---
title: "Linear_Regressions"
output:
  flexdashboard::flex_dashboard:
    orientation: rows
    vertical_layout: scroll
    theme: flatly
    social: menu
    source_code: embed
    color: blue
---

```{r setup, include=FALSE}
library(flexdashboard)
library(flexdashboard)
library(MASS)
library(lattice)
library(dplyr)
library(ggplot2)
library(shiny)
library(DT)
```

# Dataset Description

## View of dataset

```{r}
cls <- read.csv("/cloud/project/8725922/class12-2023.csv")

datatable(cls, extensions = "Buttons",options=list(dom='Bfrtip',Buttons=c('copy','csv','print','pdf')))


```

# About

## Structure of the dataset

### Structure of the dataset

```{r}
str(cls)
```

# Summary

## Summary

### Summary

```{r}
summary(cls)
```

### Tail

```{r}
tail(cls)
```

### Head

```{r}
head(cls)
```

### Checking missing values

```{r}
print(sum(is.na(cls)))
```

# EDA

## Histogram

### Histogram for Government Insitution


```{r}
ggplot(cls ,aes(x = GOVT)) +
  geom_histogram(fill = "lightblue", color = "black") +
  geom_vline(aes(xintercept = mean(GOVT)), color = "red", lwd = 1) +
  labs(title = "Histogram of Government", x = "government")

```


### Histogram for KV Insitution

```{r}
ggplot(cls ,aes(x = KV)) +
  geom_histogram(fill = "lightblue", color = "black") +
  geom_vline(aes(xintercept = mean(KV)), color = "red", lwd = 1) +
  labs(title = "Histogram of Government", x = "government")
```

### Histogram for Government aided Insitution

```{r}
ggplot(cls ,aes(x = `GOVT.AIDED`)) +
  geom_histogram(fill = "lightblue", color = "black") +
  geom_vline(aes(xintercept = mean(`GOVT.AIDED`)), color = "red", lwd = 1) +
  labs(title = "Histogram of Government Aided", x = "government aided")

```



### Histogram for JNV Insitution

```{r}
ggplot(cls ,aes(x = JNV)) +
  geom_histogram(fill = "lightblue", color = "black") +
  geom_vline(aes(xintercept = mean(JNV)), color = "red", lwd = 1) +
  labs(title = "Histogram of JNV Insitution", x = "JNV Insitution")

```

### Histogram for INDEPENDENT Insitution

```{r}
ggplot(cls ,aes(x = INDEPENDENT)) +
  geom_histogram(fill = "lightblue", color = "black") +
  geom_vline(aes(xintercept = mean(INDEPENDENT)), color = "red", lwd = 1) +
  labs(title = "Histogram of INDEPENDENT Insitution", x = "INDEPENDENT Insitution")

```


## Box plot

### Box Plot for GOVT

```{r}
boxplot(cls$GOVT)
```

### Box Plot for GOVT AIDED

```{r}
boxplot(cls$`GOVT.AIDED`)
```

### Box Plot for KV Insitution

```{r}
boxplot(cls$KV)
```

### Box Plot for Independent Insitution

```{r}
boxplot(cls$INDEPENDENT)
```

### Box Plot for JNV Insitution

```{r}
boxplot(cls$JNV)
```

## Scatter plot

### Scater plot GOVERNMENT vs GOVERNMENT AIDED

```{r}
ggplot(cls, aes(x = GOVT, y = `GOVT.AIDED`)) +
  geom_point() +
  labs(title = "Scatter plot of GOVT vs. GOVT AIDED")
```


### Scater plot for  GOVT vs INDEPENDENT

```{r}

ggplot(cls, aes(x = GOVT, y = INDEPENDENT)) +
  geom_point() +
  labs(title = "Scatter plot of GOVT vs. INDEPENDENT")
```


### Scater plot for GOVT AIDED vs KV

```{r}
ggplot(cls, aes(x = `GOVT.AIDED`, y = KV)) +
  geom_point() +
  labs(title = "Scatter plot of GOVT AIDED vs. KV")
```


### Scater plot for KV vs JNV INSITUTION

```{r}

ggplot(cls, aes(x = KV, y =JNV)) +
  geom_point() +
  labs(title = "Scatter plot of KV vs. JNV")
```

### Scater plot for GOVT vs  INDEPENDENT

```{r}

ggplot(cls, aes(x = GOVT, y =INDEPENDENT)) +
  geom_point() +
  labs(title = "Scatter plot of GOVT vs. INDEPENDENT")
```


# Linear Regression

### Visualize the data: GOVT vs INDEPENDENT

```{r}
ggplot(cls, aes(x = GOVT, y =`GOVT.AIDED`)) +
  geom_point(color = "blue") +
  ggtitle("Scatter Plot of GOVT vs GOVT AIDED Insituttion") +
  xlab("GOVT Schools") +
  ylab("GOVT AIDED Insitution")
```



### Fit Linear Regression Model

```{r}
model <- lm(`GOVT.AIDED` ~ GOVT, data = cls)
summary(model)
predicted <- predict(model, cls)
```


# Evaluate the Model

### Mean Squared Error (MSE)

```{r}
mse <- mean((cls$`GOVT.AIDED` - predicted) ^ 2)
cat("Mean Squared Error (MSE):", mse, "\n")

```

### Root Mean Squared Error (RMSE)

```{r}
rmse <- sqrt(mse)
cat("Root Mean Squared Error (RMSE):", rmse, "\n")

```

# Visualize the regression line

```{r}
ggplot(cls, aes(x = GOVT, y = `GOVT.AIDED`)) +
  geom_point(color = "blue") +
  geom_smooth(method = "lm", color = "red") +
  ggtitle("Linear Regression: GOVT vs INDEPENDENT Schools") +
  xlab("GOVT Schools") +
  ylab("INDEPENDENT Schools")

```