STATISTICA MATEMATICA 1 A.A. 2006/07 LABORATORIO DI SAS A. MICHELETTI
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1 STATISTICA MATEMATICA 1 A.A. 2006/07 LABORATORIO DI SAS A. MICHELETTI LEZIONE 5: REGRESSIONE Procedura Reg REGR1.SAS proc reg data=mylib.taranto; model lungmg=altmg; plot r.*p.; /* grafico dei residui risp. a previsti */ run; /* disegno la retta di regressione */ goptions device=win; symbol1 i=rl v=star; title 'retta di regressione'; proc gplot; plot pesomg*altmg; run; The SAS System 14:44 Tuesday, November 30, Model: MODEL1 Dependent Variable: lungmg Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var Parameter Estimates Parameter Standard Variable DF Estimate Error Valore t Pr > t Intercept <.0001 altmg <
2 /* disegno la retta di regressione */ goptions device=win; symbol1 i=rl v=star; title 'retta di regressione'; proc gplot data=mylib.taranto; plot pesomg*altmg; run; 2
3 REGR2.SAS proc reg data=mylib.taranto; model pesomg=altmg lungmg; plot pesomg * p.; /*grafico val. osservati risp. a valori previsti */ plot r.*altmg; /* grafici dei residui rispetto ai regressori*/ plot r.*lungmg; plot npp.*r.; /*normal probability plot dei residui*/ run; quit; 3
4 MODALITA.SAS data a; filename dati1 'E:\didattica\aa04-05\statmat1\spaz3.dat'; infile dati1; input z temp salinity do ph x y; xy=x*y; x2=x*x; y2=y*y; cards; proc reg; model do=x y xy x2 y2 / selection=forward; 4
5 model do=x y xy x2 y2 / selection=backward; model do=x y xy x2 y2 / selection=stepwise; model do=x y xy x2 y2 / selection=maxr; run; quit; The SAS System 15:28 Tuesday, November 30, Model: MODEL1 Forward Selection: Step 1 Variable y2 Entered: R-Square = and C(p) = Model <.0001 Error Intercept <.0001 y <.0001 Bounds on condition number: 1, 1 Forward Selection: Step 2 Variable x2 Entered: R-Square = and C(p) = Model <.0001 Error The SAS System 15:28 Tuesday, November 30, Model: MODEL1 Forward Selection: Step 2 5
6 Intercept <.0001 x <.0001 y <.0001 Bounds on condition number: , Forward Selection: Step 3 Variable xy Entered: R-Square = and C(p) = Model <.0001 Error Intercept <.0001 xy x <.0001 y Bounds on condition number: , Forward Selection: Step 4 Variable y Entered: R-Square = and C(p) = The SAS System 15:28 Tuesday, November 30, Model: MODEL1 Forward Selection: Step 4 Model <.0001 Error
7 Intercept <.0001 y xy x <.0001 y Bounds on condition number: , No other variable met the significance level for entry into the model. Summary of Forward Selection Variable Number Partial Model Valore Step Entered Vars In R-Square R-Square C(p) F Pr > F 1 y < x < xy y The SAS System 15:28 Tuesday, November 30, Model: MODEL2 Backward Elimination: Step 0 All Variables Entered: R-Square = and C(p) = Model <.0001 Error Intercept <.0001 x y xy x y Bounds on condition number: , Backward Elimination: Step 1 7
8 Variable x Removed: R-Square = and C(p) = Model <.0001 Error The SAS System 15:28 Tuesday, November 30, Model: MODEL2 Backward Elimination: Step 1 Intercept <.0001 y xy x <.0001 y Bounds on condition number: , Backward Elimination: Step 2 Variable y Removed: R-Square = and C(p) = Model <.0001 Error Intercept <.0001 xy x <.0001 y Bounds on condition number: , Backward Elimination: Step 3 8
9 Variable xy Removed: R-Square = and C(p) = The SAS System 15:28 Tuesday, November 30, Model: MODEL2 Backward Elimination: Step 3 Model <.0001 Error Intercept <.0001 x <.0001 y <.0001 Bounds on condition number: , All variables left in the model are significant at the level. Summary of Backward Elimination Variable Number Partial Model Valore Step Removed Vars In R-Square R-Square C(p) F Pr > F 1 x y xy The SAS System 15:28 Tuesday, November 30, Model: MODEL3 Stepwise Selection: Step 1 Variable y2 Entered: R-Square = and C(p) =
10 Model <.0001 Error Intercept <.0001 y <.0001 Bounds on condition number: 1, 1 Stepwise Selection: Step 2 Variable x2 Entered: R-Square = and C(p) = Model <.0001 Error The SAS System 15:28 Tuesday, November 30, Model: MODEL3 Stepwise Selection: Step 2 Intercept <.0001 x <.0001 y <.0001 Bounds on condition number: , Stepwise Selection: Step 3 Variable xy Entered: R-Square = and C(p) =
11 Model <.0001 Error Intercept <.0001 xy x <.0001 y Bounds on condition number: , All variables left in the model are significant at the level. No other variable met the significance level for entry into the model. The SAS System 15:28 Tuesday, November 30, Model: MODEL3 Summary of Stepwise Selection Variable Variable Number Partial Model Valore Step Entered Removed Vars In R-Square R-Square C(p) F Pr > F 1 y < x < xy The SAS System 15:28 Tuesday, November 30, Model: MODEL4 Maximum R-Square Improvement: Step 1 Variable y2 Entered: R-Square = and C(p) = Model <.0001 Error
12 Intercept <.0001 y <.0001 Bounds on condition number: 1, 1 The above model is the best 1-variable model found. Maximum R-Square Improvement: Step 2 Variable x2 Entered: R-Square = and C(p) = Model <.0001 Error The SAS System 15:28 Tuesday, November 30, Model: MODEL4 Maximum R-Square Improvement: Step 2 Intercept <.0001 x <.0001 y <.0001 Bounds on condition number: , The above model is the best 2-variable model found. Maximum R-Square Improvement: Step 3 Variable xy Entered: R-Square = and C(p) = Model <.0001 Error
13 Intercept <.0001 xy x <.0001 y Bounds on condition number: , The above model is the best 3-variable model found. Maximum R-Square Improvement: Step 4 The SAS System 15:28 Tuesday, November 30, Model: MODEL4 Maximum R-Square Improvement: Step 4 Variable y Entered: R-Square = and C(p) = Model <.0001 Error Intercept <.0001 y xy x <.0001 y Bounds on condition number: , The above model is the best 4-variable model found. Maximum R-Square Improvement: Step 5 Variable x Entered: R-Square = and C(p) =
14 Model <.0001 Error The SAS System 15:28 Tuesday, November 30, Model: MODEL4 Maximum R-Square Improvement: Step 5 Intercept <.0001 x y xy x y Bounds on condition number: , The above model is the best 5-variable model found. No further improvement in R-Square is possible. ESERCIZIO Si utilizzino i dati, contenuti in Africa.xls, che rappresentano l estensione, il reddito pro capite, la popolazione presente nella capitale, la popolazione attiva (adulti lavoratori) e la popolazione urbana di alcuni stati dell Africa. Superficie(Kmq) PNL pro capite Popolazione capitale Popolazione attiva Popolazione urbana C e una relazione significativa fra il reddito pro capite (PNL pro capite) e le altre variabili? 14
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