please use R software to solve this : Simulate a data set with 100 observations yi = 10 + x + 2x 2 + 3x 3 + i , where i follows independent normal distribution N(0, 1). a) Perform polynomial regression on your simulated data set and using x, I(x 2 ), I(x 3 ) as the predictors. Compare the estimated coefficients with the true model and report the R-square. b) Formulate the design matrix of this regression and write down the first two rows of the design matrix based on your data set. c) Perform polynomial regression on your simulated data set and using x, I(x 2 ), I(x 3 ), I(x 4 ) as the predictors. Compare the estimated coefficients with the true model and report the Rsquare. Is the R-square increased or decreased compared to the model in part (a)? Explain why?