Exam 10: Discriminant Analysis

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

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. $\text {Discriminant Analysis Report}$ $\quad$$\quad$$\quad$$\quad$$\text {October 3,2010}$$\quad$$\quad$$\text {6:09:36PM}$ $\text {Unpooled Estimates of within-group Covariance matrices are used, assuming they are differen}$ $\text { Group Centroids }$ Group 1 2 1 0.913333333 0.316666667 2 0.856 0.288 3 0728571420 023 $\text { Group Frequencies }$ Relative Group Frequency 1 33.33\% 2 27.78\% 3 38.80\% -Refer to Exhibit 10.7. Based on the 18 observations in the model complete the following confusion/classification matrix. Actual Group 1 Group 2 Group 3 Total Group 1 Group 2 Group 3 Total \% Correct

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}$ $\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group Quantitative Verbal 1 683.8 654.2 2 6107 6057 $\text { Classification Matrix }$ Actual / Predicted Group1 Group2 Total \% correct Group1 9 1 10 90.00\% Group2 2 8 10 80.00\% Tnta1 11 0 20 850\%\% -Refer to Exhibit 10.1. What percentage of the observations is classified incorrectly?

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}$ $\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group Quantitative Verbal 1 683.8 654.2 2 6107 6057 $\text { Classification Matrix }$ Actual / Predicted Group1 Group2 Total \% correct Group1 9 1 10 90.00\% Group2 2 8 10 80.00\% Tnta1 11 0 20 850\%\% -Refer to Exhibit 10.1. How many observations are classified correctly?

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

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}$ $\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group Quantitative Verbal 1 683.8 654.2 2 6107 6057 $\text { Classification Matrix }$ Actual / Predicted Group1 Group2 Total \% correct Group1 9 1 10 90.00\% Group2 2 8 10 80.00\% Tnta1 11 0 20 850\%\% -Refer to Exhibit 10.1. What percentage of the observations is classified correctly?

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

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}$ $\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group Quantitative Verbal 1 683.8 654.2 2 6107 6057 $\text { Classification Matrix }$ Actual / Predicted Group1 Group2 Total \% correct Group1 9 1 10 90.00\% Group2 2 8 10 80.00\% Tnta1 11 0 20 850\%\% -Refer to Exhibit 10.1. What formula is entered in cell F4 of the spreadsheet to compute the Predicted Group for the first student?

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. $\text { Regression Statistics }$ Coefficients Intercept 31.8158 Score 1 -0.14956 Score 2 0.03825 $\text {Discriminant Analysis Report}$ $\quad$$\quad$$\text {October 3,2010}$$\quad$$\quad$$\quad$ $\text {5:50:10 PM}$ $\text {Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group 1 2 1 241.85 144.2 2 236.8 1422 $\text { Group Frequencies }$ Relative Group Frequency 1 50.00\% 2 50.00\% $\text {Training Sample Classification}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {Mahalanobis Distances}$ Predicted Actual Observation Group 1 Group2 Group Group 1 0.5 1.64085+18 1 1 2 0.5 1.6759+17 1 1 3 2.09579+16 0.5 2 2 4 750135+14 05 2 2 $\text {Classification Matrix}$ Actual/ Predicted Group1 Group2 Total \% correct Group1 2 0 2 100.00\% Group2 0 2 2 100.00\% Total 2 2 4 100.00\% $\text {Test Sample Classification}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {Mahalanobis Distances}$ Predicted Observation Group 1 Group2 Group 1 0.5 1.64085+18 1 2 0.5 1.6759+17 1 3 2.09579+16 0.5 2 4 750135+14 05 2 -Refer to Exhibit 10.4. Compute the discriminant score and predicted group for someone with Score 1 of 238 and Score 2 of 140.

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}$ $\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group Quantitative Verbal 1 683.8 654.2 2 6107 6057 $\text { Classification Matrix }$ Actual / Predicted Group1 Group2 Total \% correct Group1 9 1 10 90.00\% Group2 2 8 10 80.00\% Tnta1 11 0 20 850\%\% -Refer to Exhibit 10.1. What is the straight line distance between (6,4) and (2,9)?

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

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}$ $\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group Quantitative Verbal 1 683.8 654.2 2 6107 6057 $\text { Classification Matrix }$ Actual / Predicted Group1 Group2 Total \% correct Group1 9 1 10 90.00\% Group2 2 8 10 80.00\% Tnta1 11 0 20 850\%\% -Refer to Exhibit 10.1. The straight line distance between two points (X₁, Y₁) and (X₂, Y₂) is calculated as

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}$ $\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group Quantitative Verbal 1 697.7142857 650.4285714 2 647.8571429 630.7142857 3 5876666667 6051666667 $\text { Group Frequencies }$ Relative Group Frequency 1 35.00\% 2 35.00\% 3 3000\% $\text { Classification Matrix }$ Actual / Predicted Group1 Group2 Group3 Total \% correct Group1 6 1 0 7 85.71\% Group2 0 7 0 7 100.00\% Group3 0 0 6 6 100.00\% Total 6 8 6 20 95.00\% -Refer to Exhibit 10.2. What is the quantitative test score value of the group centroid for group 2?

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. $\text { Regression Statistics }$ Coefficients Intercept 31.8158 Score 1 -0.14956 Score 2 0.03825 $\text {Discriminant Analysis Report}$ $\quad$$\quad$$\text {October 3,2010}$$\quad$$\quad$$\quad$ $\text {5:50:10 PM}$ $\text {Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group 1 2 1 241.85 144.2 2 236.8 1422 $\text { Group Frequencies }$ Relative Group Frequency 1 50.00\% 2 50.00\% $\text {Training Sample Classification}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {Mahalanobis Distances}$ Predicted Actual Observation Group 1 Group2 Group Group 1 0.5 1.64085+18 1 1 2 0.5 1.6759+17 1 1 3 2.09579+16 0.5 2 2 4 750135+14 05 2 2 $\text {Classification Matrix}$ Actual/ Predicted Group1 Group2 Total \% correct Group1 2 0 2 100.00\% Group2 0 2 2 100.00\% Total 2 2 4 100.00\% $\text {Test Sample Classification}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {Mahalanobis Distances}$ Predicted Observation Group 1 Group2 Group 1 0.5 1.64085+18 1 2 0.5 1.6759+17 1 3 2.09579+16 0.5 2 4 750135+14 05 2 -Refer to Exhibit 10.4. Compute the discriminant score and predicted group for someone with Score 1 of 242 and Score 2 of 142.

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}$ $\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group Quantitative Verbal 1 683.8 654.2 2 6107 6057 $\text { Classification Matrix }$ Actual / Predicted Group1 Group2 Total \% correct Group1 9 1 10 90.00\% Group2 2 8 10 80.00\% Tnta1 11 0 20 850\%\% -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.

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}$ $\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group Quantitative Verbal 1 683.8 654.2 2 6107 6057 $\text { Classification Matrix }$ Actual / Predicted Group1 Group2 Total \% correct Group1 9 1 10 90.00\% Group2 2 8 10 80.00\% Tnta1 11 0 20 850\%\% -Refer to Exhibit 10.1. What is the cut-off value (cell E26) for this data using the mid-point cut-off method?

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. $\text { Regression Statistics }$ Coefficients Intercept 31.8158 Score 1 -0.14956 Score 2 0.03825 $\text {Discriminant Analysis Report}$ $\quad$$\quad$$\text {October 3,2010}$$\quad$$\quad$$\quad$ $\text {5:50:10 PM}$ $\text {Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group 1 2 1 241.85 144.2 2 236.8 1422 $\text { Group Frequencies }$ Relative Group Frequency 1 50.00\% 2 50.00\% $\text {Training Sample Classification}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {Mahalanobis Distances}$ Predicted Actual Observation Group 1 Group2 Group Group 1 0.5 1.64085+18 1 1 2 0.5 1.6759+17 1 1 3 2.09579+16 0.5 2 2 4 750135+14 05 2 2 $\text {Classification Matrix}$ Actual/ Predicted Group1 Group2 Total \% correct Group1 2 0 2 100.00\% Group2 0 2 2 100.00\% Total 2 2 4 100.00\% $\text {Test Sample Classification}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {Mahalanobis Distances}$ Predicted Observation Group 1 Group2 Group 1 0.5 1.64085+18 1 2 0.5 1.6759+17 1 3 2.09579+16 0.5 2 4 750135+14 05 2 -Refer to Exhibit 10.4. What formulas should go in cells C8:D9 and E4:G10 of the spreadsheet?

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. $\text {Discriminant Analysis Report}$ $\quad$$\quad$$\quad$$\quad$$\text {October 3,2010}$$\quad$$\quad$$\text { 5:56:34 PM}$ $\text {Unpooled Estimates of within-group Covariance matrices are used, assuming they are differen}$ $\text { Group Centroids }$ Group 1 2 1 242 148.8333333 2 237.8571429 149.1428571 3 2328571420 1411428571 $\text { Group Frequencies }$ Relative Group Frequency 1 30.00\% 2 35.00\% 3 3500\% -Refer to Exhibit 10.5. What formulas should go in cells C24:D26 of the spreadsheet?

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. Regression Slatisties Coefficients Intercept 3.109577 Income -0.02112 Assets -0.0212 $\text { Discriminant Analysis Report}$ $\quad$$\quad$$\quad$$\text { October 2,2010 }$$\quad$$\text { 5:37:28PM}$ $\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ Group 1 2 1 82.86 12.6 2 483875 05625 $\text { Group Frequencies }$ Relative Group Frequency 1 55.56\% 2 44.44\% $\text {Classification Matrix}$ Actual/ Predicted Group1 Group2 Total \% correct Group1 9 1 10 90.00\% Group2 0 8 8 100.00\% Total 0 0 18 04.44\% -Refer to Exhibit 10.3. Compute the discriminant score and predicted group for someone with an income of 65 and assets of 11.

Which of the following is not true regarding discriminant analysis?