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")