Midterm Revision MH3510
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This 3 page Study Guide was uploaded by Andre Sõstar on Thursday October 1, 2015. The Study Guide belongs to MH3510 at Nanyang Technological University taught by TBA in Summer 2015. Since its upload, it has received 37 views. For similar materials see REGRESSION ANALYSIS in Applied Mathematics at Nanyang Technological University.
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I was sick all last week and these notes were exactly what I needed to get caught up. Cheers!
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Date Created: 10/01/15
MH351O Regression Analysis Nanyang Technological Univeristy Instructor Pan Guangming notes Andre Sostar October 17 2015 1 Revision for midterm 11 Simple Linear Regression The simple linear regression SLR model is y 60 lm 393 Where y is a response variable and a is a predictor variable Which both are given We want to estimate 60 and 61 For that we use formulas SJ 505 y 5031 51337 Where 2 2 Sm E 332 na 525 TL 3 32 TL To nd R2 we use the formula SSR SW 7 where SSR means regression sum of squares and SW is total sum of squares which are found respectively SSR m2 82121 W2 As simple linear regression has only one regression coef cient F test becomes F 752 To determine if model is statistically signi cant we use con dence interval which is found by A 91 Ii t8 61 Since H0 bl 0 we check if 0 is in the interval If it is we fail to reject H0 ie 1 has no effect on Otherwise reject H0 ie 1 has an effect on To nd the standard error we use SSE 92 7 n 1 where SSE 02 30 31 12 Multiple Linear Regression Simple linear regression is a special case of a multiple linear regression The regression model is 3505115226n33n6 We want to estimate bi s This time we have to use linear algebra as we are given with the matrixes X X7 X Y7 X X1 and Y Y To nd the vector of Ms we have to use the formula 8 X X 1X Y which is an matrix multiplication To nd standard errors we have to use the formula 368239 3V XIXi 11i17 which are matrix diagonal entries To nd 8 we use 8 SSE n p 1 and SSE Y Y Y X X X1X Y v Svector To construct a ttest with certain level of signi cance A 673 012 lt t 8645 quot1 we can not reject 673 012 86m npl reject
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