diff --git a/Questions concerning R language.md b/Questions concerning R language.md index 5bba07e..0d8a797 100644 --- a/Questions concerning R language.md +++ b/Questions concerning R language.md @@ -13,8 +13,7 @@ This problem involves the `OJ` data set which is part of the `ISLR` package. ***Conceptual Question*** Here we explore the maximal margin classifier on a toy data set. -* We are given n = 7 observations in p = 2 dimensions. For each observation, there is an associated class label. - +* i. We are given n = 7 observations in p = 2 dimensions. For each observation, there is an associated class label. Sketch the observations. | Obs. | X1 | X2 | Y | | -------- | -------- | -------- | -------- | @@ -26,14 +25,14 @@ Here we explore the maximal margin classifier on a toy data set. | 6 | 4 | 3 | Blue | | 7 | 4 | 1 | Blue | -Sketch the observations. -* Sketch the optimal separating hyperplane, and provide the equa- tion for this hyperplane. -* Describe the classification rule for the maximal margin classifier. It should be something along the lines of “Classify to Red if β0 + β1X1 + β2X2 > 0, and classify to Blue otherwise.” Provide the values for β0, β1, and β2. -* On your sketch, indicate the margin for the maximal margin hyperplane. -* Indicate the support vectors for the maximal margin classifier. -* Argue that a slight movement of the seventh observation would not affect the maximal margin hyperplane. -* Sketch a hyperplane that is not the optimal separating hyper- plane, and provide the equation for this hyperplane. -* Draw an additional observation on the plot so that the two classes are no longer separable by a hyperplane. +* ii. Sketch the optimal separating hyperplane, and provide the equa- tion for this hyperplane. +* iii. Describe the classification rule for the maximal margin classifier. It should be something along the lines of “Classify to Red if β0 + β1X1 + β2X2 > 0, and classify to Blue otherwise.” Provide the values for β0, β1, and β2. +* iv. On your sketch, indicate the margin for the maximal margin hyperplane. +* v. Indicate the support vectors for the maximal margin classifier. +* vi. Argue that a slight movement of the seventh observation would not affect the maximal margin hyperplane. +* vii. Repeat parts (ii) through (v) using a support vector machine with a polynomial kernel. Set `degree=2`. +Sketch a hyperplane that is not the optimal separating hyper- plane, and provide the equation for this hyperplane. +* viii. Draw an additional observation on the plot so that the two classes are no longer separable by a hyperplane.