*2.5. Statistical Analyses*

The work uses meteorological data on a year-round scale to generate a real drop in potato yields under the influence of climate change. An earlier prediction of the outbreak of the disease epidemic and an appropriately earlier response to the epidemic of potato blight, which is the cause of a significant drop in the potato yield, is possible thanks to the use of a simulator of records of adverse events in several localities by comparing modeled and observed events over a period of strong intensification of unfavorable meteorological conditions [27].

Based on the analysis of the size of yield characteristics and the course of the weather, the variability of the potato cultivation area, yielding and harvest was determined. Moreover, the partial models of the usefulness of the simulation of atmospheric conditions in the period of 20 years for this region were presented, comparing the observed cases. For this purpose, a combination of statistical methods and simulation modeling was used by using modeling techniques. The forecasts were developed for the same data model using classical statistical methods. Based on the analysis of the size of the cultivation, yield, harvest of potatoes and the course of the weather, a model for forecasting potato yielding in this part of Poland was searched. It was based on empirical data from 2000 to 2019 [28–31].

The variability of the analyzed yield characteristics and meteorological data was analyzed mainly by means of descriptive statistics (SPSS). On the basis of the diversified course of meteorological conditions during the growing season, an attempt was made to estimate the area of potato cultivation, its yield and harvest by means of a multivariate regression analysis, assuming weighted averages of selected meteorological elements for the examined localities (Table 1). The models used agronomic, phenological and meteorological data, and the correctness of their impact was verified on the basis of data sets not involved in the construction of the models.

Since the magnitude of a given phenomenon is influenced by many simultaneous factors, an attempt was made to build a model forecasting the area and harvest of potato. Such a prediction methodology is useful for optimizing the responses of the independent variables. In this case, the increase in variable y is a response and a function of the yield and the cultivated area. This function can be expressed with the following general formula.

$$\mathbf{y} = \mathbf{f}(\mathbf{x}, \mathbf{x}) + \mathbf{e},\tag{1}$$

It was assumed that the variables xj are the predictors on which the answer y depends. The dependent variable y is a function of xj and xj2, and the experimental error was denoted by e, which means any measurement error [19]. In order to determine the dependence of potato yield on meteorological indicators, a multivariate regression analysis was used, the parameters of which were determined by the least squares method. As a measure of adjusting the regression function to empirical data, the coefficient of determination R2 was used [27]. Regression analysis models were computed according to the following general formula:

$$\mathbf{y} = \mathbf{a} + \mathbf{b}\mathbf{j}\mathbf{x}\,\mathrm{j}\tag{2}$$

where y denotes the dependent variable, a denotes intercept, b denotes the value of the regression coefficient and x denotes independent variable. Partial regressions were used to examine quantitative relationships between the potato yield and individual independent variables. Partial regression coefficients (bj) indicate how much the yield changes as a given factor increases by a unit. The described relationships were considered in terms of the standard deviation from the arithmetic mean [27]. All statistical analyses were performed using SAS 9.1.

The results of the blight tests were statistically analyzed using the analysis of variance. The significance of the sources of variation was determined by the "F" Fisher–Snedecor test, and the significance of the differences was determined by Tukey's test [19]. The rate of spread of potato blight as a function of the date of observation was calculated by regression calculus. The observation dates were coded for the calculations, taking the first date as "0", the second as "10" and the third as "20", etc. Leaf infection was expressed in logarithmic values corresponding to 9◦ degrees of the scale and using the van der Plank formula [26]:

$$\mathbf{y} = \log \frac{\mathbf{x}}{1 - \mathbf{x}},\tag{3}$$

where x denotes the values expressed in one hundred parts. They make it possible to express the percentage of damage to the leaf surface in the form of a straight line. The rate of spread of potato blight was considered to be a unit increase in infection over time.
