Description

Understanding Statistics in the Behavioral Sciences 9^th Edition Pagano Test Bank

ISBN:

0495596523

ISBN-13:

9780495596523

 

 

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Chapter 7—Linear Regression

 

MULTIPLE CHOICE

 

1. The primary reason we use a scatter plot in linear regression is ____.

a.	to determine if the relationship is linear or curvilinear
b.	to determine the direction of the relationship
c.	to compute the magnitude of the relationship
d.	to determine the slope of the least squares regression line

 

 

ANS:  A                    PTS:   1

 

2. When the relation between X and Y is imperfect, the prediction of Y given X is ____.

a.	perfect
b.	always equal to Y
c.	impossible to determine
d.	approximate

 

 

ANS:  D                    PTS:   1

 

3. The regression equation most often used in psychology minimizes ____.

a.	S (Y – Y’)
b.	S (Y – Y’)2
c.	S (Y – X)2
d.
e.	none of the above

 

 

ANS:  B                    PTS:   1

 

4. The regression of Y on X ____.

a.	predicts X given Y
b.	predicts X’ given X
c.	predicts Y given X
d.	predicts Y given Y’

 

 

ANS:  C                    PTS:   1

 

5. The regression of X on Y ____.

a.	predicts Y given X
b.	predicts Y given X
c.	predicts X given Y
d.	is generally the same as the regression of Y on X
e.	c and d

 

 

ANS:  C                    PTS:   1

 

6. If the correlation between two sets of scores is 0 and one had to predict the value of Y for any given value of X, the best prediction of Y would be ____.

a.	bY
b.
c.	0
d.

 

 

ANS:  B                    PTS:   1

 

7. During the past 5 years there has been an inflationary trend. Listed below is the average cost of a gallon of milk for each year.

 

1981	1982	1983	1984	1985
$1.10	$1.23	$1.30	$1.50	$1.65

 

Assuming a linear relationship exists, and that the relationship continues unchanged through 1986, what would you predict for the average cost of a gallon of milk in 1986?

a.	$1.77
b.	$1.72
c.	$1.70
d.	$1.83

 

 

ANS:  A                    PTS:   1

 

Exhibit 7-1

A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat of the individual. The following scores are recorded.

 

Individual	1	2	3	4	5
Exercise (min)	10	18	26	33	44
% Fat	30	25	18	17	14

 

 

8. Refer to Exhibit 7-1. Assuming a linear relationship holds, the least squares regression line for predicting % fat from the amount of exercise an individual gets is ____.

a.	Y’ =   0.476X + 33.272
b.	Y’ =   1.931X + 66.363
c.	Y’ = -0.476X + 33.272
d.	Y’ = -0.432X + 32.856

 

 

ANS:  C                    PTS:   1

 

9. Refer to Exhibit 7-1. If an individual exercises 20 minutes daily, his predicted % body fat would be ____.

a.	21.63
b.	27.74
c.	27.88
d.	23.75

 

 

ANS:  D                    PTS:   1

 

10. Refer to Exhibit 7-1. The least squares regression line for predicting the amount of exercise from % fat is ____.

a.	X’ = -1.931Y + 66.363
b.	X’ = -0.476Y + 33.272
c.	X’ =   1.931Y + 66.363
d.	X’ = -1.905Y + 62.325

 

 

ANS:  A                    PTS:   1

 

11. Refer to Exhibit 7-1. If an individual has 22% fat, his predicted amount of daily exercise is ____.

a.	22.80
b.	23.88
c.	24.76
d.	20.22

 

 

ANS:  B                    PTS:   1

 

12. Refer to Exhibit 7-1. The value for the standard error of estimate in predicting % fat from daily exercise is ____.

a.	3.35
b.	4.32
c.	2.14
d.	1.66
e.	none of the above

 

 

ANS:  C                    PTS:   1

 

13. The assumption of homoscedasticity is that ____.

a.	the range of the Y scores is the same as the X scores
b.	the X and Y distributions have the same mean values
c.	the variability of Y doesn’t change over the X scores
d.	the variability of the X and Y distributions is the same

 

 

ANS:  C                    PTS:   1

 

14. You go to a carnival and a sideshow performer wants to bet you $100 that he can guess your exact weight just from knowing your height. It turns out that there is the following relationship between height and weight.

 

Height (in)	60.0	62.0	63.0	66.5	73.5	84.0
Weight (lbs)	99	107	111	125	153	195

 

Should you accept the performer’s bet? Explain.

a.	yes
b.	need more information
c.	no
d.	yes, if he measures my height in centimeters

 

 

ANS:  C                    PTS:   1

 

15. If r = 0.4582, s_Y = 3.4383, and s_X = 5.2165, the value of b_Y = ____.

a.	0.695
b.	0.458
c.	0.302
d.	1 – 0.458
e.	none of the above

 

 

ANS:  C                    PTS:   1

 

16. In multiple regression, if the second predictor variable correlates highly with the predicted variable, than it is quite likely that ____.

a.	R2 = 1.00
b.	R2 > r2
c.	R2 = r2
d.	R2 < r2

 

 

ANS:  B                    PTS:   1

 

17. If the relationship between X and Y is perfect:

a.	r = b
b.	the equation for Y‘ equals the equation for X‘
c.	prediction is approximate
d.	a and b
e.	all of the above

 

 

ANS:  D                    PTS:   1

 

18. When predicting Y, adding a second predictor variable to the first predictor variable X, will ____.

a.	always increase prediction accuracy
b.	increase prediction accuracy depending on the relationship between the second predictor variable and X
c.	Increase prediction accuracy depending on the relationship between the second predictor variable and Y
d.	b and c

 

 

ANS:  D                    PTS:   1

 

19. The higher the standard error of estimate is,

a.	the more accurate the prediction is likely to be
b.	the less accurate is the prediction is likely to be
c.	the less confidence we have in the accuracy of the prediction
d.	the more confidence we have in the accuracy of the prediction
e.	a and d
f.	b and c

 

 

ANS:  F                    PTS:   1

 

20. If s_Y|X = 0.0 the relationship between the variables is ____.

a.	perfect
b.	imperfect
c.	curvilinear
d.	unknown

 

 

ANS:  A                    PTS:   1                    MSC:  WWW

 

21. S (Y – Y’) equals ____.

a.	0
b.	1
c.	cannot be determined from information given
d.	who cares

 

 

ANS:  A                    PTS:   1

 

22. S (Y – Y’)² represents ____.

a.	the standard deviation
b.	the variance
c.	the standard error of estimate
d.	the total error of prediction

 

 

ANS:  D                    PTS:   1                    MSC:  WWW

 

23. In a particular relationship N = 80. How many points would you expect on the average to find within ±1s_Y|X of the regression line?

a.	40
b.	80
c.	54
d.	0

 

 

ANS:  C                    PTS:   1

 

24. What would you predict for the value of Y for the point where the value of X is ?

a.	cannot be determined from information given
b.	0
c.	1
d.

 

 

ANS:  D                    PTS:   1

 

25. If the value of s_Y|X = 4.00 for relationship A and s_Y|X = 5.25 for relationship B, in which relationship would you have the most confidence in a particular prediction?

a.	A
b.	B
c.	it makes no difference
d.	cannot be determined from information given

 

 

ANS:  A                    PTS:   1                    MSC:  WWW

 

26. If b_Y is negative, higher values of X are associated with ____.

a.	lower values of X’
b.	higher values of Y
c.	higher values of (Y – Y’)
d.	lower values of Y

 

 

ANS:  D                    PTS:   1

 

27. Which of the following statement(s) is (are) an important consideration(s) in applying linear regression techniques?

a.	the relationship should be linear
b.	both variables must be measured in the same units
c.	predictions for Y should be within the range of the X variable in the sample
d.	a and c

 

 

ANS:  D                    PTS:   1                    MSC:  WWW

 

28. In the regression equation Y’ = X, the Y-intercept is ____.

a.
b.
c.	0
d.	1

 

 

ANS:  C                    PTS:   1

 

29. If the value for a_Y is negative, the relationship between X and Y is ____.

a.	positive
b.	negative
c.	inverse
d.	cannot be determined from information given

 

 

ANS:  D                    PTS:   1                    MSC:  WWW

 

30. If b_Y = 0, the regression line is ____.

a.	horizontal
b.	vertical
c.	undefined
d.	at a 45° angle to the X axis

 

 

ANS:  A                    PTS:   1

 

31. The least-squares regression line minimizes ____.

a.	s
b.	sY|X
c.	S (Y – )2
d.	S (Y – Y’)2
e.	b and d

 

 

ANS:  E                    PTS:   1

 

32. The points (0,5) and (5,10) fall on the regression line for a perfect positive linear relationship. What is the regression equation for this relationship?

a.	Y’ = X + 5
b.	Y’ = 5X
c.	Y’ = 5X + 10
d.	cannot be determined from information given.

 

 

ANS:  A                    PTS:   1

 

33. For the following points what would you predict to be the value of Y’ when X = 19? Assume a linear relationship.

 

X	6	12	30	40
Y	10	14	20	27

 

a.	16.35
b.	24.69
c.	22.00
d.	17.75

 

 

ANS:  A                    PTS:   1                    MSC:  WWW

 

34. If N = 8, S X = 160, S X² = 4656, S Y = 79, S Y² = 1309, and S XY = 2430, what is the value of b_Y?

a.	0.9217
b.	-1.8010
c.	0.5838
d.	0.7922

 

 

ANS:  C                    PTS:   1

 

35. If X and Y are transformed into z scores, and the slope of the regression line of the z scores is -0.80, what is the value of the correlation coefficient?

a.	-0.80
b.	0.80
c.	0.40
d.	-0.40

 

 

ANS:  A                    PTS:   1                    MSC:  WWW

 

36. If the regression equation for a set of data is Y’ = 2.650X + 11.250 then the value of Y’ for X = 33 is ____.

a.	87.45
b.	371.25
c.	98.70
d.	76.20

 

 

ANS:  C                    PTS:   1                    MSC:  WWW

 

37. If  = 57.2,  = 84.6, and b_Y = 0.37, the value of a_Y = ____.

a.	141.80
b.	-25.90
c.	63.44
d.	27.40

 

 

ANS:  C                    PTS:   1

 

38. If the regression line for predicting X given Y were X’ = 103Y + 26.2, what would the value of X’ be if Y = 0.2?

a.	129.2
b.	25.8
c.	5.2
d.	46.8

 

 

ANS:  D                    PTS:   1

 

39. If s_Y = s_X = 1 and the value of b_Y = 0.6, what will the value of r be?

a.	0.36
b.	0.60
c.	1.00
d.	0.00

 

 

ANS:  B                    PTS:   1

 

40. When using more than one predictor variable, ____ tells us the proportion of variance accounted for by the predictor variables.

a.	r
b.	SSX
c.	SSY
d.	R2

 

 

ANS:  D                    PTS:   1                    MSC:  WWW

 

41. Which of the following statements is(are) false?

a.	bY is the slope of the line for minimizing errors in predicting Y.
b.	aY is the Y axis intercept for minimizing errors in predicting Y.
c.	sY½X is the standard error of estimate for predicting Y given X.
d.	All of the above statements are true.
e.	R2 is the multiple coefficient of nondetermination.

 

 

ANS:  E                    PTS:   1                    MSC:  WWW

 

42. The regression coefficient b_Y and the correlation coefficient r ____.

a.	necessarily increase in magnitude as the strength of relationship increases
b.	are both slopes of straight lines
c.	are not related
d.	will equal each other when the variability of the X and Y distributions are equal
e.	b and d

 

 

ANS:  E                    PTS:   1

 

43. When predicting Y given X, ____.

a.	the prediction is valid only within the range of X
b.	the variability of the Y values over the range of the X values should be the same
c.	the representativeness of the sample used to derive the regression line is an important consideration
d.	a, b, and c
e.	a and c

 

 

ANS:  D                    PTS:   1

 

44. When predicting Y from two variables relative to using only one variable, ____.

a.	prediction accuracy always increases
b.	prediction accuracy is dependent on the relationship between the second variable and the Y variable
c.	increase in prediction accuracy depends on the correlation between the two predictor variables
d.	b and c

 

 

ANS:  D                    PTS:   1

 

45. There is ____ between the s_Y|X and r.

a.	a direct relationship
b.	an inverse relationship
c.	no relationship
d.	animosity

 

 

ANS:  B                    PTS:   1

 

46. The regression coefficient for predicting Y given X is symbolized by ____

a.	bY
b.	aY
c.	bX
d.	aX

 

 

ANS:  A                    PTS:   1

 

47. The regression coefficient for predicting X given Y is symbolized by ____.

a.	bY
b.	aY
c.	bX
d.	aX

 

 

ANS:  C                    PTS:   1

 

48. The regression constant for predicting Y given X is symbolized by ____.

a.	bY
b.	aY
c.	bX
d.	aX

 

 

ANS:  B                    PTS:   1

 

49. The regression constant for predicting X given Y is symbolized by ____.

a.	bY
b.	aY
c.	bX
d.	aX

 

 

ANS:  D                    PTS:   1

 

50. The symbol for the standard error of estimate when predicting Y given X is ____.

a.	rX|Y
b.	sX|Y
c.	rY|X
d.	sY|X

 

 

ANS:  D                    PTS:   1

 

TRUE/FALSE

 

1. The total error in prediction equals S (Y – Y’).

 

ANS:  F                    PTS:   1                    MSC:  WWW

 

2. In general, the regression line for predicting X given Y is the same as the regression line for predicting Y given X.

 

ANS:  F                    PTS:   1

 

3. An imperfect relationship generally yields exact prediction.

 

ANS:  F                    PTS:   1

 

4. When the relationship is perfect, the regression of Y on X is the same as the regression of X on Y.

 

ANS:  T                    PTS:   1                    MSC:  WWW

 

5. Properly speaking, we should limit our predictions to the range of the base data.

 

ANS:  T                    PTS:   1

 

6. The least squares regression line insures the maximum number of direct hits.

 

ANS:  F                    PTS:   1                    MSC:  WWW

 

7. To do linear regression, there must be paired scores on two variables.

 

ANS:  T                    PTS:   1

 

8. If the standard deviations of the X and Y distributions are equal, then r = b_Y.

 

ANS:  T                    PTS:   1

 

9. If s_X = s_Y then b_X = b_Y.

 

ANS:  T                    PTS:   1                    MSC:  WWW

 

10. The higher the r value, the lower the standard error of estimate.

 

ANS:  T                    PTS:   1                    MSC:  WWW

 

11. Multiple regression uses more than one predictor variable.

 

ANS:  T                    PTS:   1

 

12. Multiple regression always results in greater prediction accuracy than simple regression.

 

ANS:  F                    PTS:   1

 

13. If the correlation between two variables is 1.00, the standard error of estimate equals 0.

 

ANS:  T                    PTS:   1

 

14. Pearson r is the slope of the least squares regression line when the scores are plotted as z scores.

 

ANS:  T                    PTS:   1

 

15. When there are two predictor variables, R² is the simple sum of r² for the relationship of the first predictor variable and Y and r² for the relationship of the second predictor variable and Y.

 

ANS:  F                    PTS:   1

 

DEFINITIONS

 

1. Define Homoscedasticity.

 

ANS:

Answer not provided.

 

PTS:   1

 

2. Define least-squares regression line.

 

ANS:

Answer not provided.

 

PTS:   1                    MSC:  WWW

 

3. Define multiple coefficient of determination.

 

ANS:

Answer not provided.

 

PTS:   1

 

4. Define multiple correlation.

 

ANS:

Answer not provided.

 

PTS:   1

 

5. Define regression.

 

ANS:

Answer not provided.

 

PTS:   1

 

6. Define regression constant.

 

ANS:

Answer not provided.

 

PTS:   1

 

7. Define regression line.

 

ANS:

Answer not provided.

 

PTS:   1

 

8. Define regression of X on Y.

 

ANS:

Answer not provided.

 

PTS:   1                    MSC:  WWW

 

9. Define regression of Y on X.

 

ANS:

Answer not provided.

 

PTS:   1

 

10. Define standard error of estimate.

 

ANS:

Answer not provided.

 

PTS:   1

 

SHORT ANSWER

 

1. Why is it important to know the standard error of estimate for a set of paired scores?

 

ANS:

Answer not provided.

 

PTS:   1

 

2. Why does the least squares regression line minimize S (Y – Y’)², rather than S (Y – Y’)?

 

ANS:

Answer not provided.

 

PTS:   1                    MSC:  WWW

 

3. Is it true that, generally, the regression lines for predicting Y given X and X given Y, are not the same? Explain.

 

ANS:

Answer not provided.

 

PTS:   1

 

4. The least squares regression line is the prediction line that results in the most direct “hits.” Is this true? Explain.

 

ANS:

Answer not provided.

 

PTS:   1

 

5. In what situation would the regression line for predicting Y given X be the same as the line predicting X given Y? Explain.

 

ANS:

Answer not provided.

 

PTS:   1

 

6. In multiple regression, will use of a second predictor variable always increase the accuracy of prediction? Explain.

 

ANS:

Answer not provided.

 

PTS:   1                    MSC:  WWW

 

7. If there is no relationship between the X and Y variables and we desire to predict Y given X using a least-squares criterion, it is best to predict  for every Y score. Is this correct? If so, explain why. (Hint: one of the properties of the mean might be helpful here)

 

ANS:

Answer not provided.

 

PTS:   1                    MSC:  WWW

 

8. A friend that thinks a lot about statistics asserts that, “the closer the points in the scatter plot are to the least-squares regression line, the higher the correlation.” Is your friend correct? Discuss.

 

ANS:

Answer not provided.

 

PTS:   1