Prediction Error Sum Of Squares Research Articles

Psychophysical modelling of lifting capacity of Chinese males using strength variables

This study used the psychophysical approach to determine the maximum acceptable weight of lift (MAWL) for 12 young Chinese male subjects, and used strength variables as predictors to develop prediction models. Each subject performed 12 different lifting tasks involving three lifting heights and four lifting frequencies. The results showed that both the dynamic and static models developed in this study could predict the MAWL with a reasonable degree of accuracy. However, a comparison of the models revealed that the use of the dynamic model resulted in less PRESS ( PRediction Error Sum of Squares) statistics and higher R 2 values than the static model. Isoinertial 1.83 m maximum strength (T1) and the isoinertial elbow-height strength, tested on an incremental weightlifting machine, were found to be the best screening test. This was different from a previous study that recommended T1 as the most promising single screening test for Occidentals.

A comparison of methods for linear prediction of apple flavour from gas chromatographic measurements

A comparative study of linear methods for prediction of sensory profiles from gas chromatography (GC) measurements was performed. The data used came from an experiment on the effect of storing apples at various oxygen concentrations. Partial least-squares regression and continuum regression showed the best performance, measured by a two-step cross-validation principle. The traditional prediction error sum of squares (PRESS) overestimated the predictive ability of a multiple linear regression approach. The quality of the predictions of sensory properties from GC analyses was measured in terms of a ‘panel size equivalent’. Thus, the predictions obtained in the present study were as accurate as predictions from an assessor panel consisting of 4–9 assessors, depending on the sensory property in question.

Selecting Regressors for Prediction Using PRESS and WhitetStatistics

It is shown that selecting regressors based on the prediction error sum of squares is asymptotically related to hypothesis testing with White's (1980) heteroscedasticity-consistent covariance matrix. A simulation experiment suggests that this asymptotic relation may be useful. Illustrative examples are also given.

On the predictive performance of biased regression methods and multiple linear regression

Kowalski, K.G., 1990. On the predictive performance of biased regression methods and multiple linear regression. Chemometrics and Intelligent Laboratory Systems, 9: 177–184. The predictive performance of three commonly used biased regression methods (ridge, principal components and partial least squares) and multiple linear regression (ordinary least squares) using classical model selection techniques are evaluated on five data sets published in the chemical and statistical literature. For these five data sets, the degree of collinearity among the regressors varies considerably. For each data set, cross-validation is performed and the prediction error sum of squares (PRESS) is computed to assess the predictive performance of each method. The results show that multiple linear regression using reduced models obtained by classical methods of model selection performed better (lower PRESS) than the three commonly used biased regression methods.

Calibration modeling by partial least-squares and principal component regression and its optimization using an improved leverage correction for prediction testing

Marbach, R. and Heise, H.M., 1990. Calibration modeling by partial least-squares and principal component regression and its optimization using an improved leverage correction for prediction testing. Chemometrics and Intelligent Laboratory Systems, 9: 45–63. In this paper the different approaches to quantitative analysis of spectroscopic data which are classified by their model building and parameter estimation strategies are summarized. The algorithms of principal component regression (PCR) and partial least-squares (PLS) have been proposed for solving ill-posed regression problems according to the minimum mean-square error (MSE) criterion. The latter can be favoured on the grounds of numerical and statistical properties; PLS provides a consistent estimator of the MSE-optimal predictor (Wiener filter). For model optimization, the leverage correction is discussed for approximating Allen's predicted error sum of squares (PRESS) statistic with biased generalized inverses provided by the PCR or PLS algorithms (application of an analogous Sherman—Morrison formula to rank-deficient inverses). Using some experimental examples, a means of evaluating the approximation error of the leverage correction is proposed.

Energy cost models for combined lifting and carrying tasks

Experiments were conducted on ten physically fit male subjects (age group—24.1 ± 3.35 years, body weight—78.43 ± 5.77 kg) to determine their metabolic responses to combined manual materials handling tasks, viz., lifting and carrying. A setup using a modified treadmill was employed to simulate these tasks. Oxygen uptake (V o 2 , l/min) and heart rate (HR, beats/min) were the response variables, whilst a number of task related parameters: load handled, height of lift, frequency of handling, carrying distance and load width, were manipulated using a rotatable central composite design. Energy cost equations were established for combined handling tasks under two height ranges of lift, floor to a height of 150 cm and 75 cm (table height) to a height of 150 cm. The models were compared with responses for individual handling tasks and validated using the “Prediction Error Sum of Squares”. The most stressful task appeared to be the one in which a load (even as low as 13 kg) was lifted from the floor the shoulder height and then carried over distances exceeding 3 m at relatively low frequencies. It was also established that the net metabolic energy expenditure for combined tasks cannot be estimated by summing the net steady state metabolic costs for individual task components.

Generalizing biomass equations for the boreal forest region of west-central Canada

Living tree dry weight estimates are needed for resource inventories and are usually predicted by using equations based on tree diameter and height for each species. Two procedures (prediction error sum of squares (PRESS) and covariance analysis) were used to assess errors in prediction when local regression equations were combined to form generalized regional equations for wide application. The tests showed that it was possible to derive generalized regional equations based on sampling of similar stands distributed extensively over well-defined vegetation regions in west-central Canada.