Using R$,$ please answer $($a$)$ until $($e$).$

$($a$)(1$ points$)$ Create a scatterplot where y is plotted against x$.$ Describe your findings.### Your Solution $($Code$)$

Your Solution $($Text$)$

$($b$)(3$ points$)$ Use $lm()$ to fit the three models below. Print the summary tables for the three fitted models and comment your findings.

Model I: $Y={}_0+{}_{1}x+$

Model II: $Y={}_0+{}_{1}x+{}_2{x}^2+$

Model III: $Y={}_0+{}_{1}x+{}_2{x}^2+{}_3{x}^3+$

### Your Solution $($Code$)$

Your Solution $($Text$)$

$($c$)(4\mathrm{.}5$ points$)$ Calculate the leave$-$one$-$out$-$cross$-$validation mean squared error for each model I$-$III.

### Your Solution $($Code$)$

$3$

$($d$)(4\mathrm{.}5$ points$)$ Calculate the $k-$fold cross$-$validation mean squared error for each model I$-$III for $k=10.$

### Your Solution $($Code$)$

$($e$)(1$ point$)$ Which model has the least cross$-$validation error based on your results in $($c$)$ and $($d$)?$ Briefly explain why.