Deck 10: Discriminant Analysis

Question 1

The goal of discriminant analysis is

A) to develop a model to predict new dependent values.
B) the develop a rule for predicting to what group a new observation is most likely to belong.
C) to develop a rule for predicting how independent variable values predict dependent values.
D) none of these.

Answer 1

B

Question 2

Which of the following is not true regarding discriminant analysis?

A) The classification rule translates discriminant scores into group membership.
B) Discriminant analysis is based on discrete or categorical dependent variables.
C) The classification rule selected perfectly classifies the data used to derive the classification rule.
D) The confusion matrix summarizes classification results.

Answer 2

C

Question 3

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. What is the verbal test score value of the group centroid for group 2?

A) 683.8
B) 654.2
C) 610.7
D) 605.7

Answer 3

605.7

Question 4

In discriminant analysis the averages for the independent variables for a group define the

A) centroid.
B) median.
C) mode.
D) central tendency.

Question 5

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. What is the verbal test score value of the group centroid for group 1?

A) 683.8
B) 654.2
C) 610.7
D) 605.7

Question 6

Given the following confusion matrix $$\begin{array} { l l c c c } & & { \text { Predicted Group } } & \\ & 1 & 1 & 2 & \text { Total } \\\hline \text { Actual } & 2 & 9 & 4 & 13 \\\text { Group } & 2 &2 &10 & 12 \\\text { Total } & & 11 & 14 &\end{array}$$ what is the correct classification rate?

A) 9/13 = 69%
B) 10/14 = 86%
C) 19/25 = 76%
D) 6/19 = 32%

Question 7

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. What percentage of the observations is classified incorrectly?

A) 90%
B) 80%
C) 85%
D) 15%

Question 8

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. How many observations are classified correctly?

A) 11
B) 9
C) 17
D) 20

Question 9

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. What number of observations is classified incorrectly?

A) 3
B) 9
C) 17
D) 20

Question 10

If using the regression tool for two-group discriminant analysis, in the regression dialog box, the Input Y-Range entry corresponds to

A) the Group values.
B) the independent variable values.
C) the predictor variable values.
D) (b) and (c) are both correct

Question 11

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. What percentage of the observations is classified correctly?

A) 90%
B) 80%
C) 85%
D) 100%

Question 12

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. How would you compute the centroids for the two (2) groups?

A) compute the average for cells C4:C13, C13:C23, D4:D13 and D13:D23
B) perform regression on cells C4:C13, C13:C23, D4:D13 and D13:D23
C) compute the average for cells C4:C23, D4:D23
D) use regression with cells C4:C23, D4:D23 as the independent variables and B4:B23 as the dependent variable.

Question 13

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. What is the quantitative test score value of the group centroid for group 2?

A) 683.8
B) 654.2
C) 610.7
D) 605.7

Question 14

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. What is the quantitative test score value of the group centroid for group 1?

A) 683.8
B) 654.2
C) 610.7
D) 605.7

Question 15

Discriminant analysis (DA) differs from most other predictive statistical methods because the dependent variable is

A) continuous
B) random
C) stochastic
D) discrete

Question 16

In a two-group discriminant analysis problem using regression, why is the midpoint cut-off value used to determine group classification?

A) Because the value minimizes the absolute misclassification error.
B) Because the value minimizes the probability of misclassification error.
C) Because the value represents an equal division between the groups.
D) Because the value incorporates problem specific knowledge.

Question 17

The regression approach can be used in the two-group discriminant analysis problem because

A) the data are not normally distributed.
B) the R² statistic is not very meaningful.
C) the regression equation can generate a discriminant score.
D) it scales to the k-group problem easily.

Question 18

If using the regression tool for two-group discriminant analysis, in the regression dialog box, the Input X-Range entry corresponds to

A) the Group values.
B) the independent variable values.
C) the predicted variable values.
D) the fitted variable values.

Question 19

Which of the following goodness-of-fit measures is used for discriminant analysis problems?

A) R²
B) multiple R²
C) adjusted R²
D) none of these

Question 20

Which of the following best describes a group centroid?

A) A set of averages for the independent variables for the group.
B) The average for all independent variables across all the groups.
C) The center values for the independent variables for the group.
D) The center value among all independent variables across all the groups.

Question 21

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. The straight line distance between two points (X₁, Y₁) and (X₂, Y₂) is calculated as

A) X₁ ? Y₁ + X₂ ? Y₂
B) (X₁ ? X₂)² + (Y₁ ? Y₂)²
C) $$\sqrt { \left( X _ { 1 } - X _ { 2 } \right) + \left( Y _ { 1 } - Y _ { 2 } \right) }$$
D) $$\sqrt { \left( X _ { 1 } - X _ { 2 } \right) ^ { 2 } + \left( Y _ { 1 } - Y _ { 2 } \right) ^ { 2 } }$$

Question 22

Exhibit 10.2
The following questions are based on the problem description, spreadsheet, and the Risk Solver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful (Group 1), marginally successful (Group 2) or not-successful (Group 3) in their graduate studies. The officer has data on 20 current students, 7 successful (Group 1), 6 marginally successful (Group 2) and 7 not successful (Group 3).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 4:22:38 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline1 & 697.7142857 & 650.4285714 \\2 & 647.8571429 & 630.7142857 \\ 3 & 5876666667 & 6051666667\end{array}$
$\text { Group Frequencies }$
$\begin{array}{cr}&\text { Relative }\\\text { Group } & \text { Frequency } \\\hline 1 & 35.00 \% \\2 & 35.00 \% \\3 & 3000 \%\end{array}$ $\text { Classification Matrix }$
$\begin{array}{lccccr}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Group3 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 6 & 1 & 0 & 7 & 85.71 \% \\\text { Group2 } & 0 & 7 & 0 & 7 & 100.00 \% \\\text { Group3 } & 0 & 0 & 6 & 6 & 100.00 \% \\\text { Total } & 6 & 8 & 6 & 20&95.00\%\end{array}$


-Refer to Exhibit 10.2. What is the quantitative test score value of the group centroid for group 1?

A) 697.71
B) 647.86
C) 587.67
D) 650.43

Question 23

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. What formula is entered in cell F4 of the spreadsheet to compute the Predicted Group for the first student?

A) =IF(E4?$E$26,2,1)
B) =IF(E4?$E$26,1,2)
C) =IF(E4>$E$24,1,0)
D) =IF(E4?$E$24,1,2)

Question 24

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. Suppose that for a given observation, the difference between Mahalanobis distances between group 1 and 2 (G1-G2) is small. This means that

A) The observation is likely to be classified incorrectly
B) The observation is likely to be classified correctly
C) The observation is unlikely to be classified
D) The observation should be deleted from the data set

Question 25

Exhibit 10.2
The following questions are based on the problem description, spreadsheet, and the Risk Solver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful (Group 1), marginally successful (Group 2) or not-successful (Group 3) in their graduate studies. The officer has data on 20 current students, 7 successful (Group 1), 6 marginally successful (Group 2) and 7 not successful (Group 3).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 4:22:38 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline1 & 697.7142857 & 650.4285714 \\2 & 647.8571429 & 630.7142857 \\ 3 & 5876666667 & 6051666667\end{array}$
$\text { Group Frequencies }$
$\begin{array}{cr}&\text { Relative }\\\text { Group } & \text { Frequency } \\\hline 1 & 35.00 \% \\2 & 35.00 \% \\3 & 3000 \%\end{array}$ $\text { Classification Matrix }$
$\begin{array}{lccccr}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Group3 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 6 & 1 & 0 & 7 & 85.71 \% \\\text { Group2 } & 0 & 7 & 0 & 7 & 100.00 \% \\\text { Group3 } & 0 & 0 & 6 & 6 & 100.00 \% \\\text { Total } & 6 & 8 & 6 & 20&95.00\%\end{array}$


-Refer to Exhibit 10.2. Based on the RSP output, what percentage of observations is classified incorrectly?

A) 5%
B) 15%
C) 95%
D) 90%

Question 26

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. Based on the regression output, what is the discriminant score for a student with a quantitative score of 635 and a verbal score of 570?

A) 1.72 ? discriminant score ? 1.73
B) 2.02 ? discriminant score ? 2.03
C) 3.04 ? discriminant score ? 3.05
D) 6.12 ? discriminant score ? 6.14

Question 27

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. The university has received applications from several new students and would like to predict which group they would fall into. What is the discriminant score for a student with a Quantitative score of 686 and a Verbal score of 601. Use five (5) significant figures in your coefficients.

A) 1.29 ? discriminant score ? 1.30
B) 1.69 ? discriminant score ? 1.70
C) 2.69 ? discriminant score ? 2.70
D) 6.05 ? discriminant score ? 6.06

Question 28

Exhibit 10.2
The following questions are based on the problem description, spreadsheet, and the Risk Solver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful (Group 1), marginally successful (Group 2) or not-successful (Group 3) in their graduate studies. The officer has data on 20 current students, 7 successful (Group 1), 6 marginally successful (Group 2) and 7 not successful (Group 3).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 4:22:38 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline1 & 697.7142857 & 650.4285714 \\2 & 647.8571429 & 630.7142857 \\ 3 & 5876666667 & 6051666667\end{array}$
$\text { Group Frequencies }$
$\begin{array}{cr}&\text { Relative }\\\text { Group } & \text { Frequency } \\\hline 1 & 35.00 \% \\2 & 35.00 \% \\3 & 3000 \%\end{array}$ $\text { Classification Matrix }$
$\begin{array}{lccccr}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Group3 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 6 & 1 & 0 & 7 & 85.71 \% \\\text { Group2 } & 0 & 7 & 0 & 7 & 100.00 \% \\\text { Group3 } & 0 & 0 & 6 & 6 & 100.00 \% \\\text { Total } & 6 & 8 & 6 & 20&95.00\%\end{array}$


-Refer to Exhibit 10.2. Based on the RSP output, what percentage of observations is classified correctly?

A) 100%
B) 85.71%
C) 95%
D) 90%

Question 29

Exhibit 10.2
The following questions are based on the problem description, spreadsheet, and the Risk Solver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful (Group 1), marginally successful (Group 2) or not-successful (Group 3) in their graduate studies. The officer has data on 20 current students, 7 successful (Group 1), 6 marginally successful (Group 2) and 7 not successful (Group 3).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 4:22:38 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline1 & 697.7142857 & 650.4285714 \\2 & 647.8571429 & 630.7142857 \\ 3 & 5876666667 & 6051666667\end{array}$
$\text { Group Frequencies }$
$\begin{array}{cr}&\text { Relative }\\\text { Group } & \text { Frequency } \\\hline 1 & 35.00 \% \\2 & 35.00 \% \\3 & 3000 \%\end{array}$ $\text { Classification Matrix }$
$\begin{array}{lccccr}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Group3 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 6 & 1 & 0 & 7 & 85.71 \% \\\text { Group2 } & 0 & 7 & 0 & 7 & 100.00 \% \\\text { Group3 } & 0 & 0 & 6 & 6 & 100.00 \% \\\text { Total } & 6 & 8 & 6 & 20&95.00\%\end{array}$


-Refer to Exhibit 10.2. What is the quantitative test score value of the group centroid for group 2?

A) 697.71
B) 647.86
C) 587.67
D) 650.43

Question 30

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. Suppose that for a given observation, the difference between Mahalanobis distances between group 1 and 2 (G1-G2) is big and positive. This means that

A) The observation is likely to be classified correctly to group 2
B) The observation is likely to be classified correctly to group 1
C) The observation is likely to be classified incorrectly to group 2
D) The observation is likely to be classified incorrectly to group 1

Question 31

Exhibit 10.2
The following questions are based on the problem description, spreadsheet, and the Risk Solver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful (Group 1), marginally successful (Group 2) or not-successful (Group 3) in their graduate studies. The officer has data on 20 current students, 7 successful (Group 1), 6 marginally successful (Group 2) and 7 not successful (Group 3).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 4:22:38 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline1 & 697.7142857 & 650.4285714 \\2 & 647.8571429 & 630.7142857 \\ 3 & 5876666667 & 6051666667\end{array}$
$\text { Group Frequencies }$
$\begin{array}{cr}&\text { Relative }\\\text { Group } & \text { Frequency } \\\hline 1 & 35.00 \% \\2 & 35.00 \% \\3 & 3000 \%\end{array}$ $\text { Classification Matrix }$
$\begin{array}{lccccr}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Group3 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 6 & 1 & 0 & 7 & 85.71 \% \\\text { Group2 } & 0 & 7 & 0 & 7 & 100.00 \% \\\text { Group3 } & 0 & 0 & 6 & 6 & 100.00 \% \\\text { Total } & 6 & 8 & 6 & 20&95.00\%\end{array}$


-Refer to Exhibit 10.2. What is the verbal test score value of the group centroid for group 3?

A) 697.71
B) 647.86
C) 587.67
D) 605.17

Question 32

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. What is the cut-off value (cell E26) for this data using the mid-point cut-off method?

A) 1.189
B) 1.499
C) 1.809
D) 2.000

Question 33

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. What formula is entered in cell E26 of the spreadsheet to determine the Cut-off Value, assuming that the admissions officer wants to minimize the probability of overlap between the groups?

A) =E24+E25/2
B) =(E24+E25)/2
C) =AVERAGE(E4:E13)
D) =AVERAGE(E14:E23)

Question 34

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. Suppose that for a given observation, the difference between Mahalanobis distances between group 1 and 2 (G1-G2) is big and negative. This means that

A) The observation is likely to be classified correctly to group 2
B) The observation is likely to be classified correctly to group 1
C) The observation is likely to be classified incorrectly to group 2
D) The observation is likely to be classified incorrectly to group 1

Question 35

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. What is the straight line distance between (6,4) and (2,9)?

A) 3.20
B) 6.40
C) 9
D) 41

Question 36

Exhibit 10.2
The following questions are based on the problem description, spreadsheet, and the Risk Solver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful (Group 1), marginally successful (Group 2) or not-successful (Group 3) in their graduate studies. The officer has data on 20 current students, 7 successful (Group 1), 6 marginally successful (Group 2) and 7 not successful (Group 3).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 4:22:38 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline1 & 697.7142857 & 650.4285714 \\2 & 647.8571429 & 630.7142857 \\ 3 & 5876666667 & 6051666667\end{array}$
$\text { Group Frequencies }$
$\begin{array}{cr}&\text { Relative }\\\text { Group } & \text { Frequency } \\\hline 1 & 35.00 \% \\2 & 35.00 \% \\3 & 3000 \%\end{array}$ $\text { Classification Matrix }$
$\begin{array}{lccccr}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Group3 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 6 & 1 & 0 & 7 & 85.71 \% \\\text { Group2 } & 0 & 7 & 0 & 7 & 100.00 \% \\\text { Group3 } & 0 & 0 & 6 & 6 & 100.00 \% \\\text { Total } & 6 & 8 & 6 & 20&95.00\%\end{array}$


-Refer to Exhibit 10.2. What number of observations is classified incorrectly?

A) 19
B) 20
C) 7
D) 1

Question 37

Exhibit 10.2
The following questions are based on the problem description, spreadsheet, and the Risk Solver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful (Group 1), marginally successful (Group 2) or not-successful (Group 3) in their graduate studies. The officer has data on 20 current students, 7 successful (Group 1), 6 marginally successful (Group 2) and 7 not successful (Group 3).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 4:22:38 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline1 & 697.7142857 & 650.4285714 \\2 & 647.8571429 & 630.7142857 \\ 3 & 5876666667 & 6051666667\end{array}$
$\text { Group Frequencies }$
$\begin{array}{cr}&\text { Relative }\\\text { Group } & \text { Frequency } \\\hline 1 & 35.00 \% \\2 & 35.00 \% \\3 & 3000 \%\end{array}$ $\text { Classification Matrix }$
$\begin{array}{lccccr}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Group3 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 6 & 1 & 0 & 7 & 85.71 \% \\\text { Group2 } & 0 & 7 & 0 & 7 & 100.00 \% \\\text { Group3 } & 0 & 0 & 6 & 6 & 100.00 \% \\\text { Total } & 6 & 8 & 6 & 20&95.00\%\end{array}$


-Refer to Exhibit 10.2. What number of observations is classified correctly?

A) 19
B) 20
C) 7
D) 8

Question 38

Exhibit 10.1
The following questions are based on the problem description, regression results, and the RiskSolver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful or not-successful in their graduate studies. The officer has data on 20 current students, ten of whom are doing very well (Group 1) and ten who are not (Group 2).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 3:05:44 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline 1 & 683.8 & 654.2 \\2 & 6107 & 6057\end{array}$
$\text { Classification Matrix }$
$\begin{array}{lcccc}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 9 & 1 & 10 & 90.00 \% \\\text { Group2 } & 2 & 8 & 10 & 80.00 \% \\\text { Tnta1 } & 11 & 0 & 20 & 850 \% \%\end{array}$

-Refer to Exhibit 10.1. What formula is entered in cell E4 and copied to cells E5:E25 of the spreadsheet?

A) = 7.452402 + 0.00694*C4 + 0.00232*D4
B) = 7.452402 ? 0.00694*C4 ? 0.00232*D4
C) = 1.157926 + 0.001545*C4 + 0.01297*D4
D) = 7.452402 ? 0.00694*D4 ? 0.00232*C4

Question 39

Exhibit 10.2
The following questions are based on the problem description, spreadsheet, and the Risk Solver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful (Group 1), marginally successful (Group 2) or not-successful (Group 3) in their graduate studies. The officer has data on 20 current students, 7 successful (Group 1), 6 marginally successful (Group 2) and 7 not successful (Group 3).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 4:22:38 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline1 & 697.7142857 & 650.4285714 \\2 & 647.8571429 & 630.7142857 \\ 3 & 5876666667 & 6051666667\end{array}$
$\text { Group Frequencies }$
$\begin{array}{cr}&\text { Relative }\\\text { Group } & \text { Frequency } \\\hline 1 & 35.00 \% \\2 & 35.00 \% \\3 & 3000 \%\end{array}$ $\text { Classification Matrix }$
$\begin{array}{lccccr}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Group3 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 6 & 1 & 0 & 7 & 85.71 \% \\\text { Group2 } & 0 & 7 & 0 & 7 & 100.00 \% \\\text { Group3 } & 0 & 0 & 6 & 6 & 100.00 \% \\\text { Total } & 6 & 8 & 6 & 20&95.00\%\end{array}$


-Refer to Exhibit 10.2. Based on the analysis presented in the spreadsheet, what percentage of the observations were correctly classified?

A) 80%
B) 85%
C) 95%
D) 100%

Question 40

Exhibit 10.2
The following questions are based on the problem description, spreadsheet, and the Risk Solver Platform (RSP) Discriminant Analysis report below.
A college admissions officer wants to evaluate graduate school applicants based on their GMAT scores, verbal and quantitative. Students are classified as either successful (Group 1), marginally successful (Group 2) or not-successful (Group 3) in their graduate studies. The officer has data on 20 current students, 7 successful (Group 1), 6 marginally successful (Group 2) and 7 not successful (Group 3).
$\text { Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\text { October 1,2010 }$$\quad$$\text { 4:22:38 PM}$
$\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$

$\text { Group Centroids }$
$\begin{array}{crr}\text { Group } & \text { Quantitative } & \text { Verbal } \\\hline1 & 697.7142857 & 650.4285714 \\2 & 647.8571429 & 630.7142857 \\ 3 & 5876666667 & 6051666667\end{array}$
$\text { Group Frequencies }$
$\begin{array}{cr}&\text { Relative }\\\text { Group } & \text { Frequency } \\\hline 1 & 35.00 \% \\2 & 35.00 \% \\3 & 3000 \%\end{array}$ $\text { Classification Matrix }$
$\begin{array}{lccccr}\text { Actual / Predicted } & \text { Group1 } & \text { Group2 } & \text { Group3 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 6 & 1 & 0 & 7 & 85.71 \% \\\text { Group2 } & 0 & 7 & 0 & 7 & 100.00 \% \\\text { Group3 } & 0 & 0 & 6 & 6 & 100.00 \% \\\text { Total } & 6 & 8 & 6 & 20&95.00\%\end{array}$


-Refer to Exhibit 10.2. What is the verbal test score value of the group centroid for group 1?

A) 697.71
B) 647.86
C) 587.67
D) 650.43

Question 41

The term serves which of the following purposes? $$\operatorname { LN } \left( \frac { p _ { 2 } \mathrm { C } ( 1 \mid 2 ) } { p _ { 1 } \mathrm { C } ( 2 \mid 1 ) } \right)$$

A) Accounts for prior probabilities of group membership.
B) Reduces the overlap area of the classification rules.
C) Ensures the data follow an exponential distribution.
D) Removes the midpoint information from the classification rules.

Question 42

Exhibit 10.6
The information below is used for the following questions.
An investor wants to classify companies as being either a good investment, Group 1, or a poor investment, Group 2. He has gathered Liquidity, Profitability and Activity data on 18 companies he has invested in and run a regression analysis. Discriminant Analysis output using Risk Solver Platform (RSP) has also been generated. The data for the problem and the relevant output are shown below.

Refer to Exhibit 10.6. What formulas should go in cells C22:D23, E4:G24, and F24 of the spreadsheet?

Question 43

Exhibit 10.7
The information below is used for the following questions.
An investor wants to classify companies as being a High Risk Investment, Group 1, a Medium Risk Investment, Group 2, or a Low Risk Investment, Group 3. He has gathered Liquidity, Profitability data on 18 companies he has invested in and produced the following spreadsheet. The following Discriminant Analysis output using Risk Solver Platform (RSP) has also been generated.

Refer to Exhibit 10.7. What formulas should go in cells C22:D24 of the spreadsheet?

Question 44

Refer to Exhibit 10.3. What is the percentage of observations:
a.
Correctly classified to a Group?
b.
Incorrectly classified to a Group?
c.
Correctly classified to Group 1?
d.
Correctly classified to Group 2?
ANS:
a.
94.44%
b.
5.56%
c.
90%
d.
100%
PTS: 1
Exhibit 10.4
The information below is used for the following questions.
A manager wants to classify people as belonging to one of two groups based on two scores. The manager has collected data on four current employees and has performed a regression analysis on the data. The data for the problem and the relevant output are shown below.

Refer to Exhibit 10.4. What is the percentage of observations:
a.
Correctly classified to a Group?
b.
Incorrectly classified to a Group?
c.
Correctly classified to Group 1?
d.
Correctly classified to Group 2?

Question 45

Which of the following statements is true concerning multiple discriminant analysis distance measures?

A) A data point should fall nearest the centroid of the group to which it belongs.
B) A pure distance measure ignores data variance which can influence classification accuracy.
C) Mahalanobis distance measure accounts for differences in covariance between independent variables.
D) All of these are true.

Question 46

Exhibit 10.7
The information below is used for the following questions.
An investor wants to classify companies as being a High Risk Investment, Group 1, a Medium Risk Investment, Group 2, or a Low Risk Investment, Group 3. He has gathered Liquidity, Profitability data on 18 companies he has invested in and produced the following spreadsheet. The following Discriminant Analysis output using Risk Solver Platform (RSP) has also been generated.

Refer to Exhibit 10.7. Based on the 18 observations in the model complete the following confusion/classification matrix.

Question 47

Exhibit 10.3
The information below is used for the following questions.
A loan officer wants to determine if people will be late in making loan payments. She has information of 18 current loans including the applicants income, level of assets and whether or not the person has been late on payments. She has performed an analysis on the data using Regression tool in Excel and the Risk Solver Platform (RSP). The data for the problem and the relevant output are shown below.

Refer to Exhibit 10.3. Compute the discriminant score and predicted group for someone with an income of 65 and assets of 11.

Question 48

Multiple discriminant analysis moves away from a regression approach to using a measure of distance. Which of the following characterizes the use of a distance function?

A) Each data value's distance from the origin will align with the appropriate group regression line.
B) A data value will fall nearest to the centroid point of its group.
C) The distance measure accounts for the variance of the group data as well as the group centroid.
D) Neither (b) nor (c) characterize the distance measure.

Question 49

Exhibit 10.6
The information below is used for the following questions.
An investor wants to classify companies as being either a good investment, Group 1, or a poor investment, Group 2. He has gathered Liquidity, Profitability and Activity data on 18 companies he has invested in and run a regression analysis. Discriminant Analysis output using Risk Solver Platform (RSP) has also been generated. The data for the problem and the relevant output are shown below.
$\text { Regression Statistics }$
$\begin{array}{|l|r|}\hline & \text { Coefficients } \\\hline \text { Intercept } & 4.690338 \\\hline \text { Liquidity } & -3.12192 \\\hline \text { Profitability } & -1.55793 \\\hline \text { Activity } & -0.16033 \\\hline\end{array}$
$\text {Discriminant Analysis Report}$
$\quad$$\quad$$\quad$$\quad$$\text {October 3,2010}$$\quad$$\quad$$\text {6:03:04PM}$
$\text {Unpooled Estimates of within-group Covariance matrices are used, assuming they are differen}$

$\text { Group Centroids }$

$\begin{array}{crrr}\text { Group } & \mathrm{X} 1 & \mathrm{X} 2 & \mathrm{X} 3 \\\hline 1 & 0.893 & 0.302 & 1.569 \\2 & 074125 & 074125 & 1.4875\end{array}$


$\text { Group Frequencies }$
$\begin{array}{cr}&\text { Relative }\\\text { Group } & \text { Frequency } \\\hline 1 & 55.56 \% \\2 & 44.44 \%\end{array}$ $\text {Classification Matrix}$

$\begin{array}{lccccr}\text { Actual/}\\\text { Predicted } & \text { Group1 } & \text { Group2 } & \text { Total } & \text { \% correct } \\\hline \text { Group1 } & 10 & 0 & 10 & 100.00 \% \\\text { Group2 } & 2 & 6 & 8& 75.00 \% \\\text { Total } & 12 & 6 & 18 &88.89 \% \end{array}$



-Refer to Exhibit 10.6. Based on the 20 observations and the RSP output, what percentage of the observations are correctly classified?

A) 80.00%
B) 88.89%
C) 75.25%
D) 95.14%

Question 50

Exhibit 10.3
The information below is used for the following questions.
A loan officer wants to determine if people will be late in making loan payments. She has information of 18 current loans including the applicants income, level of assets and whether or not the person has been late on payments. She has performed an analysis on the data using Regression tool in Excel and the Risk Solver Platform (RSP). The data for the problem and the relevant output are shown below.

Refer to Exhibit 10.3. What formulas should go in cells C22:D23 and E4:F24 of the spreadsheet?

Question 51

Refer to Exhibit 10.3. What is the percentage of observations:
a.
Correctly classified to a Group?
b.
Incorrectly classified to a Group?
c.
Correctly classified to Group 1?
d.
Correctly classified to Group 2?
ANS:
a.
94.44%
b.
5.56%
c.
90%
d.
100%
PTS: 1
Exhibit 10.4
The information below is used for the following questions.
A manager wants to classify people as belonging to one of two groups based on two scores. The manager has collected data on four current employees and has performed a regression analysis on the data. The data for the problem and the relevant output are shown below.

Refer to Exhibit 10.4. What formulas should go in cells C8:D9 and E4:G10 of the spreadsheet?

Question 52

Exhibit 10.5
The information below is used for the following questions.
A counselor wants to classify people as belonging to one of three groups based on two scores. The counselor has collected data on twenty people who are known to be in one of the three groups. The data for the problem are in the following spreadsheet. Output generated using Risk Solver Platform (RSP) is also included.

Refer to Exhibit 10.5. Based on the 20 observations in the model complete the following confusion/classification matrix.

Question 53

Exhibit 10.5
The information below is used for the following questions.
A counselor wants to classify people as belonging to one of three groups based on two scores. The counselor has collected data on twenty people who are known to be in one of the three groups. The data for the problem are in the following spreadsheet. Output generated using Risk Solver Platform (RSP) is also included.

Refer to Exhibit 10.5. What formulas should go in cells C24:D26 of the spreadsheet?

Question 54

Refer to Exhibit 10.3. What is the percentage of observations:
a.
Correctly classified to a Group?
b.
Incorrectly classified to a Group?
c.
Correctly classified to Group 1?
d.
Correctly classified to Group 2?
ANS:
a.
94.44%
b.
5.56%
c.
90%
d.
100%
PTS: 1
Exhibit 10.4
The information below is used for the following questions.
A manager wants to classify people as belonging to one of two groups based on two scores. The manager has collected data on four current employees and has performed a regression analysis on the data. The data for the problem and the relevant output are shown below.

Refer to Exhibit 10.4. Compute the discriminant score and predicted group for someone with Score 1 of 242 and Score 2 of 142.

Question 55

Refer to Exhibit 10.3. What is the percentage of observations:
a.
Correctly classified to a Group?
b.
Incorrectly classified to a Group?
c.
Correctly classified to Group 1?
d.
Correctly classified to Group 2?
ANS:
a.
94.44%
b.
5.56%
c.
90%
d.
100%
PTS: 1
Exhibit 10.4
The information below is used for the following questions.
A manager wants to classify people as belonging to one of two groups based on two scores. The manager has collected data on four current employees and has performed a regression analysis on the data. The data for the problem and the relevant output are shown below.

Refer to Exhibit 10.4. Compute the discriminant score and predicted group for someone with Score 1 of 238 and Score 2 of 140.

Question 56

Exhibit 10.6
The information below is used for the following questions.
An investor wants to classify companies as being either a good investment, Group 1, or a poor investment, Group 2. He has gathered Liquidity, Profitability and Activity data on 18 companies he has invested in and run a regression analysis. Discriminant Analysis output using Risk Solver Platform (RSP) has also been generated. The data for the problem and the relevant output are shown below.

Refer to Exhibit 10.6. Compute the discriminant score and predicted group for a company with Liquidity = 0.91, Profitability = 0.32 and Activity = 1.39.

Question 57

Exhibit 10.6
The information below is used for the following questions.
An investor wants to classify companies as being either a good investment, Group 1, or a poor investment, Group 2. He has gathered Liquidity, Profitability and Activity data on 18 companies he has invested in and run a regression analysis. Discriminant Analysis output using Risk Solver Platform (RSP) has also been generated. The data for the problem and the relevant output are shown below.

Refer to Exhibit 10.6. Compute the discriminant score and predicted group for a company with Liquidity = 0.80, Profitability = 0.27 and Activity = 1.55.