From d1df50a039972b5fab6d5457b3197baa9ef0c7af Mon Sep 17 00:00:00 2001 From: Jakub Adamski Date: Sun, 20 Jun 2021 10:42:15 +0200 Subject: [PATCH] lab9 --- podsumowanie/README.md | 67 +++++++++++++++++++++++++++++- podsumowanie/lab9/aic.png | Bin 0 -> 35977 bytes podsumowanie/lab9/bic.png | Bin 0 -> 19086 bytes podsumowanie/lab9/wielokrotna.png | Bin 0 -> 80690 bytes testowe/pomocnicze.R | 37 +++++++++++++++++ 5 files changed, 102 insertions(+), 2 deletions(-) create mode 100644 podsumowanie/lab9/aic.png create mode 100644 podsumowanie/lab9/bic.png create mode 100644 podsumowanie/lab9/wielokrotna.png create mode 100644 testowe/pomocnicze.R diff --git a/podsumowanie/README.md b/podsumowanie/README.md index 6177f1b..4d4a4ac 100644 --- a/podsumowanie/README.md +++ b/podsumowanie/README.md @@ -544,7 +544,7 @@ Wykonując później test ANOVA - analiza wariancji możemy zobaczyć czy porów Zagadnienia: - regresja liniowa - - wykład 9 na stronie - pierwsza część + - wykład 9 na stronie - początek ### R @@ -636,14 +636,77 @@ Założenia analizy regresji: --- ## LAB 9 Zagadnienia: - - + - regresja wielokrotna i krokowa + + - wykład 9 na stronie środek ### R +```r +# regresja wielokrotna +pairs(auto_wna_sel) +model_1 <- lm(price ~ horsepower + city.mpg + peak.rpm + curb.weight + num.of.doors, data = auto_wna) +coef(model_1) +confint(model_1) +summary(model_1) +fitted(model_1) +residuals(model_1) +# regresja krokowa w tył (jeden krok) +step(model_1) # AIC +step(model_1, k = log(nrow(auto_wna))) # BIC + +# regresja krokowa w przód (jeden krok) +model_0 <- lm(price ~ 1, data = auto_wna) +step(model_0, direction = "forward", scope = formula(model_1)) + +# predykcja +new_data <- data.frame(curb.weight = 2823, horsepower = 154) +model_2 <- lm(price ~ curb.weight + horsepower, data = auto_wna) +stats::predict(model_2, new_data, interval = "prediction") +summary(model_2)$adj.r.squared +``` ### Zagadnienia +- Regresja wielokrotna - z regresją wielokrotną (wieloraką) mamy do czynienia, jeśli zmianna zależna Y związana jest z większą ilością zmiennych niezależnych. + - Na stronie są wzory z dopasowaniem, pedykcją, odrzuceniem wyrazu wolnego i estymatorami - analogicznie jak do regresji liniowej.
+ +![wielokrotna](lab9/wielokrotna.png) + +- Regresja krokowa - regresja krokowa jest odmianą analizy regresji (nie tylko regresji liniowej), w której do modelu wprowadzane są jedynie istotne statystycznie zmienne, predyktory, które rzeczywiście „poprawiają” zbudowany model. Możemy odrzucić lub dodać zmienną w każdym kroku. + - Jeśli zaczynamy od stałej i dodajemy zmienne to jest to regresja w przód. + + - Możemy też zacząć od wszyskich zmiennych i odejmować - regresja w tył. + + - Decydujemy o dodaniu / sprawdzamy co się stanie jak odejmiemy - za pomocą kryterium np test istotności AIC, BIC

+ +- AIC - kryterium wyboru pomiędzy modelami statystycznymi o różnej liczbie predyktorów.
+![aic](lab9/aic.png) + +- BIC - w modelowaniu równań strukturalnych jest to jeden ze wskaźników dopasowania modelu. Minimalizujemy wartość wskaźnika. + - step z k=log to regresja krokowa BIC, k=2 to AIC + + - L to zmaksymalizowana funkcja prawdopodobieństwa modelu M L=p(x|theta,M) + + - n to liczba obserwacji + + - k - liczba parametrów
+ +![bic](lab9/bic.png) + + +--- +## LAB 10 +Zagadnienia: + - + + + ### R + + + + ### Zagadnienia diff --git a/podsumowanie/lab9/aic.png b/podsumowanie/lab9/aic.png new file mode 100644 index 0000000000000000000000000000000000000000..57eb82c02923ec22be418dd5012e2cea1585b9c5 GIT binary patch literal 35977 zcmd42b980Rwg(!UosQk<*h$B>ZQHi3PCB-2+vp@6+qP|Ezx~~F&v(u}_m1(#cz?Y; z*2=D|TC+H7&YHhp?QnTnF+?~VI1msJLNRALw^5W#-K zd}{=k*33+u)>Cg%4df=~>SkpeJN-h;0=Y zWEgQ!mv?3}kHHoiMCB466&)PJ^w%UVAzEFClD;%1q#Vkih}Ng?^FD8|evsTSwdk2^B%&9P-R^8g zl8mZ{epYX6JlpmVScYumyZYModX`8vFdx@*BoHt{6f5JN{uuqc=*5r=Xe@o21EE>w z5Jucc#6Cfqan}=F-vFpVhESVOahOQP<{(D2$Oi9%2OBq!N#T&S^HaeeFCr(FSF?oi z`OOcuCpb}v%}bj}0G8iN?rOa8sbBSvV2rpUUv|OpY4oLo>x7+at4`=*G!^};2kf#- z)ibJI?s}I8*~aC~#CVw|=|_K?rtp#fczyDWGXn#QqIJD#N(JF6z<(p+>XKNy3tI|2 ze?pvV2G9aWedPQ})7$&u-fb~D^AWM3Wh1HK3u=K;12aZQ3{2hXf!NJ+D3W(ar{P;j|GF7fSfdg>nT=;ts%%33@m@v=+M74I^9t59F zb4DQIL~zgGdPLn)FFbt?9pnhUtAXFIVMV)%UZ>czE_C%!py${=<=wJ(f7^Ai*?I{x zJcI1X>%$3dZ`G|8^nIE;fm|6#Zu?n~_b%XO+renJyaKlFx90sQRv8AYQ@*@ukzgL! z$wu;uA{zxW{)Q<~m&c({NyL7i53E3tge`ja!UtRz@Z~~Jqa6#}W4$Jc>1)pGHT-}! zs`U=i(Q^M-!=M0FFXonnE<%zDBQ3y^r{TvVg+7}RwdhMfFetyg>};v*dq_D4sQ31C z){TWF^by-fveRZxZ;^z56Mo@SY_|TedpjRrIE(3W0o=b=={@N!J_Tsa^>D;#44)0# z?(-NU*CVbVw8px{(GKhGU(mjrxpi%A>hv_NSWl5-C8Is-y^42mw$NbHx+qwRTKbgG z53&)Po^79mihUP_e1-mFZ_z)~n=-~et|b^LB`PV3<6ouTaQFIZ+JG-a6j}n9_AUXH z51K-#1`ujaGlHD9gXoXHgpqB-fiz%&sO5MJi4I&$%WEP3cu&p^mcwD*2I=I7(Tzcn z2Px-=KL$tBhduXawhybq1G&1RKtX;CRE~vp6yT+RBJZ`Z$Iu2z>1CNlSpCg&4Z;oe zp^wrT;5PL&6&zk4yHWrpID~>o^C$Lh@H4T3IFw@G4< z{6zSp@CQ~HefLW~tON257UNGWp>g8mSP+S5V}3`HfjCKVokG%C$dj;0!Ar42BB@xF zVNYY~^P{6-#(i!_^bmoW{8sthYa~{|m4Z%%xYCc({?dd}_);=u@>32=ye9wGkYfIZ zJdqhHbE8JIRYLrjN#T^-ikYZmx@Q`hyc9+(1aMK50+<{TGiekuY$q(G0E^#^Mo

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26.3, 24.7) +data_set <- data.frame(rok = rok, liczba_przypadkow = liczba_przypadkow) +plot(data_set, main = "Wykres rozrzutu", pch = 16) + +model <- lm(liczba_przypadkow ~ rok, data = data_set) +model$coefficients +plot(data_set, main = "Wykres rozrzutu", pch = 16) +abline(model, col = "red", lwd = 2) +coef(model) +confint(model) + +summary(model) + +fitted(model) +residuals(model) + +temp_rok <- data.frame(rok = seq(min(data_set$rok) - 10, + max(data_set$rok) + 10, + length = 100)) +pred <- stats::predict(model, temp_rok, interval = "prediction") +plot(data_set, main = "Wykres rozrzutu", pch = 16) +abline(model, col = "red", lwd = 2) +lines(temp_rok$rok, pred[, 2], lty = 2, col = "red") +lines(temp_rok$rok, pred[, 3], lty = 2, col = "red") + + +new_rok <- data.frame(rok = 2003:2007) +(pred_2003_2007 <- stats::predict(model, new_rok, interval = 'prediction')) +plot(data_set, main = "Wykres rozrzutu z predykcją na lata 2003-2007", pch = 16, + xlim = c(1995, 2007), ylim = c(10, 40)) +abline(model, col = "red", lwd = 2) +points(2003:2007, pred_2003_2007[, 1], col = "blue", pch = 16) +temp_rok <- data.frame(rok = seq(1994, 2008, length = 100)) +pred <- stats::predict(model, temp_rok, interval = "prediction") +lines(temp_rok$rok, pred[, 2], lty = 2, col = "red") +lines(temp_rok$rok, pred[, 3], lty = 2, col = "red") \ No newline at end of file