multipleLinearRegression.Rmd

---
title: "Multiple linear Regresion"
output: html_notebook
---

This is a Multiple Linear Regression analysis using Concrete Slump Data.

The UCI Machine Learning Repository has this dataset containing diferent variables (Cement, Slag, Fly ash, Water, SP, Coarse Aggr., Fine Aggr., SLUMP, FLOW, 28-day Compressive Strength). 

The dataset is maintained on their site, where it can be found by the title "Concrete Slump Test Data Set".

<b>Citation:</b>
Yeh, I-Cheng, "Modeling slump flow of concrete using second-order regressions and artificial neural networks," Cement and Concrete Composites, Vol.29, No. 6, 474-480, 2007.



```{r}
# Data Preprocessing Template

# Importing the dataset
#install.packages("tidyverse")
library(readxl)
dataset = read_excel("Concrete_Data.xls")
dataset
```
```{r}
#Split in training and test set
library(caTools)
split = sample.split(dataset$`Concrete compressive strength(MPa, megapascals)`, SplitRatio = 0.8)
training_set = subset(dataset, split == TRUE)
test_set = subset(dataset, split == FALSE)
```
```{r}
print(training_set)
```
```{r}
print(test_set)
```
```{r}
#---------------------------------
#building backward elimintation
regressor = lm(formula = `Concrete compressive strength(MPa, megapascals)` ~., data = dataset) #to see which variable is significanse
summary(regressor)  #Pr in percentage
```
Predictions with all variables
```{r}
#predict with test set
regressor_1 = lm(formula = `Concrete compressive strength(MPa, megapascals)` ~., data = training_set) #to see which variable is significanse
summary(regressor_1)  #Pr in percentage
y_pred_1= predict(regressor_1, newdata = test_set)
y_pred_error = sum(abs(y_pred_1 - test_set$`Concrete compressive strength(MPa, megapascals)`))/length(y_pred_1)

cat("Median Error ", y_pred_error)

```
```{r}
library(ggplot2)
a1 <- ggplot() 
b1 <- a1 + geom_point(aes(y = y_pred_1, x = (1:length(y_pred_2))),colour = 'red')

#linear regresion line
c1 <- b1 + geom_point(aes(y = test_set$`Concrete compressive strength(MPa, megapascals)`, x = (1:length(y_pred_2))),colour = 'blue')


#labels
d1 <- c1 + ggtitle('Concrete compressive strength (Mpa) [predicitons red, real blue] vs. count') + xlab('Count') + ylab('Concrete compressive strength (Mpa)')
d1

```
Predictions with outvariables Fine Aggregate and Coarse Aggregate

```{r}
#---------------------------------
#building backward elimintation - `Fine Aggregate (component 7)(kg in a m^3 mixture)` - `Coarse Aggregate  (component 6)(kg in a m^3 mixture)`
regressor_1 = lm(formula = `Concrete compressive strength(MPa, megapascals)` ~.-`Fine Aggregate (component 7)(kg in a m^3 mixture)`-`Coarse Aggregate  (component 6)(kg in a m^3 mixture)`, data = dataset) #to see which variable is significanse
summary(regressor_1)  #Pr in percentage
```

```{r}

#predict with test set
regressor_2 = lm(formula = `Concrete compressive strength(MPa, megapascals)` ~.-`Fine Aggregate (component 7)(kg in a m^3 mixture)`-`Coarse Aggregate  (component 6)(kg in a m^3 mixture)`, data = training_set) #to see which variable is significanse
summary(regressor_2)  #Pr in percentage
y_pred_2= predict(regressor_2, newdata = test_set)
y_pred_error_2 = sum(abs(y_pred_2 - test_set$`Concrete compressive strength(MPa, megapascals)`))/length(y_pred_2)

cat("Median Error ", y_pred_error_2)

```
```{r}
library(ggplot2)
a2 <- ggplot() 
b2 <- a2 + geom_point(aes(y = y_pred_2, x = (1:length(y_pred_2))),colour = 'red')

#linear regresion line
c2 <- b2 + geom_point(aes(y = test_set$`Concrete compressive strength(MPa, megapascals)`, x = (1:length(y_pred_2))),colour = 'blue')


#labels
d2 <- c2 + ggtitle('Concrete compressive strength (Mpa) [predicitons red, real blue] vs. count') + xlab('Count') + ylab('Concrete compressive strength (Mpa)')
d2



```