These questions are not worth any points; they're just interesting challenges for people who have finished problems 1-3 and have some time left over. - Try modifying your `power_lin_reg` function from problem 2 to accept a different standard deviation for the `noise` variable. Investigate how the standard deviation affects power. - Try modifying your `power_lin_reg` function to accept a different significance level $\alpha$ for rejecting the null hypothesis. Let it have the default value of .05. Investigate how $\alpha$ affects power. - Try writing another function that calls `power_lin_reg` multiple times, and makes a graph of power as a function of sample size (or slope)