In the case of a model with p explanatory variables, the OLS regression model writes: Equations for the Ordinary Least Squares regression Maximum likelihood and Generalized method of moments estimator are alternative approaches to OLS. In the case where there are n observations, the estimation of the predicted value of the dependent variable Y for the i th observation is given by: Where Y is the dependent variable, β 0, is the intercept of the model, X j corresponds to the j th explanatory variable of the model (j= 1 to p), and e is the random error with expectation 0 and variance σ². This minimization leads to the following estimators of the parameters of the model: The OLS method corresponds to minimizing the sum of square differences between the observed and predicted values. The vector of the predicted values can be written as follows: where β is the vector of the estimators of the β i parameters, X is the matrix of the explanatory variables preceded by a vector of 1s, y is the vector of the n observed values of the dependent variable, p* is the number of explanatory variables to which we add 1 if the intercept is not fixed, w i is the weight of the i th observation, and W is the sum of the w i weights, and D is a matrix with the w i weights on its diagonal. Y = X (X’ DX) -1 X’Dy Assumptions of the Ordinary Least Squares regressionġ) Individuals (observations) are independent.Ģ) Variance is homogeneous. Levene's test is proposed by XLSTAT to test the equality of the error variances.ģ) Residuals follow a normal distribution. XLSTAT offers several methods to test normality of residulals.
Model residuals (or errors) are the distances between data points and the fitted model. Model residuals represent the part of variability in the data the model was unable to capture. The R² statistic is the part of variability that is explained by the model. So the lower the residuals, the higher the R² statistic. Homoscedasticity and independence of the error terms are key hypotheses in linear regression where it is assumed that the variances of the error terms are independent and identically distributed and normally distributed. magna.When these assumptions are not possible to keep, a consequence is that the covariance matrix cannot be estimated using the classical formula, and the variance of the parameters corresponding to the beta coefficients of the linear model can be wrong and their confidence intervals as well.
#TESTS FOR HOMOSCEDASTICITY IN XLSTAT PLUS#
Ces résultats indiquent que les deux espèces indigènes de zooplancton des lacs patagoniens chiliens sont plus sensibles au pesticide carbendazime que l'espèce standard D. pulex avait une LC₅₀ à 48 hrs de 26,1 μg/l, et D. diabolicus avait une LC₅₀ à 48 heures de 28,1 μg/1, alors que D. magna Straus, 1820, utilisée couramment, ont aussi été utilisées. Parallèlement, des données bibliographiques sur l'espèce D. Les spécimens proviennent du lac Calafquén (sud du Chili) et ont été soumis à des essais biologiques en laboratoire pendant 48 heures à sept concentrations de carbendazime (0-77,70 μg/1), les essais biologiques ont été effectués sur des spécimens adultes.
Le but de cette étude a été de tester la sensibilité de deux espèces communes de zooplancton, Daphnia pulex Ley dig, 1860 et Tumeodiaptomus diabolicus (Brehm, 1935) au fongicide carbendazime. Au Chili, on observe une utilisation accrue de fongicides, en particulier dans le centre et le sud du pays. These results indicate that the two native Zooplankton species of Chilean Patagonian lakes are considerably more sensitive to the pesticide carbendazim, than the species D. pulex had a 48-h LC₅₀ of 26.1 μg/1, and finally D. diabolicus had a 48-h LC₅₀ of 28.1 μg/1, while D. In parallel, also literature information on the commonly used D. The specimens came from Lake Calafquén (southern Chile), and were subjected to bioassay experiments under laboratory conditions over 48 h to seven carbendazim concentrations (0-77.70 μg/1) these bioassays were performed using adult specimens. The aim of this study was to test the sensitivity of two common Zooplankton species, Daphnia pulex Ley dig, 1860 and Tumeodiaptomus diabolicus (Brehm, 1935) to the fungicide carbendazim. In Chile there is an increased use of fungicides, especially in the central and southern parts of the country.
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