# 6 Exercise 2

## 6.1 Exercise 2 part 1 - Transforming Y with ln

Note that the default understanding of log in R is $$log_e$$ = ln = log.

(a) Perform analysis the data frame SIMDATAST to create and display six graphs using a 2 by 3 layout.

1. Produce a scatterplot of $$y_1$$ versus $$x_1$$.
# Begin by setting up the 2x3 grid
par(mfrow = c(2, 3))
# Plot y1 vs x1
plot(y1 ~ x1, data = SIMDATAST)
1. Plot the residuals versus fits for the model created by regressing $$y_1$$ on $$x_1$$ (call this model modx1). Based on the first two graphs, does a logarithmic transformation for the response variable make sense?
# Define the model
modx1 <- lm(y1 ~ x1, data = SIMDATAST)
# Plot the residual graphs
plot(modx1, which = c(1,2))
#This plot function will produce many analytical graphs so using c(1,2) selects that you want the fitted residual plot and the Q-Q plot as they are the first 2 it produces.

(iii) In the second row of graphs, create a scatterplot of $$ln(y_1$$) versus $$x_1$$.

# Plot y1 vs ln(x1)
plot(log(y1) ~ x1, data = SIMDATAST)

(iv) Create a plot of the residuals versus the fits for the model and the Q-Q normal plot for log($$y_1$$) ~ $$x_1$$.

# Use the plot function:
plot(lm(log(y1) ~ x1, data = SIMDATAST), which = c(1,2))
# when Par is run along with the rest of this code it will put the 6 graphs in the grid.

1. Based on the second row of graphs, do the assumptions for the normal error model seem to be satisfied for the model log($$y_1$$) ~ $$x_1$$?

## 6.2 Exercise 2 part 2 - Transforming Y with a reciprical

(a) Perform analysis the data frame SIMDATAST to create and display six graphs using a 2 by 3 layout.

1. Produce a scatterplot of $$y_2$$ versus $$x_2$$.
# Begin by setting up the 2x3 grid
par(mfrow = c(2, 3))
# Plot y1 vs x1
plot(y2 ~ x2, data = SIMDATAST)
1. Plot the residuals versus fits for the model created by regressing $$y_2$$ on $$x_2$$ (call this model modx2).
# Define the model
modx2 <- lm(y2 ~ x2, data = SIMDATAST)
# Plot the residual graphs
plot(modx2, which = c(1,2))
#This plot function will produce many analytical graphs so using c(1,2) selects that you want the fitted residual plot and the Q-Q plot as they are the first 2 it produces.
1. Based on the first two graphs, does a reciprocal transformation for the response variable make sense?

2. In the second row of graphs, create a scatterplot of $$y_2^{-1}$$ versus$$x_2$$.

# Plot y1 vs ln(x1)
plot((y2)^-1 ~ x2, data = SIMDATAST)
1. Create a plot of the residuals versus the fits and the Q-Q normal plot for $$y_2^{-1} \sim x_2$$.
# Use the plot function:
plot(lm((y2)^-1 ~ x2, data = SIMDATAST), which = c(1,2))
# when Par is run along with the rest of this code it will put the 6 graphs in the grid.

1. Based on the second row of graphs, do the assumptions for the normal error model seem to be satisfied for the model $$y_2^{-1} \sim x_2$$?