zajecia8

zajecia8/.Rhistory

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+rok <- 1995:2002
+liczba_przypadkow <- c(39.7, 38.2, 34.7, 33.1, 30.1, 28.4, 26.3, 24.7)
+data_set <- data.frame(rok = rok, liczba_przypadkow = liczba_przypadkow)
+View(data_set)
+plot(data_set, main = "Wykres rozrzutu", pch = 16)
+model <- lm(liczba_przypadkow ~ rok, data = data_set)
+model$coefficients
+plot(data_set, main = "Wykres rozrzutu", pch = 16)
+abline(model, col = "red", lwd = 2)
+coef(model)
+confint(model)
+summary(model)
+fitted(model)
+residuals(model)
+View(data_set)
+temp_rok <- data.frame(rok = seq(min(data_set$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$rok, pred[, 3], lty = 2, col = "red")
+new_rok <- data.frame(rok = 2003:2007)
+(pred_2003_2007 <- stats::predict(model, new_rok, interval = 'prediction'))
+plot(data_set, main = "Wykres rozrzutu z predykcj<63> na lata 2003-2007", pch = 16,
+xlim = c(1995, 2007), ylim = c(10, 40))
+plot(data_set, main = "Wykres rozrzutu z predykcją na lata 2003-2007", pch = 16,
+xlim = c(1995, 2007), ylim = c(10, 40))
+abline(model, col = "red", lwd = 2)
+points(2003:2007, pred_2003_2007[, 1], col = "blue", pch = 16)
+temp_rok <- data.frame(rok = seq(1994, 2008, length = 100))
+pred <- stats::predict(model, temp_rok, interval = "prediction")
+lines(temp_rok$rok, pred[, 2], lty = 2, col = "red")
+lines(temp_rok$rok, pred[, 3], lty = 2, col = "red")
+View(temp_rok)
+View(pred)
+load(url("http://ls.home.amu.edu.pl/data_sets/braking.RData"))
+load(url("http://ls.home.amu.edu.pl/data_sets/braking.RData"))
+head(braking)
+plot(braking, main = "Wykres rozrzutu", pch = 16)
+View(braking)
+which(braking$distance > 150)
+model <- lm(distance ~ speed, data = braking)
+plot(braking, main = "Wykres rozrzutu", pch = 16)
+abline(model, col = "red", lwd = 2)
+coef(model)
+confint(model)
+summary(model)
+fitted(model)
+residuals(model)
+temp_speed <- data.frame(speed = seq(min(braking$speed) - 10,
+max(braking$speed) + 10,
+length = 100))
+pred <- stats::predict(model, temp_speed, interval = "prediction")
+plot(braking, main = "Wykres rozrzutu", pch = 16, ylim = c(-50, 200))
+abline(model, col = "red", lwd = 2)
+lines(temp_speed$speed, pred[, 2], lty = 2, col = "red")
+lines(temp_speed$speed, pred[, 3], lty = 2, col = "red")
+new_speed <- data.frame(speed = 30:50)
+(pred_30_50 <- stats::predict(model, new_speed, interval = 'prediction'))
+plot(braking, main = "Wykres rozrzutu z predykcj<63> dla pr<70>dko<6B>ci 30, 31, ..., 50", pch = 16,
+xlim = c(0, 50), ylim = c(-50, 200))
+abline(model, col = "red", lwd = 2)
+points(30:50, pred_30_50[, 1], col = "blue", pch = 16)
+temp_speed <- data.frame(speed = seq(-5, 55, length = 100))
+pred <- stats::predict(model, temp_speed, interval = "prediction")
+lines(temp_speed$speed, pred[, 2], lty = 2, col = "red")
+lines(temp_speed$speed, pred[, 3], lty = 2, col = "red")
+model <- lm(distance ~ speed - 1, data = braking)
+plot(braking, main = "Wykres rozrzutu", pch = 16)
+abline(model, col = "red", lwd = 2)
+coef(model)
+confint(model)
+summary(model)
+temp_speed <- data.frame(speed = seq(min(braking$speed) - 10,
+max(braking$speed) + 10,
+length = 100))
+pred <- stats::predict(model, temp_speed, interval = "prediction")
+plot(braking, main = "Wykres rozrzutu", pch = 16, ylim = c(-50, 200))
+abline(model, col = "red", lwd = 2)
+lines(temp_speed$speed, pred[, 2], lty = 2, col = "red")
+lines(temp_speed$speed, pred[, 3], lty = 2, col = "red")
+new_speed <- data.frame(speed = 30:50)
+(pred_30_50 <- stats::predict(model, new_speed, interval = 'prediction'))
+plot(braking, main = "Wykres rozrzutu z predykcj<63> dla pr<70>dko<6B>ci 30, 31, ..., 50", pch = 16,
+xlim = c(0, 50), ylim = c(-50, 200))
+abline(model, col = "red", lwd = 2)
+points(30:50, pred_30_50[, 1], col = "blue", pch = 16)
+temp_speed <- data.frame(speed = seq(-5, 55, length = 100))
+pred <- stats::predict(model, temp_speed, interval = "prediction")
+lines(temp_speed$speed, pred[, 2], lty = 2, col = "red")
+lines(temp_speed$speed, pred[, 3], lty = 2, col = "red")
+braking_1 <- braking[-27, ]
+model_1 <- lm(distance ~ speed, data = braking_1)
+plot(braking_1, main = "Wykres rozrzutu", pch = 16)
+abline(model_1, col = "green", lwd = 2)
+coef(model_1)
+confint(model_1)
+summary(model_1)
+fitted(model_1)
+residuals(model_1)
+temp_speed_1 <- data.frame(speed = seq(min(braking_1$speed) - 10,
+max(braking_1$speed) + 10,
+length = 100))
+pred_1 <- stats::predict(model_1, temp_speed_1, interval = "prediction")
+plot(braking_1, main = "Wykres rozrzutu", pch = 16, ylim = c(-50, 120))
+abline(model_1, col = "green", lwd = 2)
+lines(temp_speed_1$speed, pred_1[, 2], lty = 2, col = "green")
+lines(temp_speed_1$speed, pred_1[, 3], lty = 2, col = "green")
+new_speed <- data.frame(speed = 30:50)
+(pred_30_50_1 <- stats::predict(model_1, new_speed, interval = 'prediction'))
+plot(braking_1, main = "Wykres rozrzutu z predykcj<63> dla pr<70>dko<6B>ci 30, 31, ..., 50", pch = 16,
+xlim = c(0, 50), ylim = c(-50, 200))
+abline(model_1, col = "green", lwd = 2)
+points(30:50, pred_30_50_1[, 1], col = "blue", pch = 16)
+temp_speed <- data.frame(speed = seq(-5, 55, length = 100))
+pred_1 <- stats::predict(model_1, temp_speed, interval = "prediction")
+lines(temp_speed$speed, pred_1[, 2], lty = 2, col = "green")
+lines(temp_speed$speed, pred_1[, 3], lty = 2, col = "green")
+braking_1 <- braking[-27, ]
+model_1 <- lm(distance ~ speed - 1, data = braking_1)
+plot(braking_1, main = "Wykres rozrzutu", pch = 16)
+abline(model_1, col = "green", lwd = 2)
+coef(model_1)
+confint(model_1)
+summary(model_1)
+fitted(model_1)
+residuals(model_1)
+braking_1 <- braking[-27, ]
+model_1 <- lm(distance ~ speed - 1, data = braking_1)
+plot(braking_1, main = "Wykres rozrzutu", pch = 16)
+abline(model_1, col = "green", lwd = 2)
+coef(model_1)
+confint(model_1)
+summary(model_1)
+fitted(model_1)
+residuals(model_1)
+braking_1 <- braking[-27, ]
+model_1 <- lm(distance ~ speed, data = braking_1)
+plot(braking_1, main = "Wykres rozrzutu", pch = 16)
+abline(model_1, col = "green", lwd = 2)
+coef(model_1)
+confint(model_1)
+braking_1 <- braking[-27, ]
+model_1 <- lm(distance ~ speed - 1, data = braking_1)
+plot(braking_1, main = "Wykres rozrzutu", pch = 16)
+abline(model_1, col = "green", lwd = 2)
+coef(model_1)
+confint(model_1)
+summary(model_1)
+fitted(model_1)
+residuals(model_1)
+temp_speed_1 <- data.frame(speed = seq(min(braking_1$speed) - 10,
+max(braking_1$speed) + 10,
+length = 100))
+pred_1 <- stats::predict(model_1, temp_speed_1, interval = "prediction")
+plot(braking_1, main = "Wykres rozrzutu", pch = 16, ylim = c(-50, 120))
+abline(model_1, col = "green", lwd = 2)
+lines(temp_speed_1$speed, pred_1[, 2], lty = 2, col = "green")
+lines(temp_speed_1$speed, pred_1[, 3], lty = 2, col = "green")
+new_speed <- data.frame(speed = 30:50)
+(pred_30_50_1 <- stats::predict(model_1, new_speed, interval = 'prediction'))
+plot(braking_1, main = "Wykres rozrzutu z predykcj<63> dla pr<70>dko<6B>ci 30, 31, ..., 50", pch = 16,
+xlim = c(0, 50), ylim = c(-50, 200))
+abline(model_1, col = "green", lwd = 2)
+points(30:50, pred_30_50_1[, 1], col = "blue", pch = 16)
+temp_speed <- data.frame(speed = seq(-5, 55, length = 100))
+pred_1 <- stats::predict(model_1, temp_speed, interval = "prediction")
+lines(temp_speed$speed, pred_1[, 2], lty = 2, col = "green")
+lines(temp_speed$speed, pred_1[, 3], lty = 2, col = "green")
+summary(model_1)
+braking_1 <- braking[-27, ]
+model_1 <- lm(distance ~ speed, data = braking_1)
+summary(model_1)
+median(residuals(model_1))

zajecia8/README.md

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+# Zajęcia 8
+
+
+## Regresja
+Główną ideą regresji jest przewidywanie, prognozowanie danych dla pewnej zmiennej na podstawie innych zmiennych. Innymi słowy, jaką wartość przyjmie dana zmienna gdy będziemy znali wartość innej zmiennej. Oczywiście, aby móc "poszukiwać" wartości jednej zmiennej na podstawie innej zmiennej musimy za pomocą analizy regresji skonstruować model regresyjny, model, który będzie z założonym błędem statystycznym przewidywał wartość, poziom danej cechy. 
+
+
+## Regresja liniowa
+Regresja liniowa jest najprostszym wariantem regresji w statystyce. Zakłada ona, że zależność pomiędzy zmienną objaśnianą a objaśniająca jest zależnością liniową.
+
+
+## Poziom ufoności
+Jak często mamy rację. Wyrażane w procentach.
+
+
+## Reszty
+To po prostu o ile różni się wynik zmierzony od przewidzianego.
+

zajecia8/zadania.R

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+
+# ZAD1
+rok <- 1995:2002
+liczba_przypadkow <- c(39.7, 38.2, 34.7, 33.1, 30.1, 28.4, 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$rok, pred[, 3], lty = 2, col = "red")
+
+
+# ZAD2
+
+load(url("http://ls.home.amu.edu.pl/data_sets/braking.RData"))
+head(braking)
+plot(braking, main = "Wykres rozrzutu", pch = 16)
+# which(braking$distance > 150)
+
+model <- lm(distance ~ speed, data = braking)
+plot(braking, main = "Wykres rozrzutu", pch = 16)
+abline(model, col = "red", lwd = 2)
+coef(model)
+confint(model)
+
+summary(model)
+
+fitted(model)
+residuals(model)
+
+temp_speed <- data.frame(speed = seq(min(braking$speed) - 10, 
+                                     max(braking$speed) + 10, 
+                                     length = 100))
+pred <- stats::predict(model, temp_speed, interval = "prediction")
+plot(braking, main = "Wykres rozrzutu", pch = 16, ylim = c(-50, 200))
+abline(model, col = "red", lwd = 2)
+lines(temp_speed$speed, pred[, 2], lty = 2, col = "red")
+lines(temp_speed$speed, pred[, 3], lty = 2, col = "red")
+
+new_speed <- data.frame(speed = 30:50)
+(pred_30_50 <- stats::predict(model, new_speed, interval = 'prediction'))
+plot(braking, main = "Wykres rozrzutu z predykcją dla prędkości 30, 31, ..., 50", pch = 16, 
+     xlim = c(0, 50), ylim = c(-50, 200))
+abline(model, col = "red", lwd = 2)
+points(30:50, pred_30_50[, 1], col = "blue", pch = 16)
+temp_speed <- data.frame(speed = seq(-5, 55, length = 100))
+pred <- stats::predict(model, temp_speed, interval = "prediction")
+lines(temp_speed$speed, pred[, 2], lty = 2, col = "red")
+lines(temp_speed$speed, pred[, 3], lty = 2, col = "red")
+
+# bez wyrazu wolnego
+model <- lm(distance ~ speed - 1, data = braking)
+plot(braking, main = "Wykres rozrzutu", pch = 16)
+abline(model, col = "red", lwd = 2)
+coef(model)
+confint(model)
+
+summary(model)
+
+fitted(model)
+residuals(model)
+
+temp_speed <- data.frame(speed = seq(min(braking$speed) - 10, 
+                                     max(braking$speed) + 10, 
+                                     length = 100))
+pred <- stats::predict(model, temp_speed, interval = "prediction")
+plot(braking, main = "Wykres rozrzutu", pch = 16, ylim = c(-50, 200))
+abline(model, col = "red", lwd = 2)
+lines(temp_speed$speed, pred[, 2], lty = 2, col = "red")
+lines(temp_speed$speed, pred[, 3], lty = 2, col = "red")
+
+new_speed <- data.frame(speed = 30:50)
+(pred_30_50 <- stats::predict(model, new_speed, interval = 'prediction'))
+plot(braking, main = "Wykres rozrzutu z predykcją dla prędkości 30, 31, ..., 50", pch = 16, 
+     xlim = c(0, 50), ylim = c(-50, 200))
+abline(model, col = "red", lwd = 2)
+points(30:50, pred_30_50[, 1], col = "blue", pch = 16)
+temp_speed <- data.frame(speed = seq(-5, 55, length = 100))
+pred <- stats::predict(model, temp_speed, interval = "prediction")
+lines(temp_speed$speed, pred[, 2], lty = 2, col = "red")
+lines(temp_speed$speed, pred[, 3], lty = 2, col = "red")
+
+braking_1 <- braking[-27, ]
+model_1 <- lm(distance ~ speed, data = braking_1)
+plot(braking_1, main = "Wykres rozrzutu", pch = 16)
+abline(model_1, col = "green", lwd = 2)
+coef(model_1)
+confint(model_1)
+
+summary(model_1)
+
+fitted(model_1)
+residuals(model_1)
+
+temp_speed_1 <- data.frame(speed = seq(min(braking_1$speed) - 10, 
+                                       max(braking_1$speed) + 10, 
+                                       length = 100))
+pred_1 <- stats::predict(model_1, temp_speed_1, interval = "prediction")
+plot(braking_1, main = "Wykres rozrzutu", pch = 16, ylim = c(-50, 120))
+abline(model_1, col = "green", lwd = 2)
+lines(temp_speed_1$speed, pred_1[, 2], lty = 2, col = "green")
+lines(temp_speed_1$speed, pred_1[, 3], lty = 2, col = "green")
+
+new_speed <- data.frame(speed = 30:50)
+(pred_30_50_1 <- stats::predict(model_1, new_speed, interval = 'prediction'))
+plot(braking_1, main = "Wykres rozrzutu z predykcją dla prędkości 30, 31, ..., 50", pch = 16, 
+     xlim = c(0, 50), ylim = c(-50, 200))
+abline(model_1, col = "green", lwd = 2)
+points(30:50, pred_30_50_1[, 1], col = "blue", pch = 16)
+temp_speed <- data.frame(speed = seq(-5, 55, length = 100))
+pred_1 <- stats::predict(model_1, temp_speed, interval = "prediction")
+lines(temp_speed$speed, pred_1[, 2], lty = 2, col = "green")
+lines(temp_speed$speed, pred_1[, 3], lty = 2, col = "green")
+
+# bez wyrazu wolnego
+braking_1 <- braking[-27, ]
+model_1 <- lm(distance ~ speed - 1, data = braking_1)
+plot(braking_1, main = "Wykres rozrzutu", pch = 16)
+abline(model_1, col = "green", lwd = 2)
+coef(model_1)
+confint(model_1)
+
+summary(model_1)
+
+fitted(model_1)
+residuals(model_1)
+
+temp_speed_1 <- data.frame(speed = seq(min(braking_1$speed) - 10, 
+                                       max(braking_1$speed) + 10, 
+                                       length = 100))
+pred_1 <- stats::predict(model_1, temp_speed_1, interval = "prediction")
+plot(braking_1, main = "Wykres rozrzutu", pch = 16, ylim = c(-50, 120))
+abline(model_1, col = "green", lwd = 2)
+lines(temp_speed_1$speed, pred_1[, 2], lty = 2, col = "green")
+lines(temp_speed_1$speed, pred_1[, 3], lty = 2, col = "green")
+
+
+new_speed <- data.frame(speed = 30:50)
+(pred_30_50_1 <- stats::predict(model_1, new_speed, interval = 'prediction'))
+plot(braking_1, main = "Wykres rozrzutu z predykcją dla prędkości 30, 31, ..., 50", pch = 16, 
+     xlim = c(0, 50), ylim = c(-50, 200))
+abline(model_1, col = "green", lwd = 2)
+points(30:50, pred_30_50_1[, 1], col = "blue", pch = 16)
+temp_speed <- data.frame(speed = seq(-5, 55, length = 100))
+pred_1 <- stats::predict(model_1, temp_speed, interval = "prediction")
+lines(temp_speed$speed, pred_1[, 2], lty = 2, col = "green")
+lines(temp_speed$speed, pred_1[, 3], lty = 2, col = "green")

zajecia8/zajecia8.Rproj

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+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
+
+RnwWeave: Sweave
+LaTeX: pdfLaTeX