Chapter 10
Chapter 10
Linear Regression
Section A
1. Increasing the magnitude of Pearson's r in a regression problem (all else remaining equal), always causes an increase in:
a) the variance of the estimate
* b) the magnitude of the slope
c) the magnitude of the Y-intercept
d) none of the above
2. If the raw-score prediction for Y is always the same as the raw-score of X (the variable used to make the predictions), the slope of the regression line will be:
a) zero
* b) +1.0
c) infinity
d) it depends on the standard deviations of X and Y
3. The difference between the variance of the estimate and the total variance is:
a) equal to r2
* b) the explained variance
c) the unexplained variance
d) equal to the coefficient of determination
4. For a sample, r2 is equal to:
a) the ratio of the explained variance to the unexplained variance
b) the coefficient of nondetermination
* c) the proportion of the variance accounted for
d) all of the above
5. The Y-intercept is:
* a) the value of Y when X equals zero
b) the value of Y when r equals zero
c) the value of Y when the slope equals zero
d) the value of X when Y equals zero
6. A large positive slope means that:
a) the correlation will be large and positive
b) the Y-intercept will be large and positive
* c) the value of Y will increase by (at least) several units when the X value increases by one unit
d) all of the above are true
7. Suppose you draw a random sample from the population and Pearson's r is equal to +.5. If you use your regression equation to make predictions for subjects not in your sample, some error will be involved. The amount of error would be less if:
a) your correlation were higher
b) your sample were larger
c) your regression slope were larger
* d) all of the above are true
8. The standard error of the estimate increases (all else remaining equal), whenever:
a) the sample size increases
b) the slope increases
c) the correlation increases
* d) the coefficient of nondetermination increases
9. Homoscedasticity exists in the population, when for every X value:
a) the variance of the Y variable is the same
* b) the variance around the regression line is the same
c) the slope of the regression line is the same
d) the Y-intercept is the same
10. When dealing with large sample sizes, 95% of the time the true value of Y is:
a) the same as the predicted value
b) within (about) one standard deviation of the mean of Y
* c) within (about) two standard errors of the estimate on either side of the regression line
d) within (about) one standard error of the estimate on either side of the predicted value
Section B
11. Suppose that there is a .45 correlation between IQ (μ = 100, σ = 15) and verbal SAT score (μ = 500, σ = 100). What verbal SAT score would you predict for someone who has an IQ of 90?
a) 433 b) 470 c) 490 d) 510
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12. Given that μx = 57, σx = 18.5, μy = 44, σy = 16, and that the slope of the regression line for predicting Y from X, byx, is
-.52, what must the correlation between X and Y be?
a) -.45 b) -.60 c) -.67 d) +.45
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13. If the slope for predicting Y from X, byx, is 16 and the Y-intercept, ayx, is 400, what prediction for Y corresponds to X = 20?
a) 320 b) 420 c) 560 d) 720
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14. Suppose that there is a .6 correlation between IQ (μ = 100, σ = 15) and verbal SAT score (μ = 500, σ = 100). What would be the variance of the estimate when predicting IQ from verbal SAT?
a) 36 b) 64 c) 144 d) 640
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15. Given the following regression equation: Y = 16X + 5, for what value of X would 29 be predicted?
a) 1.5 b) 1.8 c) 464 d) 469
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16. Suppose that a regression equation for predicting a midterm score from the number of practice problems solved prior to the exam is as follows: Y' = .8X + 45. What midterm score is predicted for someone who does not solve any practice problems?
a) .8 b) 45 c) 56.25 d) 0
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17. A professor believes that the midterm score in her class is a good prediction of the final exam score. If the mean for the midterm () was 77, with sx = 18.5, and the mean for the final exam () was 84, with sy = 14, what final exam score would be predicted for someone whose midterm was 77?
a) 77
* b) 84
c) 91
d) cannot be answered without knowing Pearson's r
18. Given the following summary statistics: = 36, sx = 1.6,
= 44, sy = 2.8, r = .7, N = 10, what is the unbiased estimate for the standard error of the estimate?
a) 1.21 b) 1.63 c) 2.0 d) 2.12
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19. Although instructions to use imagery to link items in a list can significantly improve free recall, recall after instructions can be predicted rather well from recall performance before instructions. Data for eight subjects are given below:
Before After
8 14
11 15
7 9
10 16
9 9
12 13
8 7
10 12
What is the slope of the regression equation for predicting a subject's score after instruction from his or her score before instruction?
a) .31 b) .59 c) 1.13 d) 1.91
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20. To show that the number of hours spent studying can, to some degree, predict scores on a quiz, a professor collected the data presented below:
Study Hours Quiz Score
7 5
6 10
11 6
5 4
15 9
11 10
12 8
11 9
7 7
What is the Y-intercept of the regression equation for predicting the quiz score from the number of hours studied (i.e., what quiz score is predicted for someone who doesn't study)?
a) .31 b) 3.09 c) 4.58 d) 7.08
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Section C
21. Experiments A and B resulted in the same two-group t value, but experiment A involved more subjects. Which of the following can be concluded from this information?
a) More variance is accounted for in experiment A.
* b) More variance is accounted for in experiment B.
c) The same amount of variance is accounted for in both experiments.
d) Nothing can be concluded without knowing the separation of the sample means in each experiment.
22. Suppose that the calculated t value for a two-group experiment with 43 subjects per group is 4.0. What is the value of the point-biserial r?
a) .16
b) .19
* c) .4
d) .44
23. Suppose that the calculated t value for an experiment with two equal-sized groups is 2.0. If the point-biserial r is .3, how many subjects must have been in each group?
a) 20
* b) 21
c) 40
d) 42
24. If the effect size (d) for a two-group experiment is 1.0, what proportion of the variance in the population is accounted for by group membership?
* a) .2
b) .25
c) .4
d) 1.0
25. A large two-group t value can be associated with a very small value for the point-biserial r, if which of the following is true?
a) alpha is very large
b) the p value is very large
c) d is very large
* d) the sample sizes are very large
Chapter 11
Chapters 10-12
The Matched t-test
Section A
1. The usual null hypothesis in the matched t-test can be stated as:
a) the population mean of the difference scores is zero
b) the population means corresponding to the two sets of
scores are the same
c) the difference of the population means corresponding to
the two sets of scores is zero
* d) all of the above
2. Compared to an independent-samples t-test on the same data, the matched t-test will always yield:
a) a smaller critical t
* b) a larger critical t
c) a smaller calculated t
d) none of the above
3. The matched t-test is always preferable to the independent-samples t-test, when:
a) the correlation between the two sets of scores is positive
b) there are no carry-over effects
c) the two samples are equal in size
* d) none of the above
4. The matched t will equal the independent-samples t calculated on the same data, when:
* a) the correlation between the two sets of scores is zero
b) the correlation between the two sets of scores is 1.0
c) the variability of the difference scores is zero
d) the sample variances of the two sets of scores are equal
5. The direct-difference method:
a) requires that the correlation between the two sets of
scores be calculated first
* b) resembles the one-sample t-test
c) only applies when the same subject has been measured
twice
d) yields the same value as an independent-groups t-test
6. When the correlation between the two sets of scores in a matched t-test is 1.0:
a) the matched t will be zero
b) the difference of the sample means will be zero
* c) the variability of the difference scores will be zero
d) the independent-samples t will be larger than the
matched t
7. Matching subjects in pairs is usually preferable to repeated measures on the same subjects, whenever:
a) there are order effects
* b) there are carry-over effects
c) the correlation between the two sets of scores is low,
but positive
d) all of the above
8. The purpose of counterbalancing is:
* a) to average out order effects
b) to average out carry-over effects
c) to increase the correlation between the two sets of scores
d) none of the above
9. Drawing conclusions from a before-after design can be misleading if:
a) the same subjects are measured twice
b) the correlation between the two sets of scores is very
high
c) the design is correlational rather than experimental
* d) there is no control group
10. When the correlation between the two sets of scores in a matched t-test is high and positive, the advantage of the matched t-test (compared to the independent-samples test) is that:
a) there is less chance of making a Type I error
* b) there is less chance of making a Type II error
c) it is more reasonable to perform a one-tailed test
d) the results are more conclusive
Section B
11. If a study involves 12 pairs of matched subjects, what would be the appropriate critical t value for a .01, one-tailed test?
a) 2.492 b) 2.508 c) 2.681 d) 2.718
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12. Twenty matched pairs of subjects were given simulated work tasks under two different sets of working conditions. The mean number of tasks completed was 12.6 for one condition and 14.2 for the other. If the (unbiased) standard deviation of the difference scores was 4, what is the matched t value?
a) 1.79 b) 3.58 c) 7.16 d) 8.0
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13. Suppose you have scores taken before and after some treatment on 30 subjects. If the standard deviation of the before scores is 7.5 and the standard deviation of the after scores is 6.1, and the correlation between the before and after scores is .5, what is the standard error of the difference scores (i.e., the denominator of the matched t-test)?
a) 1.26 b) 1.59 c) 1.77 d) 2.15
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14. Given the following summary statistics: 1 = 1.6, 2 =5.1,
s1= 3, s2= 4, N = 16, r = .3, what is the value of the matched t?
a) 1.66 b) 2.80 c) 3.32 d) 6.83
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15. If the matched t equals 3.33 in an experiment, in which the standard deviation of the difference scores (sD) equals 2.7 and the difference of the two sample means equals 4.5, how many pairs of scores must have been involved?
a) 2 b) 4 c) 8 d) 16
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16. Imagine that 36 subjects are each run in two experimental conditions and that the mean for one condition is 7.2, while the mean for the other condition is 4.7. If the standard deviation of the difference scores (sD) is 4.5, what is the two-tailed p level that corresponds to the matched t?
a) > .05
b) between .05 and .02
c) between .02 and .01
* d) < .01
17. Which of the following will produce the highest matched t value, assuming that the numerator is the same in each case?
a) sD = 5, N = 12
b) sD = 6.5, N = 17
* c) sD = 4, N = 9
d) sD = 9, N = 21
18. A computer company claims that their new keyboard is designed for faster typing. In a pilot study, six subjects typed the same material on both the new and an old keyboard. Given the scores below (in words per minute), what is the value of t that would be used to test the null hypothesis?
Subject Old keyboard New keyboard
1 48 52
2 56 56
3 49 55
4 68 65
5 66 67
6 59 63
a) 1.37 b) 1.49 c) 2.74 d) 3.35
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19. A student would like to demonstrate that the final exam was significantly more difficult than the midterm. The scores for four of the student's friends are shown below. What is the matched t value for these data?
Student Midterm Final
1 88 91
2 84 80
3 86 79
4 80 65
a) .77 b) 1.54 c) 1.33 d) 2.66
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20. It has long been known that the use of imagery can improve recall in a memory test. The data below represent the number of words recalled from a list before and after the subject is given instructions to use imagery to memorize the list of words.
Subject Before After
1 8 14
2 11 15
3 7 9
4 10 16
5 9 9
6 12 13
7 8 7
8 10 12
What is the two-tailed p value that corresponds to the matched t for this experiment?
a) > .05