# 8 Exercise 4: Transformation of the response and predicator

The `Animals`

data set which pertains to Brain and Body Weights for 28 Species. You can get this data set using the `library(Mass)`

In this dataset there are three outliers which are the dinosaurs.

(a) Sort the data by body and remove the last three dinosaur elements using the following code:

```
<- Animals[order(Animals$body), ] #sorted by body weight
SA <- SA[-c(28:26), ] #remove dinosaurs NoDINO
```

Now treating the data as we done in the previous exercise transform both the response and predictor:

(b) Define a linear model for the transformed response and transformed predictor .

`<- lm(log(brain) ~ log(body), data = NoDINO) model1 `

(c) Use the function coef() to answer the below questions:

`coef(model1)`

```
## (Intercept) log(body)
## 2.1504121 0.7522607
```

i. What is the predicted brain weight of the jaguar whose weight is listed as 100 kg?

Log(Brain weight) = + ( \(\cdot\) log()) = .

*This must be back transformed to get the units of original brain measurement (grams).*

Brain weight = \(exp(\)\()\) = g

Log(Brain weight) = \(2.1504\) + (\(0.7523\) \(\cdot\) \(log(100) = 5.6149\). Back-transforming with exponential menas Brain weight = \(exp(5.6149)\) = \(274.48\)g

ii. If said jaguar were to increase its weight by 10%, what would the expected increase in brain weight be?

"With the coefficient of , an increase in body weight of 1% would lead to % increase in brain weight.
* = g"

"With the coefficient of \(0.7523\), an increase in body weight of 1% would lead to \(7.523\)% increase in brain weight. so \(1.07523 * 274.48\) = \(295.0634\)g