It has long been recognized that the least-squares estimation method of fitting the best straight line to data points having normally distributed errors yields identical results for the slope and intercept of the line as does the method of maximum likelihood estimation. We show that, contrary to previous understanding, these two methods also give identical results for the standard errors in slope and intercept, provided that the least-squares estimation expressions are evaluated at the least-squares-adjusted points rather than at the observed points as has been done traditionally. This unification of standard errors holds when both x and y observations are subject to correlated errors that vary from point to point. All known correct regression solutions in the literature, including various special cases, can be derived from the original York equations. We present a compact set of equations for the slope, intercept, and newly unified standard errors.

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The sorption of lead and cadmium from aqueous solutions by grape stalk waste (a by-product of wine production) was investigated. The effects of the contact time, pH of the solution, ionic medium, initial metal concentration, other metal ions present and ligands were studied in batch experiments at 20 degrees C. Maximum sorption for both metals was found to occur at an initial pH of around 5.5. The equilibrium process was described well by the Langmuir isotherm model, with maximum grape stalk sorption capacities of 0.241 and 0.248 mmol g(-1) for Pb(II) and Cd(II), respectively, at pH around 5.5. Kinetic studies showed good correlation coefficients for a pseudo-second-order kinetic model. The presence of NaCl and NaClO(4) in the solution caused a reduction in Pb and Cd sorption, the latter being more strongly suppressed. The presence of other metals in the uptake process did not affect the removal of Pb, while the Cd uptake was much reduced. HCl or EDTA solutions were able to desorb lead from the grape stalks completely, while an approximately 65% desorption yield was obtained for cadmium. From the results obtained it seems that other mechanisms, such as surface complexation and electrostatic interactions, must be involved in the metal sorption in addition to ion exchange.

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