multivariate regression

Statistical methods are used in the analysis of all types of data. In this paper, using multivariate analysis of variance and multivariate regression, the data related to the thermal conductivity of nanofluids have been analyzed and the results of the two methods have been compared. A two-step method was used to prepare ethylene glycol-magnesium oxide nanofluid. In order to prepare the nanofluid by suspending the nanoparticles in the base fluid, an ultrasonic homogenizer was used. For this purpose, nanoparticles with diameters of 20, 50, and 100 nm in volume fractions of 0.25, 0.5, 0.75, 1, and 1.25% have been used at temperatures of 25, 30, 35, 40, 45, and 50 degrees Celsius. Transient hot wire method was used to measure thermal conductivity in different volume fractions. Then the obtained experimental values were analyzed using SPSS.26 software. The coefficient of determination and the graphs of the errors obtained in the two methods showed that when the independent variables are defined as grouped, the use of multivariate analysis of variance can better describe the dispersion of the thermal conductivity.

Density flows are one of the most important factors in reducing the useful life of water structures, especially reservoir dams. Therefore, researchers have always been investigating solutions to eliminate these flows and increase the useful life of dams. One of the most practical methods known is to build an obstacle in the path of these currents. In this laboratory-numerical study, the effect of trapezoidal permeable obstacle (filled with 0.5 cm diameter grains) on the head of density flow is investigated and the effects of variables such as discharge, concentration, slope and height of the obstacle are studied. Based on the percentage reduction of the density flow head obtained from the experiments, the concentrated salt flow head is modeled using one of the soft computing methods known as the adaptive neural-fuzzy inference system (Anfis). Then, by comparing the results with the classical multivariable regression method, the performance of these two methods is compared. The error of training, validation and test data for the Anfis method are shown to be 0.07, 0.033 and 0.03, respectively, while for the multivariable regression method the mentioned errors are shown to be 0.12, 0.199 and 0.1084, respectively. Also, regression values for the training and test data for the Anfis method, are found to be 0.9954 and 0.9652 respectively whilst for the multivariable regression method, the mentioned parameters are shown to be 0.93108 and 0.90396 respectively which demonstrates the superiority and the efficiency of the adaptive neural-fuzzy inference system in modeling the head data.