The newly introduced long staple cotton varieties Giza 89 and Giza 90 and  the relatively older Giza 83 were spun at 30s, 40s, 50s and 60s counts , as well as , each count twisted on 3.4, 3.8, 4.2 and 4.6 twist factors to study  the response of lea strength and regularity to the increasing of twist. The first degree regression models of  linear, logarithmic and power were applied  to define the relation between lea strength and twist factors for every  individual planned count . The test of significant was according to coefficient of correlation (r).In conformity with the insigniificant relations in derived equations of the above regressions ,the second degree polynomial regression was practiced and derived equations achieved significaut relations.The results showed that lea strength increases on the act of adding  twist  beyond to 4.2 twist factor and then reduced at 4.6 twist factor  within the same count . The optimum twist factor was 4.2 for all spun yarns . Equations which were derived on the basis of the statistical polynomial regression could be applied with considerable accuracy on Giza 83 , Giza 89 and Giza 90 spun yarns at the examined twist factors. Yarn regularity was not significantly  affected by increasing twist factor within any one count.