Question $5$: Analyze the QSAR fish toxicity data set from the site:

https:$//$archive$.$ics.uci.edu$/$ml$/$datasets$/$QSAR$+$fish$+$toxicity. Perform variable selection on the six predictors using the lasso package.

a$)$ Based on the output of "lars", please provide the sequence of candidate models. $($For example, you may give the result like: the first model is $\{x_5\},$ the second model is $\{x_5,x_3\}$ and the third model is $\{x_5,x_3,x_{10}\},$ etc.$)$

b$)$ Simulate $100$ faked columns as faked predictors. $($Hint: To simulate a faked column of length $n,$ you can simulate $n$ random normal variables with mean $0$ and variance $1$ using the command: fakepred$1$i$-$rnorm$($n$,0,1).$ As you need to simulate $100$ faked columns, you need to write a "for" loop. After simulating each column, you need to add the faked predictor to the original data set by the command cbind. For example, data$=$cbind$($data$,$ fakepred$).$ This is to add the new column to the old data set.$)$

c$)$ Use the cross validation method, select the best value for the fraction $s$ based on the plot of cross validation error againt the fraction $s.$ on the new data set with all the faked predictors. Use the optimum s and perform the penalized regression. Does the selected model select the true predictors $($the original predictors in the data set$)$ and omit all the faked ones?

Write in R code pls