Problem 5. Intuition for Multivariate Linear Regression You are given a data set containing information on recently sold houses in San Diego, including 0 square footage 0 number of bedrooms a number of bathrooms 0 year the house was built - asking price, or how much the house was originally listed for, before negotiations 0 sale price, or how much the house actually sold for, after negotiations The table below shows the rst few rows of the data set. Note that since you don't have the full data set, you cannot answer the questions that follow based on calculations; you must answer conceptually. House | Square Feet Bedrooms Bathrooms Year Asking Price | Sale Price 1 1247 3 3 2005 500,000 494,000 2 1670 3 2 1927 1,000,000 985,000 3 716 1 1 1993 335,000 333, 850 4 1600 4 2 1962 830,000 815,000 5 4 3 2635 1993 1,250,000 1 ,250,000 a) Q, {3 [:3 (9') Suppose you standardize all six variables and t a linear prediction rule to predict the sale price of the house based on all ve of the other variables. Which feature would you expect to have the largest magnitude weight? Without standardizing, which feature would you expect to have the largest magnitude weight? Explain why. b) (36 (3 (3 Suppose you use multiple linear regression on the original (unstandardized) data and the weight associated with Year is a. Suppose you replace Year with a new predictor variable, Age, which is 0 if the house was built in 2020, 1 if the house was built in 2019, 2 if the house was built in 2018, etc. If we do multiple linear regression again using Age instead of Year, what will be the weight associated with Age in terms of a? c) (36 6 Suppose you add a new feature called Rooms, which is the total number of bedrooms and bathrooms in the house. Would multiple linear regression with this extra feature enable you to make better predictions