In order to identify the Correlations and relationships between different traits in the bread wheat, 30 genotypes were investigated as sub-factors under the split plot experiment in the completely randomized design in greenhouse and the randomized complete block design in the field with three replications under the normal irrigation and post-anthesis water stress conditions. The results of the canonical Correlation analysis showed that at both normal and moisture stress levels, there was a significant Correlation between the pair of canonical variables obtained from the phenological traits and the yield components. Under the normal conditions in the greenhouse, to increase the spike density and length, the number of days to 50% flowering can be considered as a suitable selection criterion. According to the results of canonical Correlation analysis, under the stressed conditions in greenhouse, to increase the spike length, the number of days to the heading, maturity and 50% of flowering were among the important and effective factors. Under the optimum irrigation conditions in the field, the number of days to maturity was considered as one of the factors influencing the seed weight per spike. The results of canonical Correlation analysis under the field stress conditions showed that to increase the 1000-seed weight, the number of days to maturity can be considered an appropriate selection criterion.

Understanding dependence structure and relationship between two sets of variables is of main interest in statistics. When encountering two large sets of variables, a researcher can express the relationship between the two sets by extracting only finite linear combinations of the original variables that produce the largest Correlations with the second set of variables.When data are continuous functions of another variable (generally time), the methods of multivariate analysis cannot be applied to the data. Therefore, some theoretical justification is needed to provide the required definitions and concepts regarding the essential nature of the data. This leads to difining canonical Correlation for pairs of random functions called functional canonical Correlation (FCCA).If the data related to functional phenomena, are observed discretely, the first task is to convert these observations to appropriate curves. This is due to functional nature of the phenomena that the data related to. On the other hand, the functional quantity of interest may be measured with error. In such cases, we should first remove the observational error bay taking a smoothing procedure to account. In this paper, Iranian weather data, collected in 2006, are treated by using FCCA. The data set contains discret measurment’s of three phenomena: temperature, humidity and precipitation and was collected from 102 weather stations. we have fitted continuous curves to the original data, and then extrated the Correlation patterns between each pair of the three phenomena.