Mathematical modeling is a widely used practice in almost all branches of modern science. One of the most popular mathematical methods of statistical analysis and development of simple models is linear regression, which finds application in solving of the vast diversity of practical and theoretical tasks [6, 10]. Agricultural science is not an exception, and linear regression models are also successfully used for satisfying the needs in statistical data evaluation and forecasting . However, nowadays linear regression is considered to be an out-of-date and insufficiently accurate method of modeling the natural processes . Most scientists tend to use some more modern and complicated methods of non-linear and spatial statistics, for example, artificial neural networks, multiple non-linear fuzzy regression analysis with improved calculations algorithm, etc. [1, 2, 4]. But we should take into account that the above-mentioned methods often may not be available and understandable for everyone. So, we decided to prove the efficiency of the linear regression analysis use in agricultural science on the example of modeling safflower seed productivity in dependence on the crop cultivation technology.
The field trials devoted to investigation of safflower productivity in dependence on the cultivation technology treatments were carried out in the period from 2010 to 2012 at the experimental field of the Institute of Rice of the National Academy of Agrarian Sciences of Ukraine. The coordinates of the experimental field are: latitude 46°08′34″N, longitude 32°57′15″E, altitude is 8 m. The trials were carried out with accordance to the common recommendations on scientific work in agronomy  in four replications by using the randomized split plot design method. The study was devoted to investigation of the effect on safflower seed productivity of such cultivation technology treatments as follows:
Cultivation technology of the crop was common for the irrigated conditions of the South of Ukraine excepting the studied factors. The previous crop was winter barley. Primary soil tillage was performed with accordance to the experimental design. Safflower cultivar Soniachnyi was sown by the means of a seed drill at the depth of 5-6 cm. The inter-row spacing width was set with accordance to the design of the trials. The crops were rolled instantly after sowing. Harrowing was performed before the sprouting stage of the crop, and then it was repeated at the stage of 2 leaves of the crop. Two inter-row cultivations were carried out on the plots with wide (60 cm) inter-row spacing. Irrigation of safflower in the trials was performed by using the frontal irrigation machine by maintaining soil moisture at 75-80% level of the field water-holding capacity. Safflower seed yields were harvested by the means of the self-propelled combine harvester “Sampo-130”. The yields volumes were recorded at the standard moisture content in the seeds.
The climate of the zone, where the trials were carried out, is a coastal moderately continental one. It feels great influence of the nearly situated Black Sea. Weather conditions and meteorological indexes were fixed at the local meteorological station installed directly on the experimental field of the Institute. The years of the study were characterized as follows: 2010 – extremely wet, 2011 – moderately dry, 2012 – extremely dry. Weather conditions during the studied period are represented.
The multi-factor analysis of variance (ANOVA) of the crop yields data was performed by using the standard methodology within AgroStat add-on for Microsoft Excel software application [5, 11, 13]. Statistical evaluation was performed for the reliability level of 95%.
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