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Unformatted text preview: 4/4/2010 http://numericalmethods.eng.usf.edu 1 Adequacy of Regression Models http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates Data-350-300-250-200-150-100-50 50 100 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 x y y vs x Is this adequate?-350-300-250-200-150-100-50 50 100 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 x y y vs x Straight Line Model Is this adequate?-350-300-250-200-150-100-50 50 100 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 x y y vs x Second Order Polynomial Model Which model to choose?-350-300-250-200-150-100-50 50 100 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 x y y vs x Quality of Fitted Data Does the model describe the data adequately? How well does the model predict the response variable predictably? Linear Regression Models Limit our discussion to adequacy of straight-line regression models Four checks 1. Plot the data and the model. 2. Find standard error of estimate. 3. Calculate the coefficient of determination. 4. Check if the model meets the assumption of random errors. Example: Check the adequacy of the straight line model for given data T (F) α ( μ in/in/F)-340 2.45-260 3.58-180 4.52-100 5.28-20 5.86 60 6.36 T a a 1 + = α END 1. Plot the data and the model Data and model T (F) α ( μ in/in/F)-340 2.45-260 3.58-180 4.52-100 5.28-20 5.86 60 6.36-350-300-250-200-150-100-50 50 100 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 T α T T 0096964 . 0325 . 6 ) ( + = α END...
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