hypothesis the method of least squares utilizes jointly the information contained in all of the separate data points statistical significance of the curvilinearity of the regression model establishes the existence of synergism or antagonism of the compounds in the biological system studied the parameters in the model describe its intensity over the range of mixture ratios from 0 to 1 the nature of which is seen readily when the regression is plotted on the isobologram this method was used to determine the best fitting ed50 regression line through the seven 7 or eight 8 ed50 data points representing equivalent levels of analgetic activity for each of the five 5 or six 6 dose ratios for nalbuphine and 4 5 bis 4 methoxyphenyl 2 trifluoromethylsulfonyl 1h imidazole given in tables i and ii as shown in both of the isobologram plots fig1 and 2 the calculated quadratic polynomial 34 ed50 regression line 34 fits the data significantly better than the straight 34 ed50 addition line 34 as established by fisher 39 s f test statistically significant at p u2266 0 05 to compare the goodness of fit between the straight line and curvilinear regressions thus consistent with loewe 39 s isobolographic model the hypothesis of analgetic additivity is refuted and analgetic synergism is established for all combinations of nalbuphine and 4 5 bis 4 methoxyphenyl 2 trifluoromethylsulfonyl 1h imidazole by substitution of the expected analgetic activity of nalbuphine alone and 4 5 bis 4 methoxyphenyl 2 trifluoromethylsulfonyl 1h imidazole alone from.