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Engineering Statistics Handbook Episode 5 Part 7

Tham khảo tài liệu 'engineering statistics handbook episode 5 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 4.I.4.2. Nonlinear Least Squares Regression Due to the way in which the unknown parameters of the function are usually estimated however it is often much easier to work with models that meet two additional criteria 3. the function is smooth with respect to the unknown parameters and 4. the least squares criterion that is used to obtain the parameter estimates has a unique solution. These last two criteria are not essential parts of the definition of a nonlinear least squares model but are of practical importance. Examples of Nonlinear Models Some examples of nonlinear models include Ji Jpt - - http www.itl.nist.gov div898 handbook pmd section1 pmd142.htm 2 of 4 5 1 2006 10 21 54 AM 4.I.4.2. Nonlinear Least Squares Regression Advantages of Nonlinear Least Squares Disadvantages of Nonlinear Least Squares The biggest advantage of nonlinear least squares regression over many other techniques is the broad range of functions that can be fit. Although many scientific and engineering processes can be described well using linear models or other relatively simple types of models there are many other processes that are inherently nonlinear. For example the strengthening of concrete as it cures is a nonlinear process. Research on concrete strength shows that the strength increases quickly at first and then levels off or approaches an asymptote in mathematical terms over time. Linear models do not describe processes that asymptote very well because for all linear functions the function value can t increase or decrease at a declining rate as the explanatory variables go to the extremes. There are many types of nonlinear models on the other hand that describe the asymptotic behavior of a process well. Like the asymptotic behavior of some processes other features of physical processes can often be expressed more easily using nonlinear models than with simpler model types. Being a least squares procedure nonlinear least squares has some of the same advantages and disadvantages that