____ 1. The closer the points on a scatter diagram fall to the regression line, the _________ between the scores.a. higher the correlationb. lower the correlationc. correlation doesn't changed. need m

____ 1. The closer the points on a scatter diagram fall to the regression line, the _________ between the scores.

a. higher the correlation

b. lower the correlation

c. correlation doesn't change

d. need more information

___ 2. The strongest  correlation shown below is _________.

a. 0.75

b. -0.33

c. -0.25

d. 0.15

____ 3. When deciding which measure of correlation to employ with a specific set of data, you should consider _________.

a. whether the relationship is linear or nonlinear

b. type of scale of measurement for each variable

c. a and b

d. none of the above

____ 4. Which of the following statements concerning Pearson r is not true?

a. r = 0.00 represents the absence of a relationship.

b. The relationship between the two variables must be nonlinear.

c. r = 0.76 has the same predictive power as r = -0.76.

d. r = 1.00 represents a perfect relationship.

e. All of the above are true statements.

____ 5. Spearman’s   Rho is used _________.

a. when both variables are dichotomous

b. when both variables are of interval or ratio scaling

c. when one or both variables are only of ordinal scaling

d. when the data is nonlinear

____ 6.  When a correlation exists, lowering the range of either of the variables will _________.

a. raise the correlation

b. lower the correlation

c. not change the correlation

d. produce a causal relationship

____ 7. If two variables are ratio scaled and the relationship is linear, what type of correlation coefficient is most appropriate?

a. Pearson

b. Spearman

c. eta

d. phi

____ 8. You have conducted a brilliant study which correlates IQ score with income and find a value of r = 0.75. At the end of the study you find out all the IQ scores were scored 10 points too high. What will the value of r be with the corrected data?

a. r will be increased

b. r will be decreased

c. r will remain the same

d. cannot be determined

____ 9. If 49% of the total variability of Y is accounted for by X, what is the value of r?

a. 0.49

b. 0.51

c. 0.70

d. 0.30

____ 10. Satisfying the assumption of homoscedasticity allows you to  _________.

a. Interpret the standard error of estimate

b. Calculate multiple R

c. Calculate a standardized regression coefficient

d. Decide who has been naughty or nice

Problem 1

(25 points) We want to examine what factors account for differences in salary in a university department by characteristics of the faculty member. The number of years since each faculty member received his Ph.D. (X1), the number of publications (X2), gender of the professor (1=F, 0=M), and number of citations in the scientific literature (X4).

CASE TIME PUBS CITS SALARY FEMALE

1 3 18 50 51876 1

2 6 3 26 54511 1

3 3 2 50 53425 1

4 8 17 34 61863 0

5 9 11 41 52926 1

6 6 6 37 47034 0

7 16 38 48 66432 0

8 10 48 56 61100 0

9 2 9 19 41934 0

10 5 22 29 47454 0

11 5 30 28 49832 1

12 6 21 31 47047 0

13 7 10 25 39115 1

14 11 27 40 59677 0

15 18 37 61 61458 0

16 6 8 32 54528 0

17 9 13 36 60327 1

18 7 6 69 56600 0

19 7 12 47 52542 1

20 3 29 29 50455 1

21 7 29 35 51647 1

22 5 7 35 62895 0

23 7 6 18 53740 0

24 13 69 90 75822 0

25 5 11 60 56596 0

26 8 9 30 55682 1

27 8 20 27 62091 1

28 7 41 35 42162 1

29 2 3 14 52646 1

30 13 27 56 74199 0

31 5 14 50 50729 0

32 3 23 25 70011 0

33 1 1 35 37939 0

34 3 7 1 39652 0

35 9 19 69 68987 0

36 3 11 69 55579 0

37 9 31 27 54671 0

38 3 9 50 57704 0

39 4 12 32 44045 1

40 10 32 33 51122 0

41 1 26 45 47082 0

42 11 12 54 60009 0

43 5 9 47 58632 0

44 1 6 29 38340 0

45 21 39 69 71219 0

46 7 16 47 53712 1

47 5 12 43 54782 1

48 16 50 55 83503 0

49 5 18 33 47212 0

50 4 16 28 52840 1

51 5 5 42 53650 0

52 11 20 24 50931 0

53 16 50 31 66784 1

54 3 6 27 49751 1

55 4 19 83 74343 1

56 4 11 49 57710 1

57 5 13 14 52676 0

58 6 3 36 41195 1

59 4 8 34 45662 1

60 8 11 70 47606 1

61 3 25 27 44301 1

62 4 4 28 58582 1

1. What percent of the total variance is accounted for by all four predictor variables after correcting for attenuation._____

1. Insert a number that reflects the error in prediction? _________

1. Insert the complete regression line below.

1. For each unit change  in Number of publications how much does salary change and in what direction?__ ___

1. For each unit change  in Number of citations how much does salary change and in what direction?___ ____

1. For each unit change  in Years since the PhD how much does salary change and in what direction?___ ____

1. For each unit change  in Gender how much does salary change and in what direction?___ ____

1. For each standard deviation change   in Number of publications how much does salary change and in what direction?____ ___

1. For each standard deviation change   Number of citations how much does salary change and in what direction?______

1. For each standard deviation change    in Years since the PhD how much does salary change and in what direction?_______

1. For each standard deviation change   in Gender how much does salary change and in what direction?______

1. What percent of the variance in salary is uniquely accounted for by Number of publications?______

1. What percent of the variance in salary is uniquely accounted for by Number of Citations?_______

1. What percent of the variance in salary is uniquely accounted for by Years since the PHd? _______

1. What percent of the variance in salary is uniquely accounted for by Sex?____

1. What number is in the denominator of the t-test that is testing the significance of the variance uniquely accounted for by Number of publications?____

1. What number is in the denominator of the t-test that is testing the significance of the variance uniquely accounted for by Number of Citations?____

1. What number is in the denominator of the t-test that is testing the significance of the variance uniquely accounted for  by Years since the PHd?____

1. What number is in the denominator of the t-test that is testing the significance of the variance uniquely accounted for by Sex?__

__

1. Which predictor variable has the strongest relationship with salary and how do you know this?

1. Is there a problem with multicollinearity?How do you know.

Problem 2

(15 points) The state of Vermont is divided into 10 health planning districts- they correspond roughly to counties. The following data represent the percentage of live births of babies weighing under 2500 grams (Y), total high-risk fertility rate for females 17 years of age or younger (X1), total high-risk fertility rate for females younger than 17 years of age or older than 35 years of age (X2), percentage of mothers with fewer than 12 years of education (X3), percentage of births to unmarried mothers (X4), and percentage of mothers not seeking medical care until the third trimester (X5).

Calculate a multiple regression using X1 to X5 as predictors and Y as the dependent variable. Compute a simultaneous multiple regression on the data posted below.

Y X1 X2 X3 X4 X5

6.10 22.80 43.00 23.80 9.20 6.00

7.10 28.70 55.30 24.80 12.00 10.00

7.40 29.70 48.50 23.90 10.40 5.00

6.30 18.30 38.80 16.60 9.80 4.00

6.50 21.10 46.20 19.60 9.80 5.00

5.70 21.20 39.90 21.40 7.70 6.00

6.60 22.20 43.10 20.70 10.90 7.00

8.10 22.30 48.50 21.80 9.50 5.00

6.30 21.80 40.00 20.60 11.60 7.00

6.90 31.20 56.70 25.20 11.60 9.00

1).Use the output to answer the following questions.

1. (1) With all five variables in the model what percent of the variance is accounted for aftere correcting for inflation?

1. (1) For model 1 with all 5 predictor variables in the equation, what is the standard error of estimate?

1. (2) From the printout what numbers make the t ratio for testing the significance of X4?  

1. (2) With all five variables in the model, for each unit change  in X1 what happens to Y and by how much.

1. (2) With all five variables in the model, for each standard deviation change in X3 how much of a standard deviation change in Y occurs and in what direction.

1. (2) What percent of the variance in Y is uniquely accounts for by X2

1. (1) What percent of the variance in Y is uniquely accounted for by X5 (that is accounted for by X5 after X1, X2, X3, X4 are accounted for).

1. (1) The null hypothesis that is tested when using regression coefficients is what?

1. (2) A correlation between predictor variables of .8 or above increases the chance of colinearity  problems. Which if any predictor variables are a risk for problems with collinearity?