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library(ggplot2)
weather <- read.csv("Data/weather.csv")


(Y.model <-lm(rain ~pressure, data = weather))

ggplot(data = weather, aes(x = pressure, y = rain)) + geom_point(size = 1) + 
  geom_line(aes(y = Y.model$coefficients[1]+pressure*Y.model$coefficients[2]), linetype = "dashed")+
  labs(title = "Precipitation (mm) against Air Pressure (hPa)")
# Exponential decay

#INTE FÄRDIGT, cbind(BLANK) ska va ngt annat, körde Y.data, men existerar ej.
Y.pred <- 
  cbind(BLANK, 
        fit = predict(Y.model),
        conf = predict(Y.model, interval = "confidence"),
        pred = predict(Y.model, interval = "prediction"))
head(Y.pred)
# get rid of the extra fits
Y.pred$conf.fit <- Y.pred$pred.fit <- NULL
head(Y.pred)

Y.pred$e <- Y.model$residuals
head(Y.pred)
(max.e <- max(abs(Y.pred$e)))
(Y.elims <- c(-max.e, max.e))
## Plot against yhat####
# Add a horizontal line at y=0,
# and expand the y-axis to include +/- max residual.

ggplot(data = Y.pred, aes(x = fit, y = e)) +
  geom_point(size = 3) +
  geom_hline(yintercept = 0) +
  expand_limits(y = Y.elims) +
  xlab("Predicted weight loss (g)") +
  ylab("Residual") +
  labs(tag = "B") +
  labs(title = "Residuals vs predicted values Y-hat") +
  theme(text = element_text(size = 18))


(Ylog.model <-lm(log(rain) ~pressure, data = weather))

ggplot(data = weather, aes(x = pressure, y = log(rain))) + geom_point(size = 1) +
  geom_line(aes(y = Ylog.model$coefficients[1] +pressure*Ylog.model$coefficients[2]), linetype = "dashed")+
labs(title = "Precipitation (log(mm)) against Air Pressure (hPa)")
# Linear to the left, but after 1010 hPa the data seems to have another slope


(Ycr.model <- lm(rain^(1/3) ~ pressure, data = weather))

ggplot(data = weather, aes(x = pressure, y = rain^(1/3))) + geom_point(size = 1) +
  geom_line(aes(y = Ycr.model$coefficients[1] +pressure*Ycr.model$coefficients[2]), linetype = "dashed")+
labs(title = "Precipitation ((mm)^1/3) Against Air Pressure (hPa)")
# Linear, fits our model Y = xB + e