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The cornlnunalities hj represent the fraction of the total variance' 'accounted for of variabie j. Ry calculating the communalities we can keep track of how much of-the original variance that was contained in variable j is still being accounted for by the 'numbcr of factors we have retained. As a consequence, when p = m2hj2 = 1, always. so long as the data was standardized first. The communalities are calculated in thc following fashion:
One can readlthink of this as: summing the squares of -the factor loadings horizontally across the factor loadings matrix.
practical application of standard error
In PCA the eigknvalues must ultimately account for all of the variance. There is no probability,'no hypothesis, no test because strictly speaking PCA is not a statistical procedure
Correspondence Analysis (CA) is a generalization of PCA to contingency tables. The factors of correspondence analysis give an orthogonal decomposi:ion of the Chi- square associated
how can we graph a trend line by semiaverages and least square method?
The total number of overtime hours (in 1000s) worked in a large steel mill was recorded for 16 quarters, as shown below. Year Quarter Overtime hour
a b c d e supply p 3 4 6 8 8 20 q 2 6 0 5 8 30 r 7 11 20 40 3 15 s 1 0 9 14 6 13 d 15 3 12 10 20
TYPE I AND II Errors If a statistical hypothesis is tested, we may get the following four possible cases: The null hypothesis is true and it is accepted; The
For the following questions we are interested in a comparison of the 16 years education vs. > 16 years. (Recall we did the analysis on the log scale, so these are actual means on t
Active Control Equivalence Studies (ACES) Clinical trials the field in which the object is easy to show that the new treatment is as good as the existing treatment. Such type
find the expected value of the mean square error and of the mean square reggression
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