#..............................
#Simple Linear Regression with R ----
# adapted from http://r-statistics.co/Linear-Regression.html

#..Data ----
#We will use the cars dataset that comes with base R
?cars
head(cars)
plot(cars)


#..Estimation ----
#Let's run a simple regression model (one predictor variable)
linearMod <- lm(dist ~ speed, data=cars)  # estimate linear regression model on full data

#Let's get information on the prediction
summary(linearMod) #get a summary of the estimation
coef(linearMod) #get only the coefficients
modelSummary <- summary(linearMod)  # capture model summary as an object
modelCoeffs <- modelSummary$coefficients  # model coefficients
beta.estimate <- modelCoeffs["speed", "Estimate"]  # get beta estimate for speed
std.error <- modelCoeffs["speed", "Std. Error"]  # get std.error for speed
t_value <- modelCoeffs["speed", "t value"]   # get t statistic
f_statistic <- linearMod$fstatistic[1]  # fstatistic
f <- summary(linearMod)$fstatistic  # parameters for model p-value calc

#..Accuracy of prediction ----
#We create a training and a test data set; we do an estimation and a prediction; we chekc prediction accuracy 

# Create Training and Test data 
set.seed(100)  # setting seed to reproduce results of random sampling
trainingRowIndex <- sample(1:nrow(cars), 0.8*nrow(cars))  # row indices for training data
trainingData <- cars[trainingRowIndex, ]  # model training data
testData  <- cars[-trainingRowIndex, ]   # test data

# Build the model on training data -
lmMod <- lm(dist ~ speed, data=trainingData)  # build the model
distPred <- predict(lmMod, testData)  # predict distance

# check accuracy
actuals_preds <- data.frame(cbind(actuals=testData$dist, predicteds=distPred))  # put together actual ad predicted values
cor(actuals_preds)



#..............................
# Multiple Linear Regression with R ----
# data from https://onlinecourses.science.psu.edu/stat501/node/284

# ..Data ----
iq.data=read.table("https://onlinecourses.science.psu.edu/stat501/sites/onlinecourses.science.psu.edu.stat501/files/data/iqsize.txt",
                   header = T)
pairs(iq.data,lower.panel = NULL,panel=panel.smooth)

# ..Estimation ----
iq.model=lm(PIQ~Brain+Height+Weight,data=iq.data)
summary(iq.model)

iq.model2=lm(PIQ~Brain+Height,data=iq.data)
summary(iq.model2)

#..............................
# Advanced Regression Model with R ----
# see http://r-statistics.co/adv-regression-models.html # Robust, Logit, Probit, Multinomial, etc models