---
title: "Untitled"
format: html
---

```{r}
link <- url("https://gregorkb.github.io/data/hrbc.csv")
hrbc <- read.csv(link)
head(hrbc)


# linear model
lm_out <- lm(hem ~ rbc, data = hrbc)

plot(hem ~ rbc, data = hrbc)
abline(lm_out)

```


Build a confidence interval for $\beta_1$:

```{r}
confint(lm_out, level = 0.99)
```


Getting the p-values:

```{r}
summary(lm_out)
```

```{r}
n <- nrow(hrbc)
n
```


Get the fitted values:

```{r}


yhat <- predict(lm_out)


plot(hem ~ rbc, data = hrbc)
abline(lm_out)
points(yhat ~ hrbc$rbc, col = "red")

```



Build a confidence interval for the true height of the line at RBC 6.
```{r}

xnew <- 6
# confidence interval for mean hem level at rbc = 6
predict(lm_out, newdata = data.frame(rbc = xnew),int="conf")

# prediction interval for a single hem level at rbc = 6
predict(lm_out, newdata = data.frame(rbc = xnew),int="pred")
```


Get ANOVA table:

```{r}
anova(lm_out)

```


Get a normal QQ plot of the residuals:
```{r}
plot(lm_out, which = 2)
```

Get a residuals versus fitted values plot:

```{r}
plot(lm_out,which=1)
```

Cook's Distance

```{r}
plot(lm_out, which = 4)
```