Quiz #4 PrepLinear Discriminant FunctionThis analysis sought to identify the variables that discriminated among students taking four types of high school curriculum. Group Statistics74.5062.7078.8082.1068.6055.4071.4078.5065.4087.9066.4074.5055.4070.3068.3089.2038.5066.5038.1038.5057.6077.2070.3068.90CalculusPhysicsMotor_SkillsEd_MotivComputerSpatial_SkillsCalculusPhysicsMotor_SkillsEd_MotivComputerSpatial_SkillsCalculusPhysicsMotor_SkillsEd_MotivComputerSpatial_SkillsCalculusPhysicsMotor_SkillsEd_MotivComputerSpatial_SkillsHS ProgramCollege PrepBusinessGeneralVocationalMeanTests of Equality of Group Means.947 3.818 3 55 .009.969 1.021 3 55 .387.962 4.294 3 55 .001.998 .065 3 55 .978.949 4.743 3 55 .000.989 3.372 3 55 .012CalculusPhysicsMotor_SkillsEd_MotivComputerSpatial_SkillsWilks'Lambda F df1 df2 Sig.Eigenvalues10.196a46.7 66.4 .7545.087a33.2 85.7 .6141.409a20.1 100.0 .109Function123Eigenvalue% ofVariance Cumulative %CanonicalCorrelationFirst 3 canonical discriminant functions were used in theanalysis.a. Wilks' Lambda.015 84.434 20 .000.164 36.123 15 .000.874 4.290 10 .319Test of Function(s)1 through 32 through 33Wilks'Lambda Chi-square df Sig.Remember to use the structure matrix values to interpret and label the ldfs – not the standardized weights!Structure Matrix.643* .241 -.328.504* -.184 -.566.162* .631 -.132.762 -.198* .471.093 -.471* .219-.213 .528 .217*CalculusComputerSpatial_SkillsPhysicsEd_MotivMotor_Skills1 2 3FunctionPooled within-groups correlations between discriminatingvariables and standardized canonical discriminant functions Variables ordered by absolute size of correlation withinfunction.Largest absolute correlation between each variableand any discriminant function*.Functions at Group Centroids1.250 .160 1.300-.800 -.600 -1.200-.960 -.690 .050-.890 1.530 -.140HS ProgramCollege PrepBusinessGeneralVocational1 2 3FunctionUnstandardized canonical discriminant functionsevaluated at group meansClassification Resultsa12 2 1 1 151 6 6 2 151 5 7 2 151 1 2 11 15HS ProgramCollege PrepBusinessGeneralVocationalCountOriginalCollege Prep Business General VocationalPredicted Group MembershipTotal39.6% of original grouped cases correctly classified.a. 1. Which variables are viable single discriminators?2. Describe the classification pattern using calculus as a single discriminator.3. Describe the classification pattern using computer as a single discriminator.4. How many ldfs are possible? How many ldfs are contributing? Be sure to explain each answer. 5. How well does the model work? Explain your answers.6. Describe persons who are at the positive end of each function.?7. Interpret the structure weight for calculus on Function 1. 8. Interpret the structure weight for educational motivation on Function 2. 9. Interpret the structure weight for computer on Function 3. 10. Tell what discriminations are and are not made using each function. Also tell what discriminations are and are not made using the overall model.Answers for Practice #11. Which variables are viable single discriminators?Calculus, Motor skills, Computer, Spatial skills all have significant F-results2. Describe the classification pattern using calculus as a single discriminator.Calculus will discriminate Vocational, from General, from Business & College Prep, but will not discriminate Business and College prep from each other.3. Describe the classification pattern using computer as a single discriminator.Computer skills will discriminate General from Vocational, Business & College Prep, but will not discriminate Vocational, Business & College prep from each other.4. How many ldfs are possible? How many ldfs are contributing? Be sure to explain each answer. With 4 groups, 3 ldfs are possible. With 6 variables, 6 ldfs are possible, the fewer of these is 3 possible ldfs for this analysis. Based on the significance tests in the “Wilks’ Lambda” table, there are two significant, contributing ldfs.5. How well does the model work? Explain your answers.The canonical correlations of .754 and .614 are large effect sizes, indicating the model works very well from a “variance accounted for” perspective. The reclassification % of 39.6% is substantially better than the nominal baserate of .25.6. Describe persons who are at the positive end of each function.?ldf1 – calculus, computer and physics all have positive structure weights, so those at the + end of ldf1 will tend to have high scores in calculus, computer and physics ldf2 – spatial skills and motor skills have positive structure weights and ed motiv has a negative structure weight, so those at the + end of the ldf2 will tend to have high spatial & motor scores and low ed motiv scores7. Interpret the structure weight for calculus on Function 1. Calculus is positively related to ldf1 – higher scores on ldf1 are associated with higher calculus scores8. Interpret the structure weight for educational motivation on Function 2. Ed motive is negatively related to ldf2 – higher scores on ldf2 are associated with lower motivational scores9. Interpret the structure weight for computer on Function 3. Ldf3 is not significant, so we don’t interpret it 10. Tell what discriminations are and are not made using each function. Also tell what discriminations are and are not made using the overall modelBased on the centroid pattern of each ldf: ldf1 discriminates College Prep from the others, while ldf2 discriminates Vocational from Business & General from College Prep. Based on the pattern of the reclassification table, this 2-function model discriminates Vocational from Business & General from College Prep.Practice #2 Linear Discriminant FunctionThis analysis sought to identify the variables that discriminated among four types of hobbiests. Group Statistics12.305.6010.006.807.3011.8013.206.1010.2014.603.404.2412.5018.3017.5012.1017.9016.303.906.70DetailsOutdoorsAnimalsDangerActionDetailsOutdoorsAnimalsDangerActionDetailsOutdoorsAnimalsDangerActionDetailsOutdoorsAnimalsDangerActionType of HobbiestModel railroaderModel rocketerSnake CharmerGardnerMeanTests of Equality of Group Means.962 8.040 3 97 .013.998 3.200 3 97 .042.949 11.300 3 97 .001.989 11.380 3 97 .001.981 5.200 3 97 .530DetailsOutdoorsAnimalsDangerActionWilks'Lambda F df1 df2 Sig.Eigenvalues10.196a46.7 58.1 .4555.087a33.2 90.5 .3141.409a20.1 100.0 .163Function123Eigenvalue% ofVariance Cumulative %CanonicalCorrelationFirst 3 canonical discriminant functions were used in theanalysis.a.