The Application of the Classical Assumption Test in Multiple Linear Regression Analysis (a Case Study of the Preparation of the Allometric Equations of Young Makila)

Abstract

The preparation of allometric equations generally uses multiple linear regression equations. The use of this regression equation is usually not carried out through various tests but goes directly to the t test and F test stages. Therefore, this paper aims to provide an example of determining the regression equation through the classical assumption test stages. Makila (Litsea angulata BI) was chosen as an example because it provides environmental services, especially in dealing with climate change and has not been widely studied. The research method used is a quantitative method. Destructive sampling was taken and the material used consisted of 40 young Makila plants planted in polybags next to the greenhouse at the Faculty of Agriculture, Pattimura University, Ambon. The diameter of each sample was measured from the ground surface to a height of 5 cm and numbered 1 to 40. After being coded, the plant samples were cut down and all young trees were divided into stem segments, branches, twigs, leaves and roots. The root segments were collected carefully to facilitate their separation from the soil in polybags. The parts of the roots that still contain soil are cleaned with a machete and brush until they are free of soil and other dirt. Next, each segment was weighed for its wet weight (in g) and dry weight, thus enabling the determination of the biomass content (in g) for each segment. Data analysis was carried out using the Multiple Linear Regression Equation method. The regression model was examined for normality and suitability in predicting independent variables, ensuring there were no issues with multicollinearity, heteroscedasticity, and autocorrelation. The results of the normality test showed that the significance value for the remaining data was 0.813 > 0.05, indicating normal distribution. TThe results of the multicollinearity test show that there is no multicollinearity problem, this is indicated by the VIF value of the two independent variables (tree diameter and tree height each 1.049) < 10 and the Tolerance value (tree diameter and tree height 0.953 each) > 0.100. The results of the heteroscedasticity test show that the two independent variables have a significance value of more than 0.05. The results of the autocorrelation test show the Durbin Watson (DW) value = 1.956 with a range of 1.65 – 2.35 which means there is no correlation problem. The results yielded a multiple linear regression: Y = -1131.146 + 684.799X1 + 4.276X2, where Y is biomass, X1 is the diameter, and X2 is the tree height. Based on the results of the t-test: variable X1 partially affected Y while variable X2 partially had no effect on Y. The F-test indicated that variables X1 and X2 jointly affected Y with R Square: 0.919 or 91.9% and the rest was influenced by other unexplored factors. To simplify biomass prediction and field measurement, a regression equation that used only 1 independent variable, namely tree diameter, was used for the experiment. Allometric equation only used 1 variable, Y = - 1,084,626 + 675,090 X1, where X1 = tree diameter, Y = Total biomass with R = 0.957, and R square = 0.915. The regression equation for young Makila plant provides assurance that the regression equation obtained is accurate in estimation, unbiased and consistent. This is because in data processing classical assumptions have been tested. This equation can save time, costs and energy, as well as make measurements easier in the field so that future researchers can develop allometric equations in other plants for efficiency.