2 Linear Regression, Cubic Style (Fall 2020 Exam Problem) Given a set of training data {xiR,yiR}i=1n, you wish to learn a predictor for the label yi given an input xi a) After plotting the data, you have a hunch that the labels are approximately a cubic function of the inputs. Write down the general form of a cubic function. b) Plot an example of a set of >10 data points that visually conform to this kind of model. c) Explain carefully how you would set up and solve this prediction problem, including assembling an appropriate data matrix X (write out the entries of X in detail) and writing the equations you would solve for the optimal least-squares predictor. d) Explain some of the things that could go awry in your solution in the previous part and how you would fix them. e) Explain how you would deal with a cubic dependence of the label on the input data when the data are now vectors xiRp,p>1. What issues might arise in this case? 2 Linear Regression, Cubic Style (Fall 2020 Exam Problem) Given a set of training data {xiR,yiR}i=1n, you wish to learn a predictor for the label yi given an input xi a) After plotting the data, you have a hunch that the labels are approximately a cubic function of the inputs. Write down the general form of a cubic function. b) Plot an example of a set of >10 data points that visually conform to this kind of model. c) Explain carefully how you would set up and solve this prediction problem, including assembling an appropriate data matrix X (write out the entries of X in detail) and writing the equations you would solve for the optimal least-squares predictor. d) Explain some of the things that could go awry in your solution in the previous part and how you would fix them. e) Explain how you would deal with a cubic dependence of the label on the input data when the data are now vectors xiRp,p>1. What issues might arise in this case