(Please use Rmarkdown to answer (e) and (f) )

Create some simulated data and will fit a linear regression models to it. Make sure to use set.seed(1) prior to starting part (a) to ensure consistent results. a. Using the rnorm() function, make a vector, X, containing 100 observations drawn from a N(0,1) distribution. This represents a feature, X. b. Using the rnorm() function, make a vector ,containing 100 observations drawn from a N(0,0.25) distribution i.e. a normal distribution with mean zero and variance 0.25. c. Using x and ,generate a vector y according to the model Y= 1 + 0 .5X+ . What is the length of the vector y? What are the values of 0,1 in this linear model? d. Make a scatterplot displaying the relationship between x and y. Fit a least squares linear model to predict y using x. Display the least squares line on the scatterplot. Draw the population regression line on the plot, in a different color. Use the legend() command to make an appropriate legend. e. Then fit a separate quadratic regression, i.e. Y= 0 + 1 X + 2 X² + .Consider the training residual sum of squares (RSS) for the linear regression, and also the training RSS for the quadratic regression. Would we expect one to be lower than the other, would we expect them to be the same, or is there not enough information to tell? Justify your answer. f. Answer (e) using a test rather than RSS.