File:Statistical studies in the New York money-market; preceded by a brief analysis under the theory of money and credit, with statistical tables, diagrams and folding chart (1902) (14757728326).jpg

Identifier: statisticalstudi00nort (find matches)
Title: Statistical studies in the New York money-market; preceded by a brief analysis under the theory of money and credit, with statistical tables, diagrams and folding chart
Year: 1902 (1900s)
Authors: Norton, John Pease, 1877-
Subjects: New York Stock Exchange Credit Money
Publisher: New York, MacMillan
Contributing Library: Robarts - University of Toronto
Digitizing Sponsor: University of Toronto

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eks, is extremely well fitted by a straightline. § 58. To determine the slopes of these lines, it is firstnecessary to calculate the coefficient of correlation. Thecoefficient of correlation has for its mathematical formula theexpression, _SZ(X-MX)(Y-My) Z = frequency of deviations (X —M;r) and (Y —My) from themeans Mx and Mj/ in the total number of observations N.o-x = standard deviation of the X series and <ry = standarddeviation of the Y series. In words, r is simply the quotientof the weighted average of the moments about the centre ofgravity of the system (i. e. the point of intersection of the twomeans), divided by the product of the two standard deviations. In perfect correlation r = 1. If no correlation exists, r=o. To illustrate this formula in the calculation of the coeffi-cient of correlation for the ratio of reserves to deposits andcall discounts for 780 weeks, the numerical values for theletters in the formula are as follows. The value of 2, the * Vol. 67, p. 164.
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■3S -3D -as -ao -15 -10 * OT Diao-ra^n No. l(p. _83— sum of the weighted moments, is 4,387.5. The number ofweeks (N) is 780. The standard deviation of the discountrate (aa) is 2.5429 with the standard deviation of the ratio(oV) 4.2228. Inserting these values in the formula 4,387.5000r = • = o. *i2\\ +0.014.2. (780) (2.5429) (4.2285) 5 3 ± 4 Thus r (0.5231) with a probable error* of 0.0142 is thequantitative index which measures the degreef of correlationexisting between the ratio of reserves to deposits and thecall discount rate, on the basis of 780 weeks of experience. ^59. In Diagram No. 15, the intersection of the means forthe whole array of 780 weeks is marked A. The recordswere split at the mean of the ratio of reserves to deposits(29.8), and the number of weeks below the mean was foundto be 488, and above the mean 292. The mean of the greaternumber of weeks is marked B upon the chart, and the meanof the minor number of weeks is marked C. Now the best fitting straight line

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