Question 518971: 1. Which of the following statements regarding the coefficient of correlation is true?
A) It ranges from 1.0 to +1.0 inclusive
B) It measures the strength of the relationship between two variables
C) A value of 0.00 indicates two variables are not related
D) All of the above
E) None of the above
2. What does a coefficient of correlation of 0.70 infer?
A) Almost no correlation because 0.70 is close to 1.0
B) 70% of the variation in one variable is explained by the other
C) Coefficient of determination is 0.49
D) Coefficient of nondetermination is 0.30
E) None of the above
3. If the correlation coefficient between two variables equals zero, what can be said of the variables X and Y?
A) Not related
B) Dependent on each other
C) Highly related
D) All of the above are correct
E) None of the above is correct
4. What can we conclude if the coefficient of determination is 0.94?
A) Strength of relationship is 0.94
B) Direction of relationship is positive
C) 94% of total variation in one variable is explained by variation in the other variable
D) All of the above are correct
E) None of the above is correct
5. Which value of r indicates a stronger correlation than 0.40?
A) 0.30
B) 0.50
C) +0.38
D) 0
E) None of the above
6. In the regression equation, what does the letter a represent?
A) Y intercept
B) Slope of the line
C) Any value of the independent variable that is selected
D) None of the above
7. In the regression equation, what does the letter b represent?
A) Y intercept
B) Slope of the line
C) Any value of the independent variable that is selected
D) Value of Y when X=0
E) None of the above
8. Suppose the least squares regression equation is Y' = 1202 + 1,133X. When X = 3, what does Y' equal?
A) 5,734
B) 8,000
C) 4,601
D) 4,050
E) None of the above
9. What is the general form of the regression equation?
A) Y' = ab
B) Y' = a + bX
C) Y' = a bX
D) Y' = abX
E) None of the above
10. Which of the following are true assumptions underlying linear regression: 1) for each value of X, there is a group of Y values which are normally distributed; 2) the means of these normal distributions of Y values all lie on the straight line of regression; and/or 3) the standard deviations of these normal distributions are equal?
A) Only (1) and (2)
B) Only (1) and (3)
C) Only (2) and (3)
D) All of them
E) None of them
11. Based on the regression equation, we can
A) predict the value of the dependent variable given a value of the independent variable.
B) predict the value of the independent variable given a value of the dependent variable.
C) measure the association between two variables.
D) all of the above.
E) none of the above.
12. What is the chart called when the paired data (the dependent and independent variables) are plotted?
A) Scatter diagram
B) Bar
C) Pie
D) Linear regression
E) None of the above
13. In the equation Y' = a + bX, what is Y'?
A) Slope of the line
B) Y intercept
C) Predicted value of Y, given a specific X value
D) Value of Y when X=0
E) None of the above
14. Assume the least squares equation is Y' = 10 + 20X. What does the value of 10 in the equation indicate?
A) Y intercept
B) For each unit increased in Y, X increases by 10
C) For each unit increased in X, Y increases by 10
D) None of the above
15. In the least squares equation, Y' = 10 + 20X the value of 20 indicates
A) the Y intercept.
B) each unit increased in X, Y increases by 20.
C) each unit increased in Y, X increases by 20.
D) none of the above.
16. If the regression equation is Y' = 2 0.4X, what is the value of Y' when
X = 3?
A) 0.8
B) 3.2
C) 10.0
D) 14.0
E) None of the above
Use the following to answer questions 17-18:
A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected:
17. What is the dependent variable?
A) Salesperson
B) Number of contacts
C) Amount of sales
D) All the above
E) None of the above
18. What is the independent variable?
A) Salesperson
B) Number of contacts
C) Amount of sales
D) All the above
E) None of the above
Use the following to answer question 19:
A regression analysis yields the following information:
Y' = 2.24 + 1.49 X
19. Estimate the value of Y' when X = 4.
A) 10.45
B) 3.73
C) 8.20
D) Cannot be computed
20. If the coefficient of multiple determination is 0.81, what percent of variation is not explained?
A) 19%
B) 90%
C) 66%
D) 81%
E) None of the above
21. When does multicollinearity occur in a multiple regression analysis?
A) Dependent variables are highly correlated
B) Independent variables are minimally correlated
C) Independent variables are highly correlated
D) Independent variables have no correlation
E) None of the above
22. How is the Y intercept in the multiple regression equation represented?
A) b1
B) x1
C) b2
D) x2
E) None of the above
23. In multiple regression, a dummy variable can be included in a multiple regression model as
A) An additional quantitative variable
B) A nominal variable with three or more values
C) A nominal variable with only two values
D) A new regression coefficient
24. Multiple regression analysis is applied when analyzing the relationship between
A) An independent variable and several dependent variables
B) A dependent variable and several independent variables
C) Several dependent variables and several independent variables
D) Several regression equations and a single sample
E) None of the above
Use the following to answer questions 25-28:
The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income.
25. What is this table called?
A) Net regression coefficients
B) Coefficients of nondetermination
C) Analysis of variance
D) Correlation matrix
E) None of the above
26. Which is the dependent variable?
A) Income
B) Age
C) Education
D) Job
E) None of the above
27. Which independent variable has the strongest association with the dependent variable?
A) Income
B) Age
C) Education
D) Job
E) None of the above
28. Which independent variable has the weakest association with the dependent variable?
A) Income
B) Age
C) Education
D) Job
E) None of the above
Use the following to answer question 29:
Twenty-one executives in a large corporation were randomly selected for a study in which several factors were examined to determine their effect on annual salary (expressed in $000's). The factors selected were age, seniority, years of college, number of company divisions they had been exposed to and the level of their responsibility. A regression analysis was performed using a popular spreadsheet program with the following regression output:
29. Which one of the following is the dependent variable?
A) Age
B) Seniority
C) Level of responsibility
D) Annual salary
E) Experience in number of company divisions
Use the following to answer questions 30-31:
A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender ( 0 = female, 1 = male) and job type (0 = clerical, 1 = technical). The following ANOVA summarizes the regression results:
30. In the regression model, which of the following are considered dummy variables?
A) Intercept
B) Service
C) Service and gender
D) Gender and job
E) Service, gender, and job
31. The results for the variable gender show that
A) males average $222.78 more than females in monthly salary
B) females average $222.78 more than males in monthly salary
C) gender is not related to monthly salary
D) Gender and months of service are correlated.
Family Food Income Size Region Variable Description
1 5.04 73.98 4 2
2 4.08 54.9 2 2 Family Identification Number
3 5.76 94.14 4 1 Food Dollars (000) Spent Per Year
4 3.48 52.02 1 3 Income Gross Pay ($000) Per Year
5 4.2 65.7 2 3 Size Family Size
6 4.8 53.64 4 1 Region Area of the Country
7 4.32 79.64 3 2
8 5.04 68.58 4 3
9 6.12 165.6 5 2
10 3.24 64.8 1 1
11 4.8 138.42 3 1
12 3.24 125.82 1 2
13 6.6 77.58 7 2
14 4.92 171.36 2 1
15 6.6 82.08 9 4
16 5.4 141.3 3 3
17 6 36.9 5 2
18 5.4 56.88 4 1
19 3.36 71.82 1 2
20 4.68 69.48 3 4
21 4.32 54.36 2 3
22 5.52 87.66 5 4
23 4.56 38.16 3 2
24 5.4 43.74 7 1
25 4.8 48.42 5 4
Results of multiple regression for Food: All Variables
Summary measures
Multiple R 0.9103
R-Square 0.8287
Adj R-Square 0.7945
StErr of Est 0.4369
ANOVA Table
Source df SS MS F p-value
Explained 4 18.4753 4.6188 24.1935 0.0000
Unexplained 20 3.8182 0.1909
Regression coefficients
Coefficient Std Err t-value p-value
Constant 2.9707 0.3516 8.4479 0.0000
Family -0.0051 0.0131 -0.3896 0.7010
Income 0.0059 0.0024 2.4723 0.0225
Size 0.4318 0.0456 9.4738 0.0000
Region -0.0296 0.0897 -0.3300 0.7448
32. Write the regression equation for the model presented in the preceding table {Results of multiple regression for Food: All Variables } on page 8.
33. If the Family identification number is 20, the Income is 80, the family Size is 2, and the Region is 4: what is the projected Food expenditure?
34. What percent of the variation can be explained in the model developed on page 8?
35. List any variable(s) that should be removed {or altered} from the equation?
Family Food Income Size Region Region_1 Region_2 Region_3 Region_4
1 5.04 73.98 4 2 0 1 0 0
2 4.08 54.9 2 2 0 1 0 0
3 5.76 94.14 4 1 1 0 0 0
4 3.48 52.02 1 3 0 0 1 0
5 4.2 65.7 2 3 0 0 1 0
6 4.8 53.64 4 1 1 0 0 0
7 4.32 79.64 3 2 0 1 0 0
8 5.04 68.58 4 3 0 0 1 0
9 6.12 165.6 5 2 0 1 0 0
10 3.24 64.8 1 1 1 0 0 0
11 4.8 138.42 3 1 1 0 0 0
12 3.24 125.82 1 2 0 1 0 0
13 6.6 77.58 7 2 0 1 0 0
14 4.92 171.36 2 1 1 0 0 0
15 6.6 82.08 9 4 0 0 0 1
16 5.4 141.3 3 3 0 0 1 0
17 6 36.9 5 2 0 1 0 0
18 5.4 56.88 4 1 1 0 0 0
19 3.36 71.82 1 2 0 1 0 0
20 4.68 69.48 3 4 0 0 0 1
21 4.32 54.36 2 3 0 0 1 0
22 5.52 87.66 5 4 0 0 0 1
23 4.56 38.16 3 2 0 1 0 0
24 5.4 43.74 7 1 1 0 0 0
25 4.8 48.42 5 4 0 0 0 1
Variable Description
Family Identification Number
Food Dollars (000) Spent Per Year
Income Gross Pay ($000) Per Year
Size Family Size
Region Area of the Country
Results of multiple regression for Food
Summary measures
Multiple R 0.9187
R-Square 0.8441
Adj R-Square 0.8031
StErr of Est 0.4277
ANOVA Table
Source df SS MS F p-value
Explained 5 18.8177 3.7635 20.5732 0.0000
Unexplained 19 3.4758 0.1829
Regression coefficients
Coefficient Std Err t-value p-value
Constant 2.7183 0.3239 8.3922 0.0000
Income 0.0061 0.0023 2.6525 0.0157
Size 0.4585 0.0486 9.4407 0.0000
Region_2 0.0210 0.2166 0.0970 0.9238
Region_3 0.1997 0.2590 0.7711 0.4502
Region_4 -0.2821 0.2856 -0.9877 0.3357
Referring to the preceding table { Results of multiple regression for Food } on page 10:
36. What is the predicted Food expenditure for a family Size of 2, with an Income of 80, living in
Region 1?
37.What is the predicted Food expenditure for a family Size of 2, with an Income of 80, living in
Region 4?
38. List any variable(s) that should be removed {or altered} from the equation?
39. Which regression model is best? The model presented on page 8 or the model presented on page 10?
40. Explain why you chose the best model.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Your length list of problems is clogging up the posted list.
Please submit your questions a few at a time.
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1. Which of the following statements regarding the coefficient of correlation is true?
A) It ranges from 1.0 to +1.0 inclusive
B) It measures the strength of the relationship between two variables
C) A value of 0.00 indicates two variables are not related
D) All of the above
E) None of the above
Ans: D
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2. What does a coefficient of correlation of 0.70 infer?
A) Almost no correlation because 0.70 is close to 1.0
B) 70% of the variation in one variable is explained by the other
C) Coefficient of determination is 0.49
D) Coefficient of nondetermination is 0.30
E) None of the above
Ans: E
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Cheers,
Stan H.
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