PS lab 14 (razvan)

#http://r-statistics.co/Linear-Regression.html

head(cars)
scatter.smooth(x=cars$speed, y=cars$dist, main="Dist ~ Speed")  # scatterplot

par(mfrow=c(1, 2))  # divide graph area in 2 columns
boxplot(cars$speed, main="Speed", sub=paste("Outlier rows: ", boxplot.stats(cars$speed)$out))  # box plot for 'speed'
boxplot(cars$dist, main="Distance", sub=paste("Outlier rows: ", boxplot.stats(cars$dist)$out))  # box plot for 'distance'

cor(cars$speed, cars$dist)  # calculate correlation between speed and distance
                            # accesarea datelor din fisierul cars

linearMod <- lm(dist ~ speed, data=cars)  # build linear regression model on full data
print(linearMod) # operatul ~ se numeste against

par(mfrow=c(1,1))

plot(cars$speed,cars$dist)
t <- seq(0,30,0.01)
lines(t, 3.932*t - 17.579, col = "magenta")

summary(linearMod) #a mai fost folosita la statistica descriptiva

modelSummary <- summary(linearMod)  # capture model summary as an object
modelCoeffs <- modelSummary$coefficients  # model coefficients
beta.estimate <- modelCoeffs["speed", "Estimate"]  # get beta estimate for speed
std.error <- modelCoeffs["speed", "Std. Error"]  # get std.error for speed
t_value <- beta.estimate/std.error  # calc t statistic
p_value <- 2*pt(-abs(t_value), df=nrow(cars)-ncol(cars))  # calc p Value
f_statistic <- linearMod$fstatistic[1]  # fstatistic
f <- summary(linearMod)$fstatistic  # parameters for model p-value calc
model_p <- pf(f[1], f[2], f[3], lower=FALSE)


# 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

actuals_preds <- data.frame(cbind(actuals=testData$dist, predicteds=distPred))  # make actuals_predicteds dataframe.