STAT 704 Homework 8
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PART 1:
Do the following problems from the textbook:

11.28, 11.29(a,b,c,e)[see note below about Muscle Mass data], 11.30(a,b,c,d,f)

PART 2:

Problem 1:

(a) For the Patient Satisfaction data set, use a random forest regression to relate Satisfaction (Y) to age (X1), illness severity (X2), and anxiety (X3). 
Use the 'randomForest' function in R with the default value of 'mtry'.  
Based on the 'importance' measure, assess the relative importance of the three predictors in the model.
Predict the satisfaction of a patient with age 52, severity 45, and anxiety 1.9.

(b) Look at the help documentation for the 'randomForest' function in R.  What was the default value of 'mtry' for this data set?
Repeat part (a), now specifying mtry=2.  How do your answers differ?


Problem 2:

For the following data on cars, where horsepower is the predictor and mileage is the response, fit and plot nonparametric 
regressions using kernel methods and spline methods.  Try different amounts of smoothing.  Comment on your results,
and comment on the relationship between horsepower and mileage.

horsepower <- c(49,55,55,70,53,70,55,62,62,80,73,92,92,73,66,73,78,92,78,90,92,74,95,81,95,92,92,92,90,52,103,84,84,102,102,81,90,90,102,102,130,95,95,102,95,93,100,100,98,130,115,115,115,115,180,160,130,96,115,100,100,145,120,140,140,150,165,165,165,165,245,280,162,162,140,140,175,322,238,263,295,236)
mileage <- c(65.4,56,55.9,49,46.5,46.2,45.4,59.2,53.3,43.4,41.1,40.9,40.9,40.4,39.6,39.3,38.9,38.8,38.2,42.2,40.9,40.7,40,39.3,38.8,38.4,38.4,38.4,29.5,46.9,36.3,36.1,36.1,35.4,35.3,35.1,35.1,35.0,33.2,32.9,32.3,32.2,32.2,32.2,32.2,31.5,31.5,31.4,31.4,31.2,33.7,32.6,31.3,31.3,30.4,28.9,28,28,28,28,28,27.7,25.6,25.3,23.9,23.6,23.6,23.6,23.6,23.6,23.5,23.4,23.4,23.1,22.9,22.9,19.5,18.1,17.2,17,16.7,13.2)

The "Muscle Mass (Problem 1.27)" and "Patient Satisfaction" data can be found on the course web page.  

NOTE: The Problem 1.27 Muscle Mass data is different from the Muscle Mass data you used for piecewise regression in HW 5!

Please write your answers neatly and clearly!