Correlation and regression analysis in barley

ABSTRACT: Two field experiments were carried out at the Experimental Station, Faculty of Agriculture, Cairo University, during the two successive winter seasons of 2008/09 and 2009/10. Six cultivars were grown in a randomized complete blocks design with three replications and evaluated for eight characteristics. Combined analysis of variance was done from the mean data obtained for each characteristic over two seasons and correlation and regression analysis were carried out to better understand the relationship between yield and some yield components. Results indicated that seasons significantly affected all traits and interaction between seasons and cultivars was also significant. Highly significant differences and adequate genetic variability were observed among cultivars for all the eight characters. The results of the correlation coefficients of traits with grain yield revealed that the grain number per spike (r=0.84**), grain weight/spike (0.87**), 1000-grain weight (r=0.88**), number of spikes per square meter (r=0.68*) and spike length (r=0.67*) had the highest significant positive correlation with grain yield, indicating dependency of these characters on each other. Heading date was negatively and highly correlated with number of spikes per square meter (r= - 0.58*), number of grains per spike (r= - 0.87**), grain weight per spike (r= - 0.89**), thousand grain weight (r= - 0.87**) and spike length (r= - 0.75**). The criteria used in identifying the best subsets are based on monotone functions of the residual sum of squares (RSS) such as R2, adjusted R2 and Mallow’s Cp. Results revealed that the best subset regression model, based on the three different criteria, the predicted equation for barley grain yield per fed (Y) was Y = 3.12 – 0.006 x1 – 0.019 x2 + 0.0007 x3 + 0.020 x6 – 0.149 x7. The simplified results from best subset regression analysis show that the highest coefficient of determination (R2=96.5%), adjusted R2 (93.6%) and lowest Mallowsʹ conceptual predictive (Cp) value (5.8), and has five-independent variable model with all variables except number of grain per spike (X4) and grain weight per spike (X5). The Best Subset Multiple Regression analysis indicates that adding the variable number of grain per spike (X4) and grain weight per spike (X5) does not improve the fit of the model.