Spearman's rank correlation coefficient is a nonparametric (distribution-free) rank statistic proposed by Charles Spearman as a measure of the strength of an association between two variables. It is a measure of a monotone association that is used when the distribution of data makes Pearson's correlation coefficient undesirable or misleading. Spearman's coefficient is not a measure of the linear relationship between two variables, as some "statisticians" declare. It assesses how well an arbitrary monotonic function can describe a relationship between two variables, without making any assumptions about the frequency distribution of the variables. Unlike Pearson's product-moment correlation coefficient, it does not require the assumption that the relationship between the variables is linear, nor does it require the variables to be measured on interval scales; it can be used for variables measured at the ordinal level. The idea of the paper is to compare the values of Pearson's productmoment correlation coefficient and Spearman's rank correlation coefficient as well as their statistical significance for different sets of data (original -for Pearson's coefficient, and ranked data for Spearman's coefficient) describing regional indices of socio-economic development.

1When fitting spatial regression models by maximum likelihood us- Where maximum likelihood methods are chosen for fitting spatial regres-3 sion models, problems can arise when data sets become large because it is 4 necessary to compute the determinant of an n × n matrix when optimizing the 5 log-likelihood function, where n is the number of observations. As Bayesian 6 methods for spatial regression may also require the handling of the same ma-7 trix, they may face the same technical issues of memory management and 8 algorithm choice. We have chosen here to term the problem we are considering 9 the "Jacobian", although the expression of interest is ln |I − λW|, where | · | 10 here denotes the determinant of matrix ·, I is the identity matrix, λ is a spatial 11 coefficient, and W is an n × n matrix of fixed spatial weights, so the problem 12 perhaps ought to be termed finding the logarithm of the determinant of the 13 Jacobian. In order to optimize the log-likelihood function with respect to λ, 14successive new values of this calculation are required. 15The often sparse matrix of spatial weights W represents a graph of rela- Although it may seem that the computation of the Jacobian is an unimpor-34 tant technical detail in comparison with the substantive concerns of analysts, 35we feel that this review may provide helpful insight for practical research using 36 spatial regression with spatial weights matrices representing spatial processes. 26We continue by defining spatial regression models to be treated here, the 27 data sets to be used for this comparison, and how we, following Higham (2002),

Accurate prognosis of male fertility based on semen measurements is still not straightforward. This study was designed to identify the best predictors of fertility and to develop a multiple regression model predicting fertility using selected parameters of semen analysis. The predictive value of standard semen parameters and selected functional tests were studied in 113 fertile men and in 109 subfertile men whose spouses had a normal infertility workup. Individual semen parameters were evaluated using the receiver operating characteristic curve. Logistic regression based on linear functions of analysed sperm parameters was used to predict the chance of spontaneous conception. Logistic regression modelling revealed that the best prediction of spontaneous conception was obtained using 12 semen parameters: sperm concentration, total progressive motility (A + B), motility grade C or D, normal sperm morphology, defects of: head, acrosome, midpiece and tail, spontaneous acrosome reaction, hypo-osmotic swelling (HOS) test and acid aniline blue test. This mathematical model reached 90.3% accuracy in predicting in vivo conception and 90.8% for its lack. A satisfactory prediction of male fertility was also obtained using only four semen measurements: sperm concentration, total progressive motility (grade A + B), normal morphology, and HOS test; this model correctly identified as fertile 84.1% of those who conceived and identified as subfertile 88.1% of those who did not achieve pregnancy. In conclusion, basic semen analysis and selected functional tests of sperm provide important information regarding male fertility status.

To study urban heat island (UHI), Landsat 5 TM data and in situ measurements of air temperature from nine points in Poznań (Poland) for the period June 2008-May 2013 were used. Based on data from measurement points located in different types of land use, the surface urban heat island (SUHI) maps were created. All available and qualitycontrolled Landsat 5 TM images from 15 unique days were used to obtain the characteristics of land surface temperature (LST) and UHI intensity. In addition, spatial analysis of UHI was conducted on the basis of Corine Land Cover 2006 dataset. In situ measurements at a height of 2 m above ground level show that the UHI is a common occurrence in Poznań with a mean annual intensity of 1.0°C. The UHI intensity is greater during the warm half of the year. Moreover, results based on the remote sensing data and the Corine Land Cover 2006 indicate that the highest value of the mean LST anomalies (3.4°C) is attained by the continuous urban fabric, while the lowest value occurs within the broad-leaved forests (−3.1°C). To re-count from LST to the air temperature at a height of 2 m above ground level (T agl ), linear and non-linear regression models were created. For both models, coefficients of determination equal about 0.80, with slightly higher value for the non-linear approach, which was applied to estimate the T agl spatial variability over the city of Poznań.

Objectives: The aim of the study was to check the quality of computer-assisted sperm analysis (CASA) system in comparison to the reference manual method as well as standardization of the computer-assisted semen assessment. Material and methods:The study was conducted between January and June 2015 at the Andrology Laboratory of the Division of Infertility and Reproductive Endocrinology, Poznań University of Medical Sciences, Poland. The study group consisted of 230 men who gave sperm samples for the first time in our center as part of an infertility investigation. The samples underwent manual and computer-assisted assessment of concentration, motility and morphology. A total of 184 samples were examined twice: manually, according to the 2010 WHO recommendations, and with CASA, using the program settings provided by the manufacturer. Additionally, 46 samples underwent two manual analyses and two computer-assisted analyses. The p-value of p < 0.05 was considered as statistically significant.Results: Statistically significant differences were found between all of the investigated sperm parameters, except for non-progressive motility, measured with CASA and manually. In the group of patients where all analyses with each method were performed twice on the same sample we found no significant differences between both assessments of the same probe, neither in the samples analyzed manually nor with CASA, although standard deviation was higher in the CASA group. Conclusions:Our results suggest that computer-assisted sperm analysis requires further improvement for a wider application in clinical practice.