Business Statistics Essay Example | Topics and Well Written Essays - 1500 words

Business Statistics - Essay Example Principal Component Analysis helps us in identifying the factors which appear in the items and also helps in determining which items contribute to each of these factors. The main assumption of PCA is that there is no error in the data. KMO and Bartlett's Test helps in determining whether it is appropriate to apply Factor Analysis and Principal Component Analysis to the given data set. The value of KMO should be greater than 0.5. Here the value is almost 0.5 and it may be appropriate to apply Principal Component Analysis to this data. Further the Chi-Square statistic is 14.312 with 6 degrees of freedom which is significant at 5 % level of significance. Thus Factor analysis may be considered for analyzing the data. The next out put is the Communalities. These values are inserted in the diagonal of the correlation matrix which help in identifying the underlying dimensions and common variance. In this table the column " initial ", the communality for the variables is 1.000 which were inserted in the diagonal of the correlation matrix. The next out put is " Total Variance Explained" gives the "eigen values". The eigen values are in decreasing order of magnitude for the component 1 to 4. the eigen value for a component indicates the total variance attributed to that factor. The total variance accounted for by all the four factors is 4 which is equal to the number of variables. Factor 1 accounts for 34.5% of the total variance. The second component accounts for 24.85% of the total variance and so on. Total Variance Explained Component Initial Eigenvalues Extraction Sums of Squared Loadings Total % of Variance Cumulative % Total % of Variance Cumulative % 1 1.381 34.536 34.536 1.381 34.536 34.536 2 .994 24.852 59.388 3 .977 24.415 83.803 4 .648 16.197 100.000 Extraction Method: Principal Component Analysis. In order to determine the number of factors based on eigen values, the value greater than one is considered. For the component 1, the eigen value is greater than one. And for the components 2 and 3 it is almost equal to 1. But the total percentage is greater than