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This 7 page Class Notes was uploaded by Dorris Borer on Monday September 28, 2015. The Class Notes belongs to ESE302 at University of Pennsylvania taught by Staff in Fall. Since its upload, it has received 6 views. For similar materials see /class/215455/ese302-university-of-pennsylvania in Electrical Engineering at University of Pennsylvania.
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Date Created: 09/28/15
SYSTEMS 302 LECTURE 22 0 MULTICOLINEARITY PROBLEM 0 Correlation Analysis 0 Variance In ation Factors 0 STEPWISE REGRESSION 0 Forward Method 0 Mixed Method 0 ADDITIONAL DIAGONOSTICS 0 Heteroscedasticity 0 Autocorrelation 0 PROJECT DUE DATE Tuesday May 12 STUDENT PERFORMANCE PROBLEM It is sometimes argued by students and even professors that nal exams are unnecessary because they have little effect in changing students grades This claim can be tested by constructing a regression which predicts nal exam performance from midtermexam performance DATA Grading records have been obtained for a representative course with 29 students where a single midterm and nal exam were given This data includes the nal exam score E midterm exam score M 1 and average homework score H 1 for each student 1 1 29 ANALYSIS Consider the following two regressions E 280 81Ml 81 i1n F 2180 181Mi182Hi 8i 7 i1 n MULTICOLINEARITY PROBLEM 0 PERFECT M ULTICOLINEARITY 3 A Vertical Plane Regression Line 39 x 9 O COEFFICIENT INSTABILITY Regression Line 3 SYSTEMS 302 LECTURE 24 0 AUTOCORRELATION PROBLEM o DurbinWatson Test 0 TwoStage Regression Approach 0 AuxiliaryVariable Approach 0 REGRESSION OUTLIERS 0 Cook s Distance 0 For next time o Logistic Regression Notes SALES FORCASTING PROBLEM One of the oldest economic laws is that increased income leads to increased expenditures This time honored relation can be tested for the US by regressing retail sales against per capita income for a number of years DATA In a study of T 15 years data was collected from 1965 to 1980 on per capita retail sales SALESI t1T per capita income PCIt t 1 T and the unemployment rate UR t 1T the US ANALYSIS Consider the two regression models SALESI 80 81PCIt 8 t1T SALESI 80 BIPCIt BZUR et t1T GENERAL TWOSTAGE ESTIlVIATION MULTIVARIATE LINEAR MODEL k 1 y 0 Z x 5 tLT 2 Efzpatilaf t2T STEP 1 Do a multiple regression to estimate 1 If Pvalne in Dnrbin Watson test is small say lt 05 continue STEP 2 Set 3 equal to the Antocorrelation value in JMPIN STEP 3 Estimate the transformed variables 3 Etzyf yH t2T 4 wix 3xy1 t2T i1k STEP 4 D0 multiple regression to estimate new linear model 5 2a0zl iwnu t1T STEP 5 Use yw k from Step 4 to estimate 1 k in 1 and use 640 from Step 4 plus p in Step 2 to estimate o in 1 by 6 o 6 01 COOK S DMEASURE FOR OUTLIERS Given a regression of Y on x1xk using data set yjx1xgj 1n if sis the root mean square error and if A Y regression prediction of E Y1 x1xg if 139 regression prediction of E Y1 x1 xkj with the 1397quot h It data pomt yix1ixkl removed then Cook s Distance Measure for point 1 is de ned by aquot i kDf 2419 19112 Data point 1 is then considered to be a statistical outlier whenever the following Rule of Thumb holds DZ n wn
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