Essay About Factor Analysis And Total Variance

Factor Analysis of Dell Running
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DELL RUNNING CASEQuestion 1: Can evaluation of Dell be represented by a reduced set of factors? If so, what would be the interpretation of these factors (q8_1 through q8_13)?Solution 1:Performance Rating of Dell Computer which involve certain features and services which may or may not be provided to personal computer customers. These are represented by 13 indicators.Factor Analysis is done to reduce the variable size to a few factors capturing majority of the data.Kaiser-Meyer-Olkin (KMO) – used to compare the magnitudes of the observed correlation coefficients to the magnitudes of the partial correlation coefficients.The below data shows the result of the KMO and Bartlett’s Test. A value of more than 0.5 for Kaiser-Meyer-Olkin Measure of Sampling Adequacy is adequate for carrying out factor analysis. The value in the following case is 0.889 which is more than 0.5. KMO and Bartletts TestKaiser-Meyer-Olkin Measure of Sampling Adequacy..889Bartletts Test of SphericityApprox. Chi-Square1363.573df78Sig..000Principal Components Analysis: It is carried out to extract the information into a few factors, making the factors un-correlated or low-correlated to each other.The below table on total variance explained shows the following analysis:The information is extracted from all the thirteen variables. Component 1 contain 37.624% of the total variance; the eigenvalue for the factor indicated the total variance attributed to that factor, i.e. 4.891. Component 2 has eigenvalue of 1.407, and Component 3 has eigenvalue of 1.042.Three factors have eigenvalue greater than 1 out of 13 variables.56.46% of the total variance is explained. If we include one more factor, the percentage will rise to 62.82%.Total Variance ExplainedComponentInitial EigenvaluesExtraction Sums of Squared LoadingsRotation Sums of Squared LoadingsTotal% of VarianceCumulative %Total% of VarianceCumulative %Total% of VarianceCumulative %14.89137.62437.6244.89137.62437.6243.75128.85228.85221.40710.82148.4441.40710.82148.4442.33717.97746.82931.0428.01756.4611.0428.01756.4611.2529.63256.4614.8276.36362.8245.7675.89768.7216.6925.32174.0427.6565.04979.0918.5884.52683.6179.4893.75987.37610.4633.55990.93511.4433.40994.34412.3832.94797.29113.3522.709100.000Extraction Method: Principal Component Analysis.The Factor Matrix contains the coefficient used to express the standardized variable in terms of the factors. These coefficient, the factor loadings, represent the correlation between the factors and the variables.[pic 1]The matrix is transformed using rotation (Varimax Procedure). The factors are correlated with many variables thus the un-rotated factors are difficult to interpret.The following data is shown for a 4 factor analysis: