Questions 26 through 30 refer to the following scenario.

Listed below are the ages of a sample of 24 couples taken from marriage licenses filed in Cumberland County, Pennsylvania in June and July of 1993.

Couple

1

2

3

4

5

6

7

8

Wife

22

32

50

25

33

27

45

47

Husband

25

25

51

25

38

30

60

54

Couple

9

10

11

12

13

14

15

16

Wife

30

44

23

39

24

22

16

73

Husband

31

54

23

34

25

23

19

71

Couple

17

18

19

20

21

22

23

24

Wife

27

36

24

60

26

23

28

36

Husband

26

31

26

62

29

31

29

35

The above data were used to produce the following two scatterplots.

40.Which scatterplot is the appropriate one if we are to regress husband’s age on wife’s age?

(a)Plot 1

(b)Plot 2

41.Give the least squares regression line for regressing husband’s age on wife’s age.

42.Interpret the value of the slope coefficient of the regression line in problem 35. Explain precisely what the value signifies about the relationship between husbands’ ages and wives’ ages.

43.Compute the residual for couple #17.

44.Calculate the correlation coefficient between P and M where P = 2(Husband’s age) and

M = (Wife’s age) – 5

Questions 45 through 48 refer to the following scenario.

Scatterplot #1 corresponds to a data set that produces a regression line of y = –0.5x+8 and correlation coefficient of r = –0.25. Using this information as a base, match the remaining scatterplots below (#2 through #4) to the correct description of its regression line and correlation coefficient. The scales on the axes of the scatterplots are the same.

Scatterplot #1

Scatterplot #2

Scatterplot #3

Scatterplot #4

Description I:Description II:Description III:

y = 2x – 2y = –2x + 15y = 5x – 6

r = 0.80r = –0.92r = 0.40

45.Scatterplot #2 corresponds to

(a)Description I

(b)Description II

(c)Description III

46.Scatterplot #3 corresponds to

(a)Description I

(b)Description II

(c)Description III

- Which of the following best describes point A in Scatterplot #2?

(a)Influential point

(b)Outlier with respect to the regression line

(c)Outlier with respect to the rest of the x-values

(d)Outlier with respect to the rest of the y-values

(e)Both (c) and (d)

48.Which of the following best describes point B in Scatterplot #3?

(a)Influential point

(b)Outlier with respect to the regression line

(c)Outlier with respect to the rest of the x-values

(d)Outlier with respect to the rest of the y-values

(e)Both (c) and (d)

Questions 49 through 53 refer to the following scenario.

(Source: Statistics for Research. Sirley Dowdy and Stanley Wearden. Wiley 1983. Page 211.)

A study of nursing activities is conducted in a 100-bed hospital in Kansas. The nursing activities staff remains constant throughout the study, but the patient load varies, so it is possible to observe how nurses allocate their duty time with different patient loads. One of the nursing activities observed and measured is patient care. A study is made of each hospital ward, and the data below represent the minutes per staff duty hour spent on patient care by the nurses in the surgery ward under varying patient loads.

Patient Load 2 3 4 6 7 8

Patient Care44.75371.7111.3129.4159.9

49.What sort of linear relationship between Patient Load and Patient Care seems most logical?

(a)positive

(b)negative

50.Write the equation of the least-squares regression line. Use patient load as the explanatory variable and staff time allocated to patient care as the response variable.

51.What are the units of measurement for the slope of the line calculated in problem 44?

52.Find the correlation coefficient between Patient Load and Patient care.

53.Predict the staff time allocated to patient care for a ward with a patient load of 5.