using the these methods:

Ridge regression

Lasso

Principal component regression

(Use R for data analysis) A real estate appraiser is interested in a reliable working method of evaluating residential home prices as a function of various features. Data on 522 recent home sales

While predicting Sales Price, we would like to reduce multi-collinearity in order to obtain a more reliable prediction. Compare performance of the following methods.

(a) Ridge regression

Find the optimal tuning parameter λ. According to the model, how is the home price expected to change if one additional bathroom and swimming pool are built, without changing other variables?

(b) Lasso

Find the optimal tuning parameter λ. List variables that lasso eliminated from the model and variables that were retained. According to the model, is a home expected to gain value if it is close to a highway? Use your results to answer this question.

(c) Principal component regression

– Fit a principal components regression based on standardized (rescaled) X variables.

– How many principal components are needed to explain 80% of the total variation of standardized X −variables.

– How many principal components are needed to explain 80% of the total variation of sales prices?

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