mean not occur?

A)

B)

C) r is between 0 and -1.00
D) r is between 0 and +1.00

Question 7

Assume a moderate positive r between father's height and son's adult height. For a father whose height is one standard deviation below the mean, we predict that his son's height will be

A) more than one standard deviation below the mean
B) one standard deviation below the mean
C) less than one standard deviation below the mean
D) at the mean

Question 8

According to their grade on the first midterm, an instructor identifies the 10 best students among his class of 100. Their average grade is A-. After the next examination he reviews their performance. He will probably find that their average grade on the second test will be

A) higher
B) about the same
C) lower, but above average
D) about average

Question 9

If a regression equation reads: we know that

A) is greater than
B) S_Y is greater than S_X
C) the correlation is negative
D) a mistake has been made in calculating r

Question 10

If a regression equation reads: we know that

A) is greater than
B) S_Y is greater than S_X
C) the correlation is negative
D) a mistake has been made in calculating r

Question 11

If a regression equation reads: we know that

A) Y increases 1 unit for every 2 units of increase in X
B) Y increases 2 units for every 1 unit of increase in X
C) is 3 units lower than X
D) the correlation is negative

Question 12

The reason that regression on the mean does not result in all individuals being of average stature after several generations is that

A) regression is not operative in problems in inheritance
B) negative regression is accompanied by positive regression
C) regression is accompanied by variability
D) regression applies only to the first generation

Question 13

If this means that

A) 75% of Y variance is associated with variation in X
B) 25% of Y variance is associated with variation in X
C) variability of predictive error is 75% of what it would be if r were zero
D) variability of predictive error is 25% of what it would be if r were zero

Question 14

If this means that

A) 75% of Y variance is associated with variation in X
B) 25% of Y variance is associated with variation in X
C) variability of predictive error is 75% of what it would be if r were zero
D) variability of predictive error is 25% of what it would be if r were zero

Question 15

Fifty percent of Y variance is associated with variation in X when r is approximately

A) .9
B) .7
C) .5
D) .25

Question 16

A large value of may be expected when r is

A) +.90
B) +.25
C) -.75
D) -1.00

Question 17

In a study concerned with the relationship between X and Y, it is found that 9% of the variance in Y is associated with X. This r_XY must have been

A) .09
B) .30
C) .81
D) .08

Question 18

In one study, a correlation of -.49 is found between the number of hours of TV watched per week and high school GPA. According to this study ___________ of the GPA variance is associated with TV watching.

A) 14%
B) 24%
C) 49%
D) 70%

Question 19

In general, an increase of .10 points in the correlation coefficient has

A) the greatest consequence for

B) the greatest consequence for

C) the greatest consequence for

D) equal consequence for all above values of r

Question 20

will be zero when

A)

B)

C)

D)

Question 21

measures variation of

A) obtained scores about the predicted scores
B) obtained scores about the mean
C) predicted scores about the obtained scores
D) predicted scores about the mean

Question 22

will be zero when

A)

B)

C)

D)

Question 23

when

A)

B)

C)

D)