Exam 10: Discriminant Analysis

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 would you compute the centroids for the two (2) groups?

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 verbal test score value of the group centroid for group 1?

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 verbal test score value of the group centroid for group 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}$ $\text { Unpooled Estimates of within-group Covariance matrices are used, assuming they are different}$ $\text { Group Centroids }$ 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. Suppose that for a given observation, the difference between Mahalanobis distances between group 1 and 2 (G1-G2) is small. This means that

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. 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

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. Based on the analysis presented in the spreadsheet, what percentage of the observations were correctly classified?

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. $\text { Regression Statistics }$ Coefficients Intercept 4.690338 Liquidity -3.12192 Profitability -1.55793 Activity -0.16033 $\text {Discriminant Analysis Report}$ $\quad$$\quad$$\quad$$\quad$$\text {October 3,2010}$$\quad$$\quad$$\text {6:03:04PM}$ $\text {Unpooled Estimates of within-group Covariance matrices are used, assuming they are differen}$ $\text { Group Centroids }$ Group 1 2 3 1 0.893 0.302 1.569 2 074125 074125 1.4875 $\text { Group Frequencies }$ Relative Group Frequency 1 55.56\% 2 44.44\% $\text {Classification Matrix}$ Actual/ Predicted Group1 Group2 Total \% correct Group1 10 0 10 100.00\% Group2 2 6 8 75.00\% Total 12 6 18 88.89\% -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.

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 1?

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 number of observations is classified incorrectly?

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

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 verbal test score value of the group centroid for group 1?

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

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. $\text { Regression Statistics }$ Coefficients Intercept 4.690338 Liquidity -3.12192 Profitability -1.55793 Activity -0.16033 $\text {Discriminant Analysis Report}$ $\quad$$\quad$$\quad$$\quad$$\text {October 3,2010}$$\quad$$\quad$$\text {6:03:04PM}$ $\text {Unpooled Estimates of within-group Covariance matrices are used, assuming they are differen}$ $\text { Group Centroids }$ Group 1 2 3 1 0.893 0.302 1.569 2 074125 074125 1.4875 $\text { Group Frequencies }$ Relative Group Frequency 1 55.56\% 2 44.44\% $\text {Classification Matrix}$ Actual/ Predicted Group1 Group2 Total \% correct Group1 10 0 10 100.00\% Group2 2 6 8 75.00\% Total 12 6 18 88.89\% -Refer to Exhibit 10.6. What formulas should go in cells C22:D23, E4:G24, and F24 of the spreadsheet?

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 E4 and copied to cells E5:E25 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. Based on the 20 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 10.7 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. What formulas should go in cells C22:D24 of the spreadsheet?

Given the following confusion matrix Predicted Group 1 1 2 Total Actual 2 9 4 13 Group 2 2 10 12 Total 11 14 what is the correct classification rate?