---
title: "A first SLR model fit to data from the class"
output: pdf_document
---

Here's the SLR model that we are going to fit using data from our class:

$$\mu\{Height|Pets\} =\beta_0 + \beta_1\times Pets$$

After randomly selecting 3 students from class (with name s S, Z and E), we asked them how many pets they had growing up (Pets) and how tall (inches) they are right now.   Here's the R code:

```{r}
Pets = c(5,3,4)
Hts =c(65,66,67)   
ID=c("S","Z","E")

m = lm(Hts ~ Pets)
summary(m)
```

The slope for the best fit line is         $$\hat\beta_1=r\times\frac{s_y}{s_x}$$

Let's check this formula with what R reported above:
```{r}
# Check R
cor(Pets,Hts)
sd(Pets)
sd(Hts)

# \hat \beta_1
sd(Hts)/sd(Pets)*cor(Pets,Hts)   

# \hat \beta_0
mean(Hts)-mean(Pets)*(-.5)
```

Let's generate a scatterplot and overlay the regression line
```{r}
# Let's add this line to the scatterplot
plot(Pets,Hts)
abline(68,-1/2)
```