We will focus on the Extent of the sea ice in this exercise and see how it has

changed over time since $1979.$ Instead of using the actual year as our explanatory

variable, to keep the size of the coefficients manageable, we will use a variable called t$,$

which measures time since $1978($the value for $1979$ is $1).$

a$.$ Produce a scatterplot that could be used to predict Extent from t$.$ Comment

on the pattern.

b$.$ Create a residuals versus fits plot for predicting Extent from t$.$ What does this

plot tell you about the idea of fitting a linear model to predict Extent from t$?$

Explain.

c$.$ Transform Extent by squaring it$.$ Plot Extent versus t$.$ Comment on the

pattern.

d$.$ Create a residuals versus fits plot for this new response variable using t$.$

Discuss whether there is improvement in this plot over the one you created

in part $($b$).$

e$.$ Redo parts $($c$)$ and $($d$)$ using the cube of Extent.

f$.$ Would you be comfortable using a linear model for any of these three

response variables? Explain.