Homework3Key

Homework3Key - Spring 2012 STAT 512 HW 3 Key Homework 3 (15...

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Spring 2012 STAT 512 HW 3 Key 1 Homework 3 (15 pts. + 1 pt. BONUS) due Feb. 3 A reminder – Please do not hand in any unlabeled or unedited SAS output. Include in your write-up only those results that are necessary to present a complete solution (what you want the grader to grade). In particular, questions must be answered in order (including graphs), and all graphs must be fully labeled (main title should include the question number, and all axes should be labeled). Don’t forget to put all necessary information (see course policies) on the first page. Include the SAS input for all questions at the very end of your homework; this could be important even though it won’t be graded. You will often be asked to continue problems on successive homework assignments so save all your SAS code. 1. (8 pts.) Consider the following data set that describes the relationship between the rate of an enzymatic reaction (V) and the substrate concentration (C). A common model used to describe the relationship between the rate and the concentration is the Michaelis- Menten model ° = ± ? ² ± ? + ² , where 1 is the maximum rate of the reaction and 2 describes how quickly the reaction will reach its maximum rate. The equation can be rearranged so that ? ° can be written as a linear model with explanatory variable ? ² : ? ° = ? ± ? + ± ? ± ? ? ² The data set is as follows: Concentratio n Rate Concentratio n Rate 0.02 49 0.22 159 0.02 47 0.22 152 0.06 97 0.56 191 0.06 107 0.56 201 0.11 123 1.10 207 0.11 139 1.10 200 Even though we know theoretically what the final equation „should‟ be, let‟s see if we can generate this. SAS Code: data HW3MM; input c v @@; cards ; 0.02 49 0.02 47 0.06 97 0.06 107 0.11 123 0.11 139 0.22 159 0.22 152 0.56 191 0.56 201 1.10 207 1.10 200 ; run ; proc print data =HW3MM; *a; title1 'Problem 1: Transformation of Y' ; data transformY; set HW3MM; vinv = 1 /v; *ai scatterplot; title2 '1/v vs c' ; symbol1 v =circle i =sm77; proc gplot data =transformY; plot vinv*c; run ; *aii residual plot; proc reg data =transformY; model vinv=c; output out =tYout r =residtY; run ;
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Spring 2012 STAT 512 HW 3 Key 2 title2 'residual plot' ; symbol1 i = none ; proc gplot data =tYout; plot residtY*c / vref = 0 ; run ; *aiii normality of residuals; title2 'normal plots of residuals' ; proc univariate data =tYout normal plot ; var residtY; histogram residtY / normal kernel ( L = 2 ); qqplot residtY / normal ( L = 1 mu =est sigma =est); run ; * b *; title1 'Problem 1: Transform X and Y' ; *transform x; data transformXY; set transformY; cinv = 1 /c; proc print data =transformXY; run ; *bi; title2 '1/v vs. 1/c' ; symbol1 v =circle i =sm77; proc gplot data =transformXY; plot vinv*cinv; run ; *bii residual plot; proc reg data =transformXY; model vinv=cinv; output out =tXYout r =residtXY p =predtXY; run ; title2 'residual plot' ; symbol1 i = none ; proc gplot data =tXYout; plot residtXY*cinv / vref = 0 ; run ; *biii normality of residuals;
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Homework3Key - Spring 2012 STAT 512 HW 3 Key Homework 3 (15...

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