Normally and homoscedastic
distributed continuous variables were tested with student's t test, while non-normally distributed variables were log-transformed or assessed with Mann-Whitney U test.
In the case where data was not homoscedastic
, we applied the Kruskal-Wallis ranks' test with a 0.05 of significance.
We transformed the data of the matrices A and B (log x + 1) and applied the tests of Shapiro-Wilk and Cochran to evaluate if the data were normal and homoscedastic
, respectively, what was confirmed.
Where, Yi* is the dependent variable which displays the measure of household poverty with subscription i which shows specific household, [alpha] stand for the model intercept, Xk are the independent variables used in the model, while k embodies the specific explanatory variable that effect the poverty status of the farm household i; [beta]k are the parameters to be projected and ui is the error term which is normally distributed and homoscedastic
(Zero mean and constant variance (Schmidheiny, 2013).
[epsilon], were random, had a normal distribution and were homoscedastic
, and that x was measured without error.
In the GLS method, the error terms are said to be homoscedastic
and the derived estimators under GLS would be unbiased (Greene, 2003).
All data groups were first checked to avoid violation of the linearity and homoscedastic
assumptions of simple linear regression by interpreting residual plots and histograms of residuals constructed using residPlot from the Fisheries Stock Assessment package (Ogle 2016) and Shapiro--Wilk's test assessed normality.
Since the [delta] values were not normally distributed, nor homoscedastic
, but exhibited the same one-tailed shape, a non-parametric Kruskal-Wallis Rank Sum and Multiple Comparison tests were conducted using R software to determine if there are significant differences (p < 0.05) in the mean distances to nearest restaurant within each SDI level (Low, Moderate and High).
Another practical problem arises when, in homoscedastic
specifications of the model, the implied ce becomes sufficiently large to cause [[sigma].sub.v] < 0, which violates the assumptions of the econometric theory.
Thus, it is desired to adjust nonlinear models with homoscedastic
and heteroscedastic errors in order to evaluate each ground cover system, taking the number of thrips as response.
The assumptions of the simple moderation model in question are the same as those of the multiple linear regression model: independent, homoscedastic
and normally distributed residuals.