Assignment
1. Analysis of Variance(ANOVA) is a statistical method of comparing the ________ of severalpopulations.
a) Standard deviations
b) Variances
c) Means
d) None of the above
2.If H0: b1 = b2 = b3=0 is rejected, then we can conclude that there is no linear relationship between the dependent (y) and independent(x) variables in the model.
a) True
b) False
3.In an ANOVA, when testing the significance at α= 0.05, the p-value is 0.003, it can be concluded that:
a) there is no statistical evidence that any population mean is different from any other
b) no two population means are equal
c) no two variances are equal
d) there is strong statistical evidence that not all the population means are equal
4.When independent variables are correlated with each other, multicollinearity is present.
a) True
b) False
5.The F-ratio used to test for the existence of a linear relationship between the dependent variable and any independent variable is:
a) MSR/MSE
b) MSR/MST
c) MSE/MSR
d) None of the above
Use the information below to answer Questions 6 to 9.
Students were randomly selected from TSU undergraduate ECON 3050-01 Class. Their undergraduate performance was compared to their high school GPA and scores on standardized tests.The multiple regression analysis output was asfollows:
|
Predictor
|
Coefficients
|
Standard Error
|
t-ratio
|
p-value
|
|
Intercept
|
1.1066
|
0.2059
|
5.37
|
0.003
|
|
High School GPA
|
0.4755
|
0.1630
|
2.93
|
0.033
|
|
Standard score
|
0.0013392
|
0.0006693
|
2.00
|
0.102
|
Analysis of Variance (ANOVA)
|
Source
|
df
|
SS
|
MS
|
F
|
p-value
|
|
Regression
|
2
|
1.02751
|
0.51375
|
170.77
|
0.000
|
|
Residual
|
5
|
0.01504
|
0.00301
|
|
|
|
Total
|
7
|
1.04255
|
|
|
|
6.Using degrees of freedom (df), the total number of students (n) in this sample was:
a) 7 students
b) 8 students
c) 5 students
d) Cannot be determined
7.Assuming that high school GPA is (x1) and standard score (x2), the regression equation to predict the independent variable (y) is:
a) y = 0.4775 x1 + 0.0013392x2
b) y = 0.2059 + 0.1630x1 + 0.0006693x2
c) y = 1.1066 + 0.4775x1 + 0.0013392x2
d) Not enough information given
8.At the 5% level of significance, are high school GPA scores and standard scores significant?
a) Both are significant
b) Neither are significant
c) Only high school GPA is significant
d) Only standard scores are significant
9.What is the value of R2 using the information from the above table?
a) 99.4%
b) 98.6%
c) 20.8%
d) Insufficient information to determine
10. When all members of every block are randomly assigned to all factors/treatments, the design is called:
a) Repeated measures design
b) Tukey design
c) One-way ANOVA
d) Randomized complete block design
11. Dummy variables are used when:
a) Qualitative variables are involved in the model
b) Quantitative variables are involved in the model
c) Making transformations of quantitative variables
d) None of the above
12. Multicollinearity may cause the signs of some estimated regression parameters to be the opposite of what we would expect.
a) True
b) False
13. As more independent variables are added to a multiple regression model, ___________ will increase; this is not always so with ___________, which will only increase if the additional variables add substantial explanatory power to the model.
a) R2; adjusted R2
b) adjusted R2; R2
c) Both a) and b)
d) None of the above
14. TSU wanted to see if there is a relationship between installation of security cameras and crime rate in hostels. A randomly select 5 hostels had security cameras set up at TSU. If we see that crime has decreased in all 5 hostels, we can conclude that the security cameras caused the decrease in crime rate.
a) True
b) False
15. When the null hypothesis, H0: b1 = b2 = b3 =0, is not rejected, the interpretation should be:
a) There is no linear relationship between y and any of the three independent variables
b) There is a regression relationship between y and at least one of the three independent variables
c) All three independent variables have equal slopes
d) There is a regression relationship between y and all three independent variables
16. A variance inflation factor (VIF) of ______ means there is no correlation between independent variables while a VIF exceeds __________ shows that there is enough correlation
a) 5 and 0
b) 5 and 1
c) 1 and 5
d) None of the above
17. If the purpose of the regression model is to provide a prediction for the dependent variable (y), the presence of multicollinearity is not necessarily a problem in using the model.
a) True
b) False
18. When One-Way ANOVA F-test is found to be significant, which statistical method is used as a follow-up procedure to determine means that are statistically different?
a) t-test for related mean
b) Tukey-Kramer test
c) t-test for differences between independent means
d) None of the above
19. In a one-Way ANOVA, if the computed F-statistic exceeds the critical F value, we may reject the null hypothesis since there is evidence that at least one of the means differs.
a) True
b) False
Consider the one-way ANOVA table below and answer Questions 20 and 21
|
Source
|
df
|
Sum of Squares
|
|
Regression
|
3
|
213.88
|
|
Residual/Error
|
20
|
11.21
|
|
Total
|
23
|
225.09
|
20. What is the mean square error (MSE)?
a) 0.56
b) 213.88
c) 9.70
d) None of the above
21. Assuming there are equal number of observations in each factor (treatment), then the facto consists _________ observations
a) 3
b) 4
c) 6
d) 23
22. Stepwise regression is one of the ways to prevent the problem of multicollinearity.
a) True
b) False
23. The range of feasible values for the multiple coefficient of determination is from
a) 0 to 1
b) - 1 to + 1
c) - 1 to 0
d) None of the above
24. In order to test the significance of a single independent variable, we use:
a) t-test
b) The overall F-test
c) Adjusted R2
d) All of the above
For Questions 25 and 26 use the table below. In the tableare absolute differences in pairs of population means for x1, x2 and x3 and their associate critical ranges (CRs).
|
Absolute Means
|
Absolute Means
|
Critical Range (CR)
|
|
|x1‾ - x2‾|
|
|5.0 - 7.0| = 2.0
|
1.67
|
|
|x1‾ - x3‾|
|
|5.0 - 5.4| = 0.2
|
1.67
|
|
|x2‾ - x3‾|
|
|7.0 - 5.4| = 1.6
|
1.67
|
25. From the table above and, using the decision rule for comparing pairs of population means, which of the following statement is correct?
a) Population means for ¯x 1 and ¯x 2 are different
b) Population means for ¯x 1 and ¯x3 are different
c) Population means for ¯x 2 and ¯x 3 are different
d) Neither of the above statements are correct
26. From the above table, we can conclude that population means for pairs ¯x 1 and ¯x 3 and ¯x 2 and ¯x 3 are not different
a) True
b) False
27. No matter how many groups are being compared, the F test from the one-way ANOVA uses only one significance test.
a) True
b) False
28. Qualitative data cannot be incorporated into linear regression models.
a) True
b) False
29. Which of the following iterative search procedures for model-building in a multiple regression analysis adds variables to model as it proceeds?
a) Backward elimination
b) Stepwise regression
c) Forward selection
d) All possible regressions
30. A one-way ANOVA uses 5 factors/treatments and a total of 40 observations. This means there are 35 degrees of freedom (df) within group variation
a) True
b) False
31. The ______ sum of squares measures the variability of the observed values around their respective treatment means.
a) Factor/treatment
b) Residual/error
c) Interaction
d) Total
32. One-way ANOVA partitions the total variation into "between" and "within" groups.
a) True
b) False
33. It is possible to test the effect of each factor in a two-way ANOVA
a) True
b) False
34. The table below shows correlation coefficients for variables in a multiple regression analysis. If the correlation coefficient was the chosen criterion to build regression model using forward selection procedure. The fist variable to be selected is
|
|
y
|
x1
|
x2
|
x3
|
x4
|
x5
|
|
y
|
1
|
|
|
|
|
|
|
x1
|
0.854168
|
1
|
|
|
|
|
|
x2
|
-0.11828
|
-0.00383
|
1
|
|
|
|
|
x3
|
-0.12003
|
-0.08499
|
-0.14523
|
1
|
|
|
|
x5
|
-0.18105
|
-0.07371
|
0.995886
|
-0.14151
|
-0.16934
|
1
|
a) x1
b) x2
c) x3
d) x4
35. The table below shows correlation coefficients for variables in a multiple regression. The analysis reveals potential multicollinearity between which variables?
|
|
y
|
x1
|
x2
|
x3
|
x4
|
x5
|
|
y
|
1
|
|
|
|
|
|
|
x1
|
-0.0857
|
1
|
|
|
|
|
|
x2
|
-0.20246
|
0.868358
|
1
|
|
|
|
|
x3
|
-0.22631
|
-0.10604
|
-0.14853
|
1
|
|
|
|
x4
|
-0.28175
|
-0.0685
|
0.41468
|
-0.14151
|
1
|
|
|
x5
|
0.271105
|
0.150796
|
0.129388
|
-0.15243
|
0.00821
|
1
|
a) x4 and x5
b) x1 and x2
c) x1 and x4
d) x4 and x3
36. The null hypothesis for conducting a one-way ANOVA is that "not all the means are equal."
a) True
b) False
37. A two-way ANOVA examines the simultaneous effect that two main factors have on the observed data
a) True
b) False
For Questions 35 to 39, use the ANOVA summary table below
|
Source
|
Sum of Squares (SS)
|
Degrees of Freedom (df)
|
Mean Sum of Squares
|
F
|
|
Between
|
(a)
|
4
|
(b)
|
(e)
|
|
Within
|
60
|
(c)
|
(d)
|
|
|
Total
|
76
|
24
|
|
|
38. The value of sum squares between (a) is:
a) 76
b) 16
c) 60
d) 24
39. What is the total number of observations in this ANOVA analysis?
a) 24
b) 25
c) 20
d) None of the above
40. The mean sum of squares between(MSB)as represented by (b)is:
a) 15
b) 19
c) 4
d) 6
41. The mean sum squares within (MSW) shown as (d)is:
a) 20
b) 3
c) 3.8
d) Cannot be determined
42. What is the value of F-calculated?
a) 1.33
b) 1
c) 3
d) None of the above
43. The one-way ANOVA partitions the total variance into four components. These include variance attributable to (i) Factor A, (ii) Factor B, (iii) interaction (Factor A & B), and (iv) that which is unaccounted for.
a) True
b) False
44. How is the degree of association between a set of independent variables and a dependent variable measured?
a) Confidence intervals.
b) Autocorrelation
c) Coefficient of multiple determination
d) Standard error of estimate
45. The best example of a null hypothesis for testing an individual regression coefficient is:
a) H0 : β1 = β2 = β3 = β4
b) H0 : μ1 = μ2 = μ3 = μ4
c) H0: β1 = 0
d) None of the above
46. The Mean Square Error (MSE) is a biased estimator for the variance of the population, denoted by s2.
a) True
b) False
47. In testing for interaction between two factors (A and B) under a two-way ANOVA, the null hypothesis statement reads -- H0: Factors A and B do not interact. If we fail to reject the null hypothesis we can proceed testing Factors A and B.
a) True
b) False
48. Suppose that in a multiple regression the F is significant, but none of the t-ratios for independent coefficients are significant. This means that:
a) Multicollinearity may be present
b) The regression is good
c) Either a) or b)
d) None of the above
49. A factor in ANOVA describes the cause of variation in the data
a) True
b) False
50. The process of deciding which independent variable should be part of the final regression is known as
a) Model building
b) Residual analysis
c) Multicollinearity
d) None of the above