SLR_model.qmd

# Simple linear regression model: Example

## Read data

```{r}
senic <- read.table('./Datasets/SENIC_data.txt')
```

## Data pre-processing

```{r}
colnames(senic) <- c("ID", "LOS", "AGE", "INFRISK", "CULT", "XRAY", "BEDS", "MEDSCHL", "REGION", "CENSUS", "NURSE", "FACS")
```

## Model

Develop a linear regression model to Predict the length of stay based on probability of the person getting infected.

```{r}
model <- lm(LOS~INFRISK, data = senic)
summary(model)
```

```{r}
library(ggplot2)
ggplot(data = senic, aes(x = INFRISK, y = LOS))+
  geom_point()+
  geom_smooth(method = "lm")
```

## Error variance

```{r}
sum(model$residuals**2)/(111)
```

## Confidence and Prediction intervals

```{r}
library(ggplot2)

ci <- predict(model, newdata = senic, interval = "confidence", level = 0.95)

pi <- predict(model, newdata = senic, interval = "prediction", level = 0.95)

data_ci <- cbind(senic, ci)
data_pi <- cbind(senic, pi)

ggplot(data = senic, aes(y = LOS, x = INFRISK))+
  geom_point()+
  geom_line(data = data_ci, aes(x = INFRISK, y = lwr), color = "red")+
  geom_line(data = data_ci, aes(x = INFRISK, y = upr), color = "red")+
  geom_line(data = data_pi, aes(x = INFRISK, y = lwr), color = "green")+
  geom_line(data = data_pi, aes(x = INFRISK, y = upr), color = "green")+
  geom_smooth(method = "lm")+
  labs(
    y = "Length of stay"
  )

```