Update page 'Questions concerning R language'

Questions concerning R language.md

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+*###Applied*
+This problem involves the `OJ` data set which is part of the `ISLR` package.	
+* Create a training set containing a random sample of 800 observations, and a test set containing the remaining observations.	
+* Fit a support vector classifier to the training data using `cost=0.01`, with `Purchase` as the response and the other variables as predictors. Use the `summary()` function to produce summary statistics, and describe the results obtained.
+* What are the training and test error rates?
+* Use the `tune()` function to select an optimal cost. Consider values in the range 0.01 to 10.
+* Compute the training and test error rates using this new value for `cost`.
+* Repeat parts (ii) through (v) using a support vector machine with a radial kernel. Use the default value for `gamma`.
+* Repeat parts (ii) through (v) using a support vector machine with a polynomial kernel. Set `degree=2`.
+* Overall, which approach seems to give the best results on this data? 
+
+*###Conceptual*
+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.
+| Obs. | X1 | X2 | Y |
+| -------- | -------- | -------- | -------- |
+| 1    | 3   | 4   | Red   |
+| 2    | 2   | 2   | Red   |
+| 3    | 4   | 4   | Red   |
+| 4    | 1   | 4   | Red   |
+| 5    | 2   | 1   | Blue  |
+| 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. 
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