Practice Multiple Choice Set 1 ­ Due FRIDAY, APRIL 16, 2004 ­ Time yourself:  Complete in under 67.5min

 

1.  As reported in a newspaper,  a study determined that for every 10 grams of saturated fat consumed per day, a womanıs risk of developing ovarian cancer rises 20%.  What is the meaning of the slope of the appropriate regression line?

 

A.  Taking 10 grams of fat results in a 20% increased risk of developing ovarian cancer.

 

B.  Consuming 0 grams of fat per day results in a zero increase in the risk of developing ovarian cancer.

 

C.  Consuming 50 grams of fat doubles the risk of developing ovarian cancer.

 

D.  Increase intake of fat causes higher rates of developing ovarian cancer.

 

E.  A womanıs risk of developing ovarian cancer  rises 2% for every gram of fat consumed per day. 

 

Questions 2 and 3 are based on the following:  Jay Bennett  calculated the regression line for average1991 SAT scores versus number of dollars spent per student  in 1991 for New Jersey school districts and obtained a slope of 0.0227 and a y-intercept of 707.

 

2.  What average SAT result does this regression line predict for students in a district that spends $10,000 per student?

 

A.  467            B.  480            C.  730            D.  934            E.  More info is needed to make this calculation

 

3.  According to this analysis, how much should a district spend per student in order for its students to average 1000 on the SAT exam?

 

A.  $6,651       B.  $12,907     C.  $16,049     D.  $44,053     E.  More info is needed to make this calculation 

 

4.  Consider  the following three scatterplots:

             

 

Which has the greatest correlation coefficient?

 

A.  I                 B. II                 C.  III              D.  They are all the same.                    E.  Not enough info

 

 

5.  Suppose the correlation is negative.  Given two points from the scatterplot, which of the following is possible?

 

            I.  The first point has a larger x-value and a smaller y-value than the second point.

           

            II.  The first point has a larger x-value and a larger y-value than the second point.

 

            III.  The first point has a smaller x-value and a larger y-value than the second point.

 

 

A.  I only         B.  II only        C.  III only      D.  I and III     E.  I, II, and III

 

6.     Which of the following would you expect to be true about the correlation between distances and tolls on the New York State Thruway?

 

A.  Strong and positive            B.  Weak and positive             C.  Strong and negative

 

D.  Weak and negative E.  Zero

 

7.     Suppose the regression line for a set of data, y = 3x + b, passes through the point (2, 5).  What must the average of the y values be?

 

A.                  B.                        C.                        D.               E.

 

8.     Suppose a study finds that the correlation coefficient relating family income to SAT scores is r = 1.  Which of the following are proper conclusions?

 

I.               Poverty causes low SAT scores

II.             Wealth causes high SAT scores

III.           There is a very strong association between family income and SAT scores

 

A.  I only         B.  II only        C.  III only      D.  I and II      E.  I, II, and III

 

9.     A study of department head ratings and student ratings of the performance of high school stat teachers reports a correlation of r = 1.15 between the two ratings.  From this information we may conclude that:

 

A.    Department heads and students tend to agree on who is a good teacher

B.    Department heads and students tend to disagree on who is a good teacher

C.    There is little relationship between department head and student ratings of teachers

D.   There is a strong association between department head and student ratings of teacher, but it would be incorrect to infer causation

E.    A mistake in arithmetic has been made

 

10.  Which of the following statements about correlation are true?

 

I.               A correlation of 0.2 means 20% of the points are highly correlated

II.             The square of the correlation measures the proportion of the y-variance that is predictable from a knowledge of x

III.           Perfect correlation, that is, when the points lie exactly on a straight line, results in a correlation of r = 0.

 

A.  I only         B.  II only        C.  III only      D.  None of these statements are true 

F.    None of the above gives a complete set of true responses

 

11.  Which of the following statements about the correlation are true?

 

I.               It is not affected by changes in the measurement units of the variables

II.             It is not affected by which variable is called x and which is called y

III.           It is not affected by extreme values

 

A.  I and II       B.  I and III     C.  II and III    D.  I, II,.and III            E.  None of the Above

 

12.  With regard to regression, which of the following statements about outliers are true?

 

I.               Outliers in the y-direction have large residuals

II.             A point may not be an outlier even though its x-value is an outlier in the x-variable and its y-value is an outlier in the y-variable

III.           Removal of an outlier sharply affected the regression line

 

A.  I and II       B.  I and III     C.  II and III    D.  I, II, and III            E.  None of the Above

 

13.  Which of the following statements about influential scores are true?

 

I.               Influential scores have large residuals

II.             Removal of an influential score sharply affects the regression line

III.           An x-value that is an outlier in the x-variable is more indicative that a point is influential than a y-value that is an outlier in the y-variable

 

A.  I and II       B.  I and III     C.  II and III    D.  I, II, and III            E.  None of the Above

 

14.  Which of the following are true statements about residuals?

 

I.               The mean of the residuals is always zero

II.             The regression line for a residual plot is a horizontal line

III.           A definite pattern in a residual plot is an indication that a nonlinear model will show a better fit tot he data than the straight line regression line

 

  A. I and II      B.  I and III     C.  II and III    D.  I, II, and III            E.  None of the Above

 

15.  Data are obtained for a group of college freshmen examining their SAT scores from their senior year of high school and their GPAs during their first year of college. The resulting regression equation is:

 

y = 0.00161x + 1.35 with r = 0.632

 

What percentage of the variation in GPAs can be explained by looking at SAT scores?

 

A.  0.161%      B.  16.1%        C.  39.9%        D.  63.2%        E.  Not enough information

 

Questions 16 and 17 are based on the following:  The heart disease death rates per 100,000 people in the US for certain years, as reported by the National Center for Health Statistics, were:

Year:

1950

1960

1970

1975

1980

Death Rate:

307.6

286.2

253.6

217.8

202.0

 

16.  Which one of the following is a correct interpretation of the slope of the least squares regression line for the above data?

 

A.    The heart disease rate per 100,000 people has been dropping by about 3.627 per year

 

B.    The baseline heart disease rate is 7386.87

 

C.    The regression line explains 96.28% of the variation in heart disease death rates over the years.

 

D.   The regression line explains 98.12% of the variation in heart disease death raters over the years.

 

E.    Heart disease will be cured in the year 2036.

 

17.  Based on the regression line, what is the predicted death rate for the year 1983?

 

A.  145.8 per 100,000 people              B.  192.5 per 100,000 people

 

C.  196.8 per 100,000 people              D.  198.5 per 100,000 people

 

F.    None of the above

 

18.  Consider the following scatterplot of midterm and final exam scores for a class of 15 students.

 

Which of the following are true statements?

 

I.               The same number of students scored 100 on the midterm exam as scored 100 on the final exam.

II.             Students who scored higher on the midterm exam tended to score higher on the final exam

III.           The scatterplot shows a moderate negative correlation between midterm and final exam scores

 

A.  I and II       B.  I and III     C.  II and III    D.  I, II, and III            E.  None of the above

 

19.  If every woman married a man who was exactly 2 inches taller than she, what would the correlation between the heights of married men and women be? 

 

A.  Somewhat negative B.  0                C.  Somewhat  positive            D.  Nearly 1                E. 1

 

20.  Which of the following statements about correlation are true?

 

I.               A correlation and the slope of the regression line have the same sign.

II.             A correlation of -0.35 and a correlation of 0.35 show the same degree of clustering around the regression line.

III.           A correlation of 0.75 indicates a relationship that is 3 times as linear as one for which the correlation is only 0.25.

 

21.  Suppose the correlation between two variables is r = 0.23. What will the new correlation be if 0.14 is added to all values of the x-variable and every value of the y-variable is doubled and the two values are interchanged?

 

A. 0.23            B.  0.37                       C.  0.74                       D.  -0.23          E.  -0.74

 

22.  As reported in the AMA, for a study of ten nonagenarians (subjects were age 90 ħ 1), the following tabulation shows a measure of strength (heaviest weight subject could lift using knee extensors) versus a measure of functional mobility (time taken to walk 6 meters).  Note that functional mobility is greater with lower walk times. 

 

    

Strength (kg)

7.5

6

11.5

10.5

9.5

18

4

12

9

3

Walk time (s)

18

46

8

25

25

7

22

12

10

48

 

What is the sign of the slope of the regression line and what does it signify?

 

A.    The sign is positive, signify a direct cause and effect relationship between strength and functional mobility.

 

B.    The sign is positive, signifying the greater the strength, the greater the functional mobility

 

C.    The sign is negative, signifying the relationship between strength and functional mobility is weak

 

D.   The sign is negative, signifying that the greater the strength, the greater the functional mobility.

 

E.    The slope is close to zero, signifying that the relationship between strength and functional mobility is weak. 

 

23.  Suppose the correlation between two variables is -0.57.  If each of the y-scores is multiplied by -1, which of the following is true about the new scatterplot?

 

A.    It slopes up to the right and the correlation is -0.57.

 

B.    It slopes up to the right and the correlation is 0.57.

 

C.    It slopes down to the right and the correlation is -0.57.

 

D.   It slopes down to the right and the correlation is 0.57.

 

E.    None of the above.

 

24.  A study of 100 elementary school children showed a strong positive correlation between weight and reading speed.  Which of the following are proper conclusions?

 

I.               Heavier elementary school children tend to have higher reading speeds.

II.             Among elementary school children, faster readers tend to be heavier

III.           If you want to improve the reading speed of elementary school children, you should feed them more.

IV.           Eric Cartman isn't fat, he's just big boned.

 

A.  I only         B.  I and II       C.  I, II, and III D.  None of the above is a proper conclusion 

E.  None of the above gives the complete set of proper conclusions

 

25.  Consider the set of points {(2, 5), (3, 7), (4, 9), (5, 12), (10, n)}.  What should the value of n be so that the correlation between the x and y values is 1?

 

A. 21               B.  24              C.  25              D.  A value different from any of the above 

E.  No value for n can make the correlation 1.

 

26.  A study is conducted relating GPA to number of study hours per week and the correlation is found to be 0.5.  Which of the following are true statements?

 

I.               On the average, a 30% increase in study time per week results in a 15% increase in GPA.

II.             Fifty percent of a student's GPA can be explained by the number of study hours per week.

III.           Higher GPAs tend to be associated with higher numbers of study hours.

 

A.  I and II       B.  I and III     C.  II and III    D.  I, II, and III            E.  None of the above

 

27.  Consider the following three scatterplots:

                   

 

 

Which of the following is a true statement about the correlations for the three scatterplots?

 

A.  None are 0             B.  One is 0, one is negative, and one is positive

 

C.  One is 0, and the others are positive           D.  Two are 0 and the other is 1

 

F.    Two are 0 and the other is close to 1

 

28.  Consider the three points (2, 11), (3, 17), and (4, 29).  Given any straight line, we can calculate the sum of the squares of the three vertical distances from these points to the line.  What is the smallest possible value this sum can be?

 

A.  6                B.  9                C.  29              D.  57              E.  None of the above

 

29.  Suppose that the scatterplot of log X and log Y shows a strong positive correlation close to 1.  Which of the following is true?

 

I.               The variables X and Y also have a correlation close to 1

II.             A scatterplot of the variables X and Y shows a strong nonlinear pattern

III.           The residual plot of the variables X and Y shows a random pattern

 

A.  I only         B.  II only        C.  III only      D.  I and II      E.  I,II, and III

 

30.  Which of the following statements about correlation are true?

 

I.               When r = 0, there is no relationship between the variables

II.             When r = 0.5, 50% of the variables are closely related

III.           When r = 1, there is a perfect cause and effect relationship between the variables

 

A.  I only         B.  II only        C.  III only      D.  I, II, and III            E.  All the statements are false