Model Selection

This problem practicesapplication of proper model selection techniques, with a multiple linear regression model.

We will continue working with the predictive model using multiple linear regression. However, we will now consider selection between 6 possible models:

Model 1:Volume = ?₀ + ?₁Girth + ?₂Height + ?₃Girth * Height + ?₄Girth² + ?₅Girth² * Height

Volume=?0+?1Girth+?2Height+?3Girth?Height+?4Girth2+?5Girth2?Height

Model 2:Volume = ?₀ + ?₁Girth + ?₂Height

Model 3:Volume = ?₀ + ?₁Girth + ?₂Height + ?₃Girth * Height

Model 4:Volume = ?₀ + ?₁Girth + ?₂Height + ?₄Girth² + ?₅Girth² * Height

Model 5:Volume = ?₀ + ?₄Girth² + ?₅Girth₂ * Height

Model 6:Volume = ?₀ + ?₅Girth² * Height

Note: This problem continues to use the data contained inTrees.csv(Links to an external site.).Reference with description of the original measurements may be found at:(Links to an external site.)

https://stat.ethz.ch/R-manual/R-devel/library/datasets/html/trees.html(Links to an external site.)

Use LOOCV (noten= 31) method to calculateCV₍₃₁₎ foreachof Models 1-6.

Report theCV₍₃₁₎ for Models 1 and 2.

Question 1:

Model1:CV₍₃₁₎ =

Question 2

Model2:CV₍₃₁₎ =

Question 3

Enter your R code for computing the CV(31)measure for Model 1 below.

Question 4

Which model would you select based on the values ofCV₍₃₁₎

Choose One Answer

1. Model 1
2. Model 2
3. Model 3
4. Model 4
5. Model 5
6. Model 6

Question 5

Explainwhy you chose the model selected in the previous question.

Split the data use 5-fold cross-validation method to calculateCV₍₅₎ foreachof Models 1-6.Report theCV₍₅₎ for Models 1 and 2.

Question 6

Model1:CV₍₅₎ =

Question 7

Model2:CV₍₅₎ =

Question 8

Which model would you select based on the values ofCV₍₅₎

Choose one of the following:

1. Model 1
2. Model 2
3. Model 3
4. Model 4
5. Model 5
6. Model 6

Question 9

Considering the form of the model that was selected by 5-fold cross-validation, why does this model make sense from a practical standpoint?

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