#	Potrebne knihovny
library (Hmisc)			#	rcorr
library (ppcor)			#	pcor, spcor, pcor.test, spcor.test
library (corrplot)	#	corrplot
library (rgl)				# 3D grafika 

#	Nacteni dat
tabulka <- read.csv2 ("../data/deti.csv")

str (tabulka)
summary (tabulka)

hmotnost <- tabulka$hmotnost
body <- tabulka$body
vek <- tabulka$vek
X <- as.matrix (tabulka[,2:4])

#	Ciselne charakterisitky 
apply (X, 2, mean)
cov (X)
cor (X)

#	Scatter-plot
pairs (X)



#	MNOHONASOBNA LINEARNI REGRESE

#	Linearni regresni model
model <- lm (body ~ hmotnost + vek, data = tabulka)
#	Koeficienty mnohonasobne linearni regrese
summary (model)

#	Predikce vynosu (V) v zavislosti na poctu clenu domacnosti (C) a prijmech (P)
h <- seq (20, 60, by = 0.1)
v <- seq (5, 15, by = 0.1)
grid.2d <- expand.grid (hmotnost = h, vek = v)
prediction <- predict (model, grid.2d, interval = "prediction")
body.predicted <- matrix (prediction[,1], length (h), length (v))

#	Okno 3D grafiky
open3d ()

#	col <- rainbow (length (body.predicted))[rank(body.predicted)]	#	paleta barvy duhy
col <- terrain.colors (length (body.predicted))[rank(body.predicted)]	#	paleta topograficka mapa
#	3D plocha
persp3d (h, v, body.predicted, col = col, lit = FALSE, front = "fill", back = "fill", smooth = FALSE, alpha = 0.9, xlab = "H", ylab = "V", zlab = "B")
#	Body ve 3D
spheres3d (tabulka$hmotnost, tabulka$vek, tabulka$body, col = "black", radius = 1, lit = FALSE)

#	Uzavreni okna s 3D grafikou
rgl.close ()



#	KORELACNI ANALYZA

#	Korelacni matice a testy vyznamnosti
R <- rcorr (X)
R$r
R$P

#	Matice parcialnich korelaci a testy vyznamnosti
R.parc <- pcor (X)
R.parc$estimate
R.parc$p.value

#	Matice semiparcialnich korelaci a testy vyznamnosti
R.semiparc <- spcor (X)
R.semiparc$estimate
R.semiparc$p.value

#	Korelogramy 
corrplot (R$r, p.mat = R$P, method = "circle")
corrplot (R.parc$estimate, p.mat = R.parc$p.value, method = "circle")
corrplot (R.semiparc$estimate, p.mat = R.semiparc$p.value, method = "circle")



#	MNOHONASOBNA KORELACE

#	body . hmotnost vek

# 1. jako korelace s nejlepsim linearnim odhadem
m <- lm (body ~ hmotnost + vek, data = tabulka)
v <- summary (m)
cor (body, m$fitted.values)

# 2. jako r.squared v linearnim regresnim modelu
sqrt (v$r.squared)

# Dopocitejte dalsi mnohonasobne korelace 



#	PARCIALNI KORELACE

#	body hmotnost . vek
R.parc$estimate["body","hmotnost"]
R.parc$estimate["hmotnost","body"]

# 1. jako korelace mezi dvema rezidui
m1 <- lm (body ~ vek, data = tabulka)
m2 <- lm (hmotnost ~ vek, data = tabulka)
v1 <- summary (m1)
v2 <- summary (m2)
cor (m1$residuals, m2$residuals)

# 2. pomoci r.squared v linearnich regresnich modelech
m01 <- lm (body ~ hmotnost + vek, data = tabulka)
v01 <- summary (m01)
sqrt ( (v01$r.squared - v1$r.squared) / (1 - v1$r.squared) )

m02 <- lm (hmotnost ~ body + vek, data = tabulka)
v02 <- summary (m02)
sqrt ( (v02$r.squared - v2$r.squared) / (1 - v2$r.squared) )

# Dopocitejte dalsi parcialni korelace 



#	SEMIPARCIALNI KORELACE

#	hmotnost (body . vek)
R.semiparc$estimate["body","hmotnost"]

# 1. jako korelace mezi jednou velicinou a reziduem druhe veliciny
m2 <- lm (hmotnost ~ vek, data = tabulka)
cor (body, m2$residuals)

# 2. pomoci r.squared v linearnich regresnich modelech
m01 <- lm (body ~ hmotnost + vek, data = tabulka)
v01 <- summary (m01)
m1 <- lm (body ~ vek, data = tabulka)
v1 <- summary (m1)
sqrt (v01$r.squared - v1$r.squared)


#	V (P . C)
R.semiparc$estimate["hmotnost","body"]

# 1. jako korelace mezi jednou velicinou a reziduem druhe veliciny
m1 <- lm (body ~ vek, data = tabulka)
cor (hmotnost, m1$residuals)

# 2. pomoci r.squared v linearnich regresnich modelech
m02 <- lm (hmotnost ~ body + vek, data = tabulka)
v02 <- summary (m02)
m2 <- lm (hmotnost ~ vek, data = tabulka)
v2 <- summary (m2)
sqrt (v02$r.squared - v2$r.squared)


# Dopocitejte dalsi semiparcialni korelace