Correlation and Regression Analysis
correlation & regression (students).ppt (Size: 656 KB / Downloads: 104)
Many engineering design and analysis problems involve factors that are interrelated and dependent. E.g., (1) runoff volume, rainfall; (2) evaporation, temperature, wind speed; (3) peak discharge, drainage area, rainfall intensity; (4) crop yield, irrigated water, fertilizer.
Due to inherent complexity of system behaviors and lack of full understanding of the procedure involved, the relationship among the various relevant factors or variables are established empirically or semi-empirically.
Regression analysis is a useful and widely used statistical tool dealing with investigation of the relationship between two or more variables related in a non-deterministic fashion.
Least Square Criterion
What are the values of b0 and b1 such that the resulting line “best” fits the data points?
But, wait !!! What goodness-of-fit criterion to use to determine among all possible combinations of b0 and b1 ?
The least squares (LS) criterion states that the sum of the squares of errors (or residuals, deviations) is minimum. Mathematically, the LS criterion can be written as:
Any other criteria that can be used?