In this formula r_{ab} means correlation coefficient between A and B, etc.; σ_{a} means standard deviation of A. Substituting, we get: A equals ((+.87 − .53)/(.65))((2.1)/(3.0))B − ((−.89 + .51)/(.65))((2.1)/(2.55))C or, A equals .37B − .49C [Illustration: Chart III. Cycles of hog prices secured by dividing the percentage deviation of actual prices from the secular corrected seasonally, by the standard deviation. ] [Illustration: Chart IV—Cycles of hog receipts, secured by dividing the percentage deviation from secular trend corrected seasonally, by the standard deviation. ] [Illustration: Chart V—Cycles of bank clearings outside of New York City, secured by dividing the percentage deviation from the secular trend corrected seasonally, by the standard deviation. ] Applying this formula, we find that when C is +2 and B is −5, as in the year 1901, we would expect A to be −2.83, and when C is +3 and B is +1, as in 1902, we would expect A to be −1.1. In like manner, in 1903, we would expect A to be +2.60 and in 1904 +1.35. The results expressed in a table are: ════╤════════╤══════════════════════════════════════ │Actual A│A as predicted by formula from B and C ────┼────────┼────────────────────────────────────── 1901│ −3│ −2.83 1902│ −1│ −1.10 1903│ +2│ +2.60 1904│ +2│ +1.35 ────┴────────┴────────────────────────────────────── The practical problem is to express hog prices in terms of hog receipts and bank clearings. Practically the same method is used with the 168 months from 1903 thru 1916, as with the four years which have just been used for illustration. The standard deviations are 10.1 for hog receipts, 10.5 for hog prices and 9.8 for bank clearings. The correlation coefficients are +.39 between hog prices and bank clearings, +.26 between hog receipts and bank clearings, and −.4 between hog receipts and hog prices. Using the formula: A equals r((σ_{a})/(σ_{b}))B and allowing A to represent hog prices and B to represent bank clearings, we get: Hog prices equal .39((10.5)/(0.8)) bank clearings, or Hog prices equal .417 bank clearings This formula is converted back into percentage departures from secular trend modified seasonally, and finally into hog prices as affected by bank clearings. The demand, or bank clearing, price, of hogs as compared with the actual is shown in Chart VI. In like manner we get: Hog prices equal −.4((10.5)/(10.1)) hog receipts, or Hog prices equal −.426 hog receipts