The school system of a major city wanted to determine the characteristics of a great teacher, and so they asked 120 students to rate the importance of each of the following 9 criteria using a Likert scale of 1 to 10 with 10 representing that a particular characteristic is extremely important and 1 representing that the characteristic is not importa
- Setting high expectations for the students
- Entertaining
- Able to communicate effectively
- Having expertise in their subject
- Able to motivate
- Caring
- Charismatic
- Having a passion for teaching
- Friendly and easy-going
Review Outputs 1, 2, and 3 in order to answer the following questions:
- (5 points) Based on our discussions in class which of the 9 variables should be included in a Principal Components Analysis and why?
- (5 points) If data reduction is the purpose of the analysis. How many components should be selected and why?
- (6 points) If researchers decided to use your component selection from (b.) for interpretation, describe and evaluate the challenges that they may face and possible ways to remedy the issue(s) identified.
- (6 points) Compare and discuss your results from (b.) with the output from the Variable Clustering analysis.
A Varimax Rotation was performed for 3 components: Cluster Members RSquare with RSquare with 1-RSquare Ratio / Rotated Factor Loading Cluster Members Own Cluster Next Closest 0.119 Factor 3 0.209085 -0.743220 0.3 27085 0.565728 0.530594 0.1 05244 0.830783 -0.0674370.1 55896 .006694-0.067518 0.346985 0.0834440.637552 0.825862 0.0568870.156655 0.569944 0.167349 0.370161 0.142208 0.836583 -0.210964 Factor 2 0 Entertain 0.124 0.148 0.009 0.455632 Passion Expect Motivate 0.024884 0.854047 0.030196 0.339 Charisma Passion 0.151 0.547 Variable Clustering JMP Results A Standardized Components Cluster 2Cluster 3 Variable Coefficients Coefficients Coefficients Cluster 1 Cluster Summary 0 -0.707107 Number Most Representative Cluster Proportion of Variation Explained Variation Explained 2 A 6 & Entertain 04552963 0.542254 Total Proportion of Cluster of Members Variable 0 0.4357429 0 0.6840825 0 0.5849438 Charisma 0.5563756 Passion 2 0.43487 0 0.7071068 Proportion of vanatio explae b clustering: 0.572 Output 2 -8 variables (Friendly removed) Kaiser's leasure of Sampling Adequacy: Overall MSA 0.72560338 Expect Entertain Comm Expert MotivateCaring Charisma Passion 0.43757935 0.83924943 0.67092692 0.61461252 0.81760081 0.70398388 0.69459115 0.84017099 4 Eigenvalues Number Eigenvalue Percent 20 40 60 80 Cum Percent 35.323 2.8259 35.323 1.2376 15.470 1.0608 13.260 0.8574 O.7 0.6680 0.5619 7.024 0.5475 6.844 0.2409 3.011 64.053 74.771 83.121 90.145 96.989 100.000 Output 3 - 7 variables (Friendly and Expect removed) Loading Matrix Prin1Prin Prin3 Prin4 Prin5Prin6Prin 0.65325 -0.26207 -0.29949 0.39535 -0.15753 0.48340 0. Kaiser's Measure of Sampling Adequacy: Overall MSA 0.74749113 Entertain Comm Expert Motivate Caring Charisma Passion 0.85058260 0.696196620.68224050 0.82568846 0.68274755 0.69276195 0.83986108 Ente Comm0.79116 -0.32548 -0.08986 -0.29488 0.23668 -0.08400 0.33170 Expert 0.36286 0.24675 0.84360 0.06107 0.14461 0.26256 0.04693 Motivate 0.59071 0.44590 Caring 0.317140.74695-0.39720 0.04259 0.41962 0.07393 -0.01895 Charisma 0.83362 -0.28012 0.04351 -0.23903 0.17192 0.06022 -0.36660 Passion 0.69668 0.10392 0.10567 0.49969 0.11071 -0.47964 0.35464 -0.56897 0.02761 0.01828 0.02155 Eigenvalues A Varimax Rotation was performed for 2 components: Number Eigenvalue Percent 20 40 60 80 Cum Percent 40.202 55.652 69.683 79.417 88.608 96.459 100.000 2.8141 40.202 1.0815 15.450 0.9821 14.030 0.6814 9.734 0.64349.191 0.5496 7.851 0.2479 3.541 A Rotated Factor Loading 2 Factor 1 Factor 2 Entertain 0.696682 0.100241 0.847806 0.114415 0.190538 0.395280 Motivate 0.288051 0.681752 Caringy-0.099496 0.805364 Charisma 0.861851 0.174937 0.551014 0.438795 Comm Expert Scree Plot 3.5 3.0 2.5 2.0 Passion A Varimax Rotation was performed for 3 components 4 Rotated Factor Loading 1.0 0.5 0.0 Factor 1 Factor 2 Factor 3 Entrtain 0.740267 0.136992 -0.135456 0.060152 0.083979 0.948208 Motivate 0.312429 0.620280 0.258938 0.900070 -0.078311 Charisma 0.847096 0.066635 0.230808 Passion 0.538653 0.317228 0.341695 Comm Expert 0.853973 0.057065 0.043144 -0.5 Ca ring 0.004776 0 2 6 8 Number of Components Automatic Variable Clustering JMP Results 4 Cluster Summary Number Most Representative Cluster Proportion Total Proportion of Cluster of Members Variable 4 Charisma 3 Motivate of Variation Explained Variation Explained .2 4 .6 .8 0.609 0456 0.348 0.195 Proportion of variation explained by clustering: 0.543 Cluster Members RSquare with RSquare with 1-RSquare Cluster Members Own Cluster Next ClosestRatio 0.754 0.716 0.505 046 0.64 0468 0.26 0.119 0.082 0.048 0.148 0.633 0.151 0.425 0.028 0.547 0.05 0.779 0.28 0.31 0.52 Charisma Comm Entertain Passion Motivate Caring Expert Standardized Components Cluster 1 Cluster 2 Variable Coefficients Coefficients 04552963 0.542254 Comm Expert Motivate Caring Charisma 0.5563756 Passion 0 04357429 0 0.6840825 0 0.5849438 043487 A Varimax Rotation was performed for 3 components: Cluster Members RSquare with RSquare with 1-RSquare Ratio / Rotated Factor Loading Cluster Members Own Cluster Next Closest 0.119 Factor 3 0.209085 -0.743220 0.3 27085 0.565728 0.530594 0.1 05244 0.830783 -0.0674370.1 55896 .006694-0.067518 0.346985 0.0834440.637552 0.825862 0.0568870.156655 0.569944 0.167349 0.370161 0.142208 0.836583 -0.210964 Factor 2 0 Entertain 0.124 0.148 0.009 0.455632 Passion Expect Motivate 0.024884 0.854047 0.030196 0.339 Charisma Passion 0.151 0.547 Variable Clustering JMP Results A Standardized Components Cluster 2Cluster 3 Variable Coefficients Coefficients Coefficients Cluster 1 Cluster Summary 0 -0.707107 Number Most Representative Cluster Proportion of Variation Explained Variation Explained 2 A 6 & Entertain 04552963 0.542254 Total Proportion of Cluster of Members Variable 0 0.4357429 0 0.6840825 0 0.5849438 Charisma 0.5563756 Passion 2 0.43487 0 0.7071068 Proportion of vanatio explae b clustering: 0.572 Output 2 -8 variables (Friendly removed) Kaiser's leasure of Sampling Adequacy: Overall MSA 0.72560338 Expect Entertain Comm Expert MotivateCaring Charisma Passion 0.43757935 0.83924943 0.67092692 0.61461252 0.81760081 0.70398388 0.69459115 0.84017099 4 Eigenvalues Number Eigenvalue Percent 20 40 60 80 Cum Percent 35.323 2.8259 35.323 1.2376 15.470 1.0608 13.260 0.8574 O.7 0.6680 0.5619 7.024 0.5475 6.844 0.2409 3.011 64.053 74.771 83.121 90.145 96.989 100.000 Output 3 - 7 variables (Friendly and Expect removed) Loading Matrix Prin1Prin Prin3 Prin4 Prin5Prin6Prin 0.65325 -0.26207 -0.29949 0.39535 -0.15753 0.48340 0. Kaiser's Measure of Sampling Adequacy: Overall MSA 0.74749113 Entertain Comm Expert Motivate Caring Charisma Passion 0.85058260 0.696196620.68224050 0.82568846 0.68274755 0.69276195 0.83986108 Ente Comm0.79116 -0.32548 -0.08986 -0.29488 0.23668 -0.08400 0.33170 Expert 0.36286 0.24675 0.84360 0.06107 0.14461 0.26256 0.04693 Motivate 0.59071 0.44590 Caring 0.317140.74695-0.39720 0.04259 0.41962 0.07393 -0.01895 Charisma 0.83362 -0.28012 0.04351 -0.23903 0.17192 0.06022 -0.36660 Passion 0.69668 0.10392 0.10567 0.49969 0.11071 -0.47964 0.35464 -0.56897 0.02761 0.01828 0.02155 Eigenvalues A Varimax Rotation was performed for 2 components: Number Eigenvalue Percent 20 40 60 80 Cum Percent 40.202 55.652 69.683 79.417 88.608 96.459 100.000 2.8141 40.202 1.0815 15.450 0.9821 14.030 0.6814 9.734 0.64349.191 0.5496 7.851 0.2479 3.541 A Rotated Factor Loading 2 Factor 1 Factor 2 Entertain 0.696682 0.100241 0.847806 0.114415 0.190538 0.395280 Motivate 0.288051 0.681752 Caringy-0.099496 0.805364 Charisma 0.861851 0.174937 0.551014 0.438795 Comm Expert Scree Plot 3.5 3.0 2.5 2.0 Passion A Varimax Rotation was performed for 3 components 4 Rotated Factor Loading 1.0 0.5 0.0 Factor 1 Factor 2 Factor 3 Entrtain 0.740267 0.136992 -0.135456 0.060152 0.083979 0.948208 Motivate 0.312429 0.620280 0.258938 0.900070 -0.078311 Charisma 0.847096 0.066635 0.230808 Passion 0.538653 0.317228 0.341695 Comm Expert 0.853973 0.057065 0.043144 -0.5 Ca ring 0.004776 0 2 6 8 Number of Components Automatic Variable Clustering JMP Results 4 Cluster Summary Number Most Representative Cluster Proportion Total Proportion of Cluster of Members Variable 4 Charisma 3 Motivate of Variation Explained Variation Explained .2 4 .6 .8 0.609 0456 0.348 0.195 Proportion of variation explained by clustering: 0.543 Cluster Members RSquare with RSquare with 1-RSquare Cluster Members Own Cluster Next ClosestRatio 0.754 0.716 0.505 046 0.64 0468 0.26 0.119 0.082 0.048 0.148 0.633 0.151 0.425 0.028 0.547 0.05 0.779 0.28 0.31 0.52 Charisma Comm Entertain Passion Motivate Caring Expert Standardized Components Cluster 1 Cluster 2 Variable Coefficients Coefficients 04552963 0.542254 Comm Expert Motivate Caring Charisma 0.5563756 Passion 0 04357429 0 0.6840825 0 0.5849438 043487
