The paper investigates the problem of performing correlation analysis when\nthe number of observations is very large. In such a case, it is often necessary\nto combine the random observations to achieve dimensionality reduction of the\nproblem. A novel class of statistical measures is obtained by approximating the\nTaylor expansion of a general multivariate scalar function by a univariate\npolynomial in the variable given as a simple sum of the original random\nvariables. The mean value of the polynomial is then a weighted sum of\nstatistical central sum-moments with the weights being application dependent.\nComputing the sum-moments is computationally efficient and amenable to\nmathematical analysis, provided that the distribution of the sum of random\nvariables can be obtained. Among several auxiliary results also obtained, the\nfirst order sum-moments corresponding to sample means are used to reduce the\nnumerical complexity of linear regression by partitioning the data into\ndisjoint subsets. Illustrative examples are provided assuming the first and the\nsecond order Markov processes.\n