Weighted Least-squares Regression Research Articles

Modeling thermal processes using the equivalent point method

Evaluation of thermal processes requires accurate treatment of the time-temperature history of exposure. For the Equivalent Point Method (EPM) of thermal evaluation, the effectiveness of five different numerical methods has been assessed for estimation of both the equivalent time and the equivalent temperature. The performance of each method was tested with three simulated data sets. The traditional method of Line Intersections resulted in significant error. Both Least Squares Linear Regression and Least Absolute Value Linear Regression yielded only a slight improvement. By contrast, Nonlinear Least Squares Regression and Weighted Least Squares Regression (WLSR) resulted in excellent estimations with WLSR being easier to use. Error analysis demonstrated accurate predictions of concentration changes for constituents over a wide range of activation energies.

A weighted least-squares fit of the Australian apparent polar wander path for the last 100 Myr

Summary. Recent versions of the Australian apparent polar wander path (APWP) for the late Mesozoic and Tertiary show considerable variation. Re-examination of the Australian igneous data suggests that they are more reliable than assumed by some recent authors. The trajectory of the Australian APWP is defined by fitting the position of a set of poles including both igneous and laterite/overprint data. This allows the dated igneous poles to be used to determine age as a function of distance along the trajectory. Both the trajectory and the age are fitted by means of weighted least-squares regression, and are given approximate confidence limits. Age is best fitted in the Australian case as a linear function of distance along the APWP. This result contrasts with that of Idnurm, who suggested a variable rate of polar wander during the Tertiary. The new APWP is in better agreement with hot-spot data. Dating of New Caledonian laterites by the new APWP gives a result consistent with geological evidence, while dating by reference to Idnurm's path does not. Large non-dipole components or significant true polar wander are not needed to explain the Australian Tertiary APWP.

Another Cautionary Note about R 2 : Its Use in Weighted Least-Squares Regression Analysis

Another Cautionary Note about R 2 : Its Use in Weighted Least-Squares Regression Analysis

Regional Hydrologic Analysis, 2, Model‐Error Estimators, Estimation of Sigma and Log‐Pearson Type 3 Distributions

For a number of cases, weighted and generalized least squares regression procedures were shown by Stedinger and Tasker (1985, 1986) to provide better estimators of the parameters of models of hydrologic statistics as a function of drainage basin characteristics. These procedures require estimation of the true model's standard error of prediction. Evaluated here are three model error estimators for weighted least squares (WLS) regression and two for generalized least squares (GLS) regression. The generalized mean square estimator employed by Stedinger and Tasker (1985) was nearly unbiased, and comparable in accuracy to and easier to compute than the maximum likelihood estimator. GLS and WLS regression estimators of the log‐streamflows' standard deviation are shown to be substantially more accurate than ordinary least squares estimators. Finally, the consequences and impact of nonlognormal streamflows were evaluated. In the cases considered, GLS procedures continued to perform well even when the normality assumption was violated.

Preweaning Survival in Swine: Heritability of Direct and Maternal Effects

Summary The heritabilities of direct and maternal effects on litter survival to weaning (LS) were estimated from records of 1,243 litters of pigs from the Nebraska Gene Pool population born from 1968 to 1981. Heritabilities were estimated by: (1) weighted least-squares regressions of average survival for litters of sons on average survival for litters of their sire, (2) nested analysis of variance with LS fitted to a model including year-line and sire of litter, (3) weighted least-squares regression of average survival for the litter of daughters on the survival of the litter of their dam and (4) nested analysis of variance with LS fitted to a model including year-line and sire of dam of litter. Analyses were conducted with and without adjustment for litter size born. Estimates of the heritability of direct effects from methods 1 and 2 were negative. Adjustment to a common litter size born had no effect. If direct effects are considered to be negligible, as indicated by these analyses, then LS may be considered a trait of the dam. The heritability of maternal effects estimated from daughter-dam regression was .01 +- .02. The estimate of heritability of maternal effects obtained from analysis 4 was .07 + .03. Again, there were no effects from adjustment to a common litter size born. These estimates were not significantly different and the pooled estimate was .03 + .02. These analyses indicate that some additive genetic variance might exist for maternal effects but none for direct effects on LS. Selection for increased survival is not expected to be successful.

DIVIDEND REMITTANCE BEHAVIOR WITHIN THE INTERNATIONAL FIRM: A THEORETICAL AND EMPIRICAL ANALYSIS*

IN THE RAPIDLY GROWING literature on the activities of the international firm, there is a notable absence of quantitative research directed at explaining the dividend remittance behavior of foreign subsidiaries toward domestic parent corporations, except for a few unsuccessful extensions of Lintner's stable payout hypothesis. The inadequacy of this hypothesis to account for the repatriation of foreign subsidiary earnings is not surprising. In the first place, foreign subsidiary dividends are equity transfers within the same international firm, rather than disbursements to individual shareholders who expect a steady dividend flow. Secondly, foreign subsidiaries tend to finance capital expansion through retained earnings. The present study integrates these two points into a well-defined optimizing behavior of the international firm. To be specific, a dividend behavior model is derived from the neoclassical theory of the international firm, subject to the constraint of internal financing. Maximization of global net worth determines the equilibrium stock of fixed assets of each foreign subsidiary in terms of the ratio of the value of output to capital costs. Subsequently, the subsidiary earmarks the portion of current earnings necessary to finance the desired capital accumulation. Any internal funds left over after satisfying capital requirements are remitted to the parent in the form of dividends. In sum, foreign subsidiary dividends are specified as a function of the supply and demand for internal funds, given by current earnings and changes in the ratio of the value of output to capital costs, respectively. Also, the dividend decision is contingent on several policy variables: implicitly, on domestic and foreign corporate tax rates, and explicitly, on capital controls and split foreign tax rates. For the U.S.-owned foreign subsidy, the relationship between dividends and taxes is further determined-on account of tax deferral-by the manner in which the international firm maximizes subsidiary earnings, namely, before or after repatriation to the parent. The model is estimated by fitting weighted least-squares regressions to cross-section data for 1962 on controlled foreign corporations, published recently by the Treasury Department. The dividend equation performs best for manufacturing controlled foreign corporations established in developed countries, when specified according to pre-repatriation view of subsidiary earnings: over four-fifths of the variation in dividend remittances is explained by the equation, and all predetermined variables exhibit correct signs and statistically significant coefficients. As for controlled foreign corporations located in less developed countries, the model fails the statistical tests primarily because of the risky investment climate faced by these subsidiaries as well as because of their heavy reliance on outside funds-contrary to the assumptions of certainty of expectations and internal financing. On the basis of the obtained parameter estimates, the impact of changes in various tax variables on dividends is measured for developed country manufacturing sub-