ch.14. (statistics)

30. The F-ratio evaluating the significance of a linear regression equation based on n = 10 pairs of X and Y scores has df = 1, 9.

f

1. A negative correlation means that decreases in the X variable tend to be accompanied by decreases in the Y variable.

f

20. The line defined by the equation Y = -3X + 6 slopes up to the right.

f

21. The line produced by the equation Y = 4X - 5 crosses the vertical axis at Y = 5.

f

4. If you measured hearing acuity and age for a group of people who are 50 to 90 years old, you should obtain a positive correlation between the two variables.

f

9. A set of X and Y scores has a Pearson correlation of r = -0.60. For these data, 60% of the variability in the Y scores can be predicted from the relationship with X.

f

13. Assuming that other factors are constant, a correlation of r = -0.95 will result in more accurate predictions than a correlation of r = +0.70.

t

14. If the Pearson correlation for a set of scores is equal to +1.00, then the Spearman correlation for the same scores would also be equal to +1.00.

t

17. The sign of the correlation (+/-) is generally meaningless for the point-biserial correlation and the phi-coefficient.

t

3. A Pearson correlation of r = -0.90 indicates that the data points are clustered close to a line that slopes down to the right.

t

5. The value obtained for the sum of products, SP, determines the sign (+/-) for the Pearson correlation.

t

1. What is indicated by a positive value for a correlation? a. Increases in X tend to be accompanied by increases in Y b. Increases in X tend to be accompanied by decreases in Y c. A much stronger relationship than if the correlation were negative d. A much weaker relationship than if the correlation were negative

a

47. A linear regression equation is computed for a sample of n = 13 pairs of X and Y scores. For the analysis of regression testing the significance of the equation, what are the df values for the F-ratio? a. 1, 11 c. 2, 10 b. 1, 12 d. 2, 11

a

48. For linear regression calculated for a sample of n = 20 pairs of X and Y values, what is the value for degrees of freedom for the predicted portion of the Y-score variance, MSregression? a. 1 c. 19 b. 2 d. 18

a

15. A set of n = 15 pairs of scores (X and Y values) has SSX = 4, SSY = 25, and SP = 6. What is the Pearson correlation for these data? a. 6/100 c. 6/(100/15) b. 6/10 d. 6/(100-15))

b

16. Which of the following best describes the Pearson correlation for these data? a. Positive b. Negative c. Zero d. Cannot be determined X Y 2 5 5 1 3 4 4 2

b

17. A set of n = 5 pairs of X and Y values has SSX = 16, SSY = 4 and SP = 2. For these data, what is the Pearson correlation? a. r = 2/64 c. r = Ö2/8 b. r = 2/8 d. r = 64/64

b

22. A researcher obtains a Pearson correlation of r = 0.60 for a sample of n = 6 pairs of X and Y scores. If the researcher tests the significance of the correlation, what value will be obtained for the t statistic? a. 0.6/0.16 = 3.75 c. 0/6/0.8 = 0.77 b. 0.6/0.4 = 1.50 d. 0.6/1.0 = 0.6

b

29. The effect size for the data from an independent-measures t test can be measured by r2, which is the percentage of variance accounted for. Which of the following also produces the value for r2? a. Squaring the Spearman correlation for the same data b. Squaring the point-biserial correlation for the same data c. Squaring the Pearson correlation for the same data d. None of the other options will produce r2.

b

31. For a group of graduating college seniors, a researcher records each student's rank in his/her high school graduating class and the student's rank in the college graduating class. Which correlation should be used to measure the relationship between these two variables? a. Pearson correlation c. Point-biserial correlation b. Spearman correlation d. Phi-coefficient

b

32. For the linear equation Y = 2X + 4, if X increases by 1 point, how much will Y increase? a. 1 points c. 3 points b. 2 points d. 4 points

b

9. A researcher records the age and price for a group of used Hondas. What kind of correlation is likely to be obtained for these two variables? a. A positive correlation c. A correlation near zero b. A negative correlation d. A correlation near one

b

11. A set of n = 10 pairs of scores has ΣX = 20, ΣY = 30, and ΣXY = 74. What is the value of SP for these data? a. 74 c. 14 b. 24 d. -14

c

28. Under what circumstances is the phi-coefficient used? a. When one variable consists of ranks and the other is regular, numerical scores b. When both variables consists of ranks c. When both X and Y are dichotomous variables d. When one variable is dichotomous and the other is regular, numerical scores

c

3. The scatter plot for a set of X and Y values shows the data points clustered in a nearly perfect circle. For these data, what is the most likely value for the Pearson correlation? a. A positive correlation near 0 c. Either positive or negative near 0 b. A negative correlation near 0 d. A value near +1.00 or -100

c

1. Compute the Pearson correlation for the following data. X Y 2 3 3 1 6 5 4 4 5 2

ANS: SSX = 10, SSY = 10, SP = 5, r = 0.500

12. A set of n = 5 pairs of X and Y scores has ΣX = 15, ΣY = 5, and ΣXY = 10. For these data, what is the value of SP? a. -5 c. 10 b. 5 d. 25

a

19. A set of n = 15 pairs of scores (X and Y values) produces a correlation of r = 0.40. If each of the X values is multiplied by 2 and the correlation is computed for the new scores, what value will be obtained for the new correlation? a. r = 0.20 b. r = 0.40 c. r = 0.80 d. Cannot be determined without knowing all the X and Y scores

b

20. For a two-tailed hypothesis test evaluating a Pearson correlation, what is stated by the null hypothesis? a. There is a non-zero correlation for the general population. b. The population correlation is zero. c. There is a non-zero correlation for the sample. d. The sample correlation is zero.

b

13. What is the value of SP for the following set of data? a. 5 X Y b. -5 1 4 c. 15 2 4 d. -15 9 1

d

36. A set of n = 15 pairs of X and Y scores has SSX = 10, SSY = 40, and SP = 30. What is the slope for the regression equation for predicting Y from X? a. 10/30 c. 40/10 b. 10/40 d. 30/10

d

38. For the regression equation Y = 2X - 3, if the mean for X is MX = 5, what is the mean for Y? a. 2 c. 5 b. 4 d. 7

d

18. The phi-coefficient is the correct correlation to use when both X and Y are dichotomous variables.

t

27. A set of X and Y scores has MX = 4, MY = 10, SSX = 10, and SP = 5. The regression equation for these scores is Y = 0.5X + 8.

t

14. What is the value of SP for the following set of data? a. -1 b. -5 c. 5 d. None of the other 3 choices is correct. X Y 4 3 1 2 1 5 2 6

a

21. The Pearson correlation is calculated for a sample of n = 20 individuals. If a hypothesis test is used to determine whether the correlation is significant, what df value would be used for the t statistic? a. 18 c. 20 b. 19 d. 21

a

10. A researcher finds a significant correlation between the amount of time spent watching television and blood pressure for a sample of 40-year-old men. This means that watching more television causes high blood pressure.

f

2. If the value of the Pearson correlation is r = +1.00 or -1.00, then all data points in a scatter plot fit perfectly on a straight line.

t

2. A sample of n = 25 pairs of scores (X and Y values) produces a correlation of r = -0.40. Are these sample data sufficient to conclude that there is a significant non-zero correlation between X and Y in the population? Use a two-tailed test at the .05 level of significance.

ANS: The standard error = 0.19 and t(23) = 2.09. Reject the null hypothesis

28. For a regression equation with a slope of b = 3, if MX = 3 and MY = 10, then the Y-intercept for the equation is 1.

t

29. For linear regression, the value of SSresidual can be computed directly by Σ(Y -Ŷ)2.

t

8. One or two extreme data points can have a dramatic effect on the size of a correlation.

t

8. A researcher measures driving distance from college and weekly cost of gas for a group of commuting college students. What kind of correlation is likely to be obtained for these two variables? a. A positive correlation c. A correlation near zero b. A negative correlation d. A correlation near one

a

40. A set of X and Y scores has MX = 4, SSX = 10, MY = 5, SSY = 40, and SP = 20. What is the regression equation for predicting Y from X? a. Ŷ = 0.25X + 4 c. Ŷ = 0.5X + 3 b. Ŷ = 4X - 9 d. Ŷ = 2X - 3

d

45. The distance between the Y value in the data and the predicted Y value from the regression equation is known as the residual. What is the value for the sum of the squared residuals? a. SSresidual = r2(SSX) c. SSresidual = r2(SSY) b. SSresidual = (1 - r2)(SSX) d. SSresidual = (1 - r2)(SSY)

d

49. The following X and Y scores produce SSX = 2 and SP = 8. What is regression equation for predicting Y? X Y 1 2 2 3 3 10 a. Y = 0.25X + 4.5 c. Y = 4X + 3 b. Y = 0.25X - 4.5 d. Y = 4X - 3

d

6. A researcher obtains SSX = 20, SSY = 5, and SP = 7 for a set of n = 25 pairs of scores. The Pearson correlation for these scores is r = 7/10 = 0.70.

t

5. Suppose that a sample of n = 12 pairs of X and Y scores has SSY = 90 and a Pearson correlation of r = +0.40. a. What proportion of the variance for the Y scores is predicted by the regression equation? b. Does the regression equation predict a significant portion of the variance? Test with α = .05.

ANS: a. r2 = 0.16 or 16% b. F = 14.4/7.56 = 1.90 With df = 1, 10 the regression equation is not significant

34. For the regression equation Ŷ = -2X + 6, what can be determined about the correlation between X and Y? a. The correlation definitely will be positive. b. The correlation definitely will be negative. c. The correlation will be relatively large and positive d. The correlation will be relatively large and negative.

B

10. What is indicated by a Pearson correlation of r = +1.00 between X and Y? a. Each time X increases, there is a perfectly predictable increase in Y b. Every change in X causes a change in Y c. Every increase in X causes an increase in Y d. All of the other 3 choices occur with a correlation of +1.00.

a

24. If the following seven scores are ranked from smallest (#1) to largest, what rank should be assigned to a score of X = 6? Scores: 1, 1, 3, 6, 6, 6, 9 a. 3 c. 5 b. 4 d. 6

c

30. Which correlation should be used to measure the relationship between gender and grade point average for a group of college students? a. Pearson correlation c. Point-biserial correlation b. Spearman correlation d. Phi-coefficient

c

33. For the linear equation Y = 2X - 3, which of the following points will not be on the line? a. 0, -3 c. 3, 0 b. 2, 1 d. 4, 5

c

35. The regression equation is determined by finding the minimum value for which of the following? a. S(X - Y)2 c. S(Y - Ŷ)2 b. S(Y - Ŷ) d. r2S(Y - Ŷ)2

c

39. For the regression equation Y = X - 2, if the mean for Y is MY = 6, what is the mean for X? a. 4 c. 8 b. 6 d. 10

c

11. For a two-tailed hypothesis test evaluating the significance of a correlation, the null hypothesis states that the sample correlation is zero.

f

24. If other factors are held constant and the Pearson correlation between X and Y is r = 0.80, then the regression equation will produce more accurate predictions than would be obtained if r = 0.60.

t

25. If the Pearson correlation between X and Y is r = 0.60, then the regression equation predicts 36% of the variance in the Y scores.

t

26. A set of X and Y scores has SSX = 10, SSY = 36, and SP = 20. The regression equation for these scores will have a slope constant of 2.

t

4. For the data below: a. Find the regression equation for predicting Y from X. b. Calculate the predicted Y for each X value, find each residual (Y - Ŷ), square each residual and add the squared values to obtain SSresidual. X Y 5 10 3 6 6 7 4 3 2 4

ANS: a. Ŷ = X + 2 b. X Y Ŷ (Y- Ŷ) (Y- Ŷ)2 5 10 7 3 9 3 6 5 1 1 6 7 8 -1 1 4 3 6 -3 9 2 4 4 0 0 SSresidual = 20

3. A psychologist would like to evaluate the relationship between verbal skills as measured by the Scholastic Achievement Test (SAT) and performance on an anagram task. (Anagrams are words with the letters scrambled. The task is to unscramble the letters and identify the word.) Each subject is given a set of 10 anagrams, and the psychologist records how much time is needed to solve all 10. The anagram times and each subject's SAT score are as follows. (Note that two subjects failed to complete all 10 anagrams.) Use a Spearman correlation to measure and describe the relationship between SAT and anagram performance.

Anagram SAT Subject Time Score 1 104 480 2 195 410 3 50 590 4 93 510 5 failed 420 6 170 460 7 failed 380 8 67 570 9 45 640 10 58 600 ANS: After ranking the data for SAT and anagram times, the value of the Spearman correlation is rS= -0.961.

43. Assuming that SSY is constant, which of the following correlations would have the largest SSresidual? a. r = -0.10 b. r = +0.40 c. r = -0.70 d. There is no relationship between the correlation and SSresidual.

a

44. A linear regression equation has b = 3 and a = - 6. What is the predicted value of Y for X = 4? a. Ŷ = 6 b. Ŷ = -21 c. Ŷ = -2 d. Cannot be determined without additional information

a

50. An analysis of regression is used to test the significance of a linear regression equation based on a sample of n = 20 individuals. What are the df values for the F-ratio? a. 1, 18 c. 2, 18 b. 1, 19 d. 2, 19

a

6. The results from a research study indicate that adolescents who watch more violent content on television also tend to engage in more violent behavior than their peers. The correlation between amount of TV violence content and amount of violent behavior is an example of _______. a. a positive correlation c. a correlation near zero b. a negative correlation d. a correlation near one

a

23. As the sample size gets larger, what happens to the size of the correlation that is needed for significance? a. It also gets larger. b. It gets smaller. c. It stays constant. d. There is no consistent relationship between sample size and the critical value for a significant correlation.

b

41. For the regression equation, Ŷ = -2X + 6, if the X value is above the mean (positive deviation), what can be determined about the predicted Y value? a. The predicted Y value will be above the mean for the Y scores. b. The predicted Y value will be below the mean for the Y scores. c. The predicted Y value will be equal to the mean for the Y scores. d. It is impossible to determine where the predicted Y value will be.

b

7. A researcher measures IQ and weight for a group of college students. What kind of correlation is likely to be obtained for these two variables? a. A positive correlation c. A correlation near zero b. A negative correlation d. A correlation near one

c

46. A set of n = 25 pairs of scores (X and Y values) has a Pearson correlation of r = 0.80. How much of the variance for the Y scores is predicted by its relationship with X? a. 0.36 or 36% c. 0.80 or 80% b. 0.20 or 20% d. 0.64 or 64%

d

15. If the Spearman correlation for a set of scores is equal to +1.00, then the Pearson correlation for the same scores would also be equal to +1.00.

f

16. The phi-coefficient is used to measure relationships for data that would also be appropriate for an independent-measures t test.

f

19. If people are classified by age (over 30/under 30) and by political affiliation (Democrat/Republican), then the point-biserial correlation would be the proper technique to measure the relationship between the two variables.

f

2. What would the scatter plot show for data that produce a Pearson correlation of r = +0.88? a. Points clustered close to a line that slopes up to the right b. Points clustered close to a line that slopes down to the right c. Points widely scattered around a line that slopes up to the right d. Points widely scattered around a line that slopes down to the right

a

26. The Pearson and the Spearman correlations are both computed for the same set of data. If the Spearman correlation is rS = +1.00, what can you conclude about the Pearson correlation? a. It will be positive. b. It will have a value of 1.00. c. It will be positive and have a value of 1.00. d. There is no predictable relationship between the Pearson and the Spearman correlations.

a

27. What correlation is obtained when the Pearson correlation is computed for data that have been converted to ranks? a. The Spearman correlation c. The phi coefficient b. The point-biserial correlation d. It is still called a Pearson correlation.

a

37. A set of X and Y scores has a regression equation with a slope of b = 4. If the mean for the X values is MX = 2 and the mean for the Y values is MY = 6, what is the Y-intercept value for the regression equation? a. -2 c. 4 b. -22 d. -4

a

4. Which of the following Pearson correlations shows the greatest strength or consistency of relationship? a. -0.90 c. +0.85 b. +0.74 d. -0.33

a

42. If there is a positive correlation between X and Y, then the regression equation Y = bX + a will have _____. a. b > 0 c. a > 0 b. b < 0 d. a < 0

a

18. Suppose the correlation between height and weight for adults is +0.40. What proportion (or percent) of the variability in weight can be explained by the relationship with height? a. 40% c. 16% b. 60% d. 84%

c

25. If the following nine scores are ranked from smallest (#1) to largest, what rank should be assigned to a score of X = 1? Scores: 1, 1, 1, 1, 3, 6, 6, 6, 9 a. 1 c. 2.5 b. 2 d. 4

c

5. For which of the following Pearson correlations would the data points be clustered most closely around a straight line? a. -0.10 b. +0.40 c. -0.70 d. There is no relationship between the correlation and how close the points are to a straight line.

c

12. In a test for significance of a Pearson correlation for a sample of n = 30 individuals, you determine the critical value by using df = 29.

f

22. It is possible for none of the actual (observed) data points to be located on the regression line described by the regression equation.

t

23. For a regression equation with a positive slope, if the X value is above the mean for the X scores, then the predicted Y value will be above the mean for the Y scores.

t

7. Suppose that there is a correlation of r = 0.41 between the amount of time that each student reports studying for an exam and the student's grade on the exam. This correlation would mean that there is a tendency for people who study more to get better grades.

t