# 7 Exercise 3: Transformation of the response and predicator

At times it will be necessary to transform both the response and the predictor. Using the `SIMDATAST`

data set produce an ouput of your graphs in a 2 rows x 3 columns grid:

(a) i. Plot \(y_1\) against \(x_3\)

Define the model for \(y_1\) against \(x_3\) and create the residual vs fitted values plot.

Log transform the response variable and produce a new scatterplot.

Define the model for \(log(y_1)\) against \(x_3\) and create a residual vs fitted values plot.

Square-root predictor and plot a scatterplot of \(log(y_1)\) against \(\sqrt{x_3}\)

Define the model for \(log(y_1)\) against \(\sqrt{x_3}\) and create a residual vs fitted values plot.

```
# create 2 rows x 3 columns grid
par(mfrow = c(2, 3))
# plot y vs x3
plot(y1 ~ x3, data = SIMDATAST,main="Scatterplot of y1~x3")
# define model for log transformed response y1 vs x3
<- lm(y1 ~ x3, data = SIMDATAST)
mod1 # you can choose to add the model line to the plot with abline(mod1)
# residual plot for mod1
plot(mod1, which = 1, main = "Residuals vs Fitted value for y1~x3")
# plot of log transformed y against x3
plot(log(y1) ~ x3, data = SIMDATAST, main = "Scatterplot of log(y1)~x3")
# define model for log transformed response y1 vs x3
<- lm(log(y1) ~ x3, data = SIMDATAST)
mod2 # optionally add abline(mod2) to the plot
# residual plot for mod2
plot(rstandard(mod2) ~ fitted(mod2), main="Residuals vs Fitted value for log(y1)~x3")
# optional to add abline(h=0,lty=3) to the plot
# plot of log transformed y against sqrt(x3)
plot(log(y1) ~ I(x3^0.5), data = SIMDATAST, main = "Scatterplot of log(y1)~sqrt(x3)")
<- lm(log(y1) ~ I(x3^.5), data = SIMDATAST) # define model for log transformed response y1 vs sqrt(x3)
mod3 #optional to add abline(mod3) to the plot
# residual plot for mod3
plot(rstandard(mod3) ~ fitted(mod3), main="Residuals vs fitted of log(y1)~sqrt(x3)")
```

`# optional to add abline(h=0,lty=3) to the plot`