Modelos lineales - Regresion lineal simple

# En esta publicacion quiero compartir con ustedes el codigo de mi video que abajo comparto #sobre modelos lineales para regresion lineal simple.

####  ------------   problem 1--------------------#

# Values of height   ---- predictor
# 151, 174, 138, 186, 128, 136, 179, 163, 152, 131

# Values of weight.  ---- response
# 63, 81, 56, 91, 47, 57, 76, 72, 62, 48

## ---- using  lm function ---

x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131)
y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48)

plot(y,x)

# En este capitulo una explicacion sobre regresion lineal simple.

#Igualmente, la introduccion a este capitulo lo encuentra aqui:

# Apply the lm() function.

## model:     height = a + b*weight

## Proposed model is:  height=  a +  b*weight  + e
## e ~  N(0, s^2)
##
## Ho: b=0
## HA:  b not equal to 0

#  model = lm( formula= var1~ var2 ,data= mydata)

relation <- lm(x~y)

print(relation)    # or simply   relation

summary(relation)

## Equation

#   height = 61.3803 + 1.4153*weight

confint(relation)   # interval confidence

#  coef + (-1,1) * sigma^2 * t(alpha, df)

# Find height of a person with weight 75.
#predict
# predict( object, newdata)

a <- data.frame(y = 75)   # 75 kg
result <-  predict(relation,a)
result

61.3803 + 1.4153*75

plot(y,x,col = "blue",main = "Height & Weight Regression",
     abline(lm(x~y)),cex = 1.3,pch = 16,xlab = "Weight (Kg)",ylab = "Height (cm)")

### -----  test model assumptions
par( mfrow=c(2,2))
plot( relation)
par(mfrow=c(1,1))


## element 7,  weight= 76
#  Individually

qqnorm( residuals(relation))
qqline( residuals(relation))

plot(residuals(relation))    # plot(fitted(relation),residuals(relation))
   
plot(rstandard(relation))
   
#####--------------- problem 2--------------
   
height = c(100, 200, 300, 450, 600, 800, 1000)
distance = c(253, 337, 395, 451, 495, 534, 574) # data from Galileo
##   distance = a + b1*height + b2*height^2 +  e,   e ~ N(0,s^2)

##  Ho: b1 = b2= 0
##  Ha: at least one b not equal 0

model.r = lm(distance ~ height + I(height^2))   # a quadratic model
model.r   

## Also, it is possible to use
## mod.r = lm( distance ~ poly(height,2,raw=TRUE))

## raw  --  if true, use raw and not orthogonal polynomials
# Thus, in the raw coding you can only interpret the p-value of height if height^2
# remains in the model
## mod.r

# However, in the orthogonal coding height^2 only captures the quadratic part
# that has not been captured by the linear term.

summary(model.r)
newh = seq(100, 1000, 10)  #  100 110  120 ... 990 1000
newh
fit = 200.211950 + 0.706182*newh - 0.000341*newh^2 
fit   # predicted values for distance
   
predict( model.r, data.frame(height=newh))
   
plot(height, distance) # original data
lines(newh, fit, lty=1) # display best fit

par( mfrow=c(2,2))
plot( model.r)
par(mfrow=c(1,1))

#######--------------------------------------------------------------------------------------


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