2) This question should be answered using the Marketing data set, which is provided on Blackboard.

Consider observations 1 to 120 as training data and rest of them as testing data.

Use the training data set to perform a k-nearest neighbor model with pop_density as

the response and rest of the variables as predictors (google_adwords. Facebook,

twitter, marketing_total, revenues, employees). Where choose k as 5.

Calculate the training error of k-nearest neighbor method by using R.

Calculate the testing error of k-nearest neighbor method by using R.

Observation	google_adwords	facebook	twitter	marketing_total	revenues	employees	pop_density
1	65.66	47.86	52.46	165.98	39.26	5	High
2	39.1	55.2	77.4	171.7	38.9	7	Medium
3	174.81	52.01	68.01	294.83	49.51	11	Medium
4	34.36	61.96	86.86	183.18	40.56	7	High
5	78.21	40.91	30.41	149.53	40.21	9	Low
6	34.19	15.09	12.79	62.07	38.09	3	High
7	225.71	15.91	33.31	274.93	44.21	10	Low
8	90.03	17.13	34.33	141.49	40.23	6	High
9	238.4	35.1	13.9	287.4	48.8	6	Medium
10	43.53	42.23	71.83	157.59	36.63	4	Low
11	118.24	15.74	14.14	148.12	38.14	7	Medium
12	224.64	40.84	52.74	318.22	47.24	9	High
13	219.51	59.21	63.21	341.93	54.21	10	High
14	89.79	45.99	122.19	257.97	42.19	6	Low
15	306.09	51.69	66.69	424.47	56.79	12	Medium
16	91.98	30.68	27.28	149.94	41.78	6	High
17	242.72	39.42	63.92	346.06	50.02	10	Medium
18	263.64	18.74	35.94	318.32	46.44	6	Low
19	35.16	25.26	57.76	118.18	35.26	5	Low
20	253.04	29.04	37.14	319.22	47.94	10	High
21	88.14	25.84	30.34	144.32	43.24	6	High
22	163.68	37.48	19.58	220.74	43.48	6	Low
23	263.96	27.96	32.96	324.88	47.46	9	Medium
24	268.98	34.68	29.28	332.94	46.78	9	Low
25	314.07	36.87	50.57	401.51	50.27	9	Low
26	134.9	26.8	46.8	208.5	41.6	8	High
27	284.99	26.79	5.89	317.67	44.49	10	Medium
28	117.68	10.78	15.58	144.04	39.18	3	Low
29	316.09	16.89	20.09	353.07	45.89	10	Medium
30	288.58	52.88	12.88	354.34	54.78	10	Low
31	97.37	59.47	54.57	211.41	45.07	10	Medium
32	66.6	37.6	44.8	149	41.3	7	High
33	250.75	47.85	40.95	339.55	51.95	12	Medium
34	223.1	30.3	38.4	291.8	44.9	6	High
35	202.09	45.89	49.99	297.97	49.89	9	Medium
36	317.58	39.08	11.98	368.64	52.38	9	High
37	231.76	20.66	37.46	289.88	45.46	8	High
38	45.16	33.16	49.56	127.88	36.26	6	Medium
39	199.47	34.27	42.07	275.81	46.97	8	Low
40	262.08	51.08	26.88	340.04	53.08	9	Low
41	224.85	15.55	45.85	286.25	44.15	9	Low
42	124.23	20.83	13.63	158.69	42.23	8	Medium
43	241.18	53.88	50.58	345.64	55.08	9	Low
44	205.77	56.77	68.07	330.61	52.07	10	Medium
45	285.71	39.21	25.11	350.03	50.91	10	Low
46	32.13	40.33	52.43	124.89	38.03	6	Low
47	155.66	26.06	22.26	203.98	40.36	9	High
48	233.44	59.64	46.54	339.62	54.14	10	Low
49	235.13	41.33	19.93	296.39	50.53	12	High
50	77.65	13.55	31.75	122.95	39.95	7	Medium
51	283.94	52.74	63.54	400.22	54.54	10	Medium
52	128.03	42.33	19.93	190.29	47.03	7	High
53	153.47	52.57	37.47	243.51	48.07	9	Low
54	90.01	17.71	8.11	115.83	38.01	4	Low
55	51.29	31.79	8.19	91.27	36.99	4	Medium
56	159.3	21.9	16.4	197.6	41.1	9	Medium
57	258.91	36.41	18.71	314.03	48.11	10	High
58	239.73	54.23	36.33	330.29	52.93	11	Low
59	133.73	25.63	41.83	201.19	44.03	8	Medium
60	48.95	42.55	27.65	119.15	38.65	3	Low
61	155.09	18.79	43.19	217.07	44.39	8	High
62	234.76	33.36	20.66	288.78	46.06	8	High
63	50.01	11.51	29.41	90.93	37.11	3	Low
64	142.13	37.53	22.03	201.69	43.53	10	High
65	29.26	41.16	19.46	89.88	36.86	6	High
66	137.11	16.21	30.41	183.73	39.81	3	Medium
67	262.45	14.15	45.75	322.35	42.65	7	Medium
68	99.96	32.36	43.36	175.68	43.66	7	Low
69	88.29	51.79	41.69	181.77	41.19	7	Low
70	238.93	55.83	45.43	340.19	54.83	11	Medium
71	214.87	27.47	73.57	315.91	44.57	6	Medium
72	101.48	40.08	27.38	168.94	44.88	7	High
73	132.43	49.73	71.13	253.29	45.43	8	High
74	109.94	34.54	81.24	225.72	42.24	6	Low
75	132.43	57.83	60.23	250.49	47.03	10	High
76	159.85	17.85	21.05	198.75	44.45	8	Medium
77	243.05	46.25	70.55	359.85	52.45	10	Medium
78	272.93	45.93	80.53	399.39	51.93	9	Medium
79	132.14	26.14	21.84	180.12	43.94	10	High
80	189.32	45.02	65.12	299.46	50.62	12	Medium
81	219.94	13.24	14.44	247.62	41.74	8	Low
82	313.99	53.99	61.69	429.67	57.39	12	Low
83	157.3	51.2	54.2	262.7	47	7	Low
84	243.98	13.28	57.58	314.84	40.98	7	Medium
85	321	48.3	111.7	481	56.1	12	High
86	300.92	18.22	28.32	347.46	43.22	9	Medium
87	262.48	45.98	15.78	324.24	52.68	9	High
88	158.05	53.95	65.35	277.35	47.05	8	High
89	46.02	19.42	36.92	102.36	35.92	6	Low
90	110.7	8	29.7	148.4	36.7	6	High
91	34.08	8.78	32.78	75.64	33.98	5	Low
92	275.11	34.01	11.41	320.53	47.21	7	Low
93	249.6	19.4	66.5	335.5	44.9	9	High
94	267.13	50.83	34.83	352.79	54.93	11	Low
95	200.45	27.55	13.35	241.35	46.55	6	Low
96	234.48	32.88	21.78	289.14	48.48	10	Low
97	100.69	56.69	43.19	200.57	44.79	10	High
98	97.27	44.57	61.07	202.91	42.47	8	High
99	164.18	26.68	36.78	227.64	44.88	8	High
100	99.93	11.73	24.53	136.19	40.63	8	High
101	43.28	27.28	32.38	102.94	38.18	5	Medium
102	163.07	35.97	54.17	253.21	44.97	10	Low
103	245.19	10.99	22.99	279.17	40.49	7	Low
104	149.35	48.25	24.85	222.45	49.15	10	Medium
105	253.23	43.43	84.13	380.79	51.13	10	Medium
106	107.99	19.99	32.89	160.87	39.09	5	Medium
107	28.01	46.51	57.01	131.53	34.51	6	Low
108	102.85	10.05	18.05	130.95	39.15	5	High
109	246.07	62.17	15.17	323.41	58.17	10	Low
110	83.09	22.89	52.79	158.77	40.89	10	Low
111	26.83	53.13	21.03	100.99	35.43	4	Medium
112	289.62	14.72	53.62	357.96	44.82	6	Low
113	30.2	36.4	10.1	76.7	35.2	3	Low
114	59.22	48.32	74.12	181.66	40.82	7	Low
115	68.64	54.74	15.04	138.42	39.64	6	Medium
116	44.99	45.79	14.89	105.67	36.59	4	High
117	298.01	40.61	70.21	408.83	52.81	12	High
118	63.02	33.32	26.72	123.06	37.32	7	High
119	207.32	53.72	10.32	271.36	50.82	12	Medium
120	97.18	28.18	22.88	148.24	42.38	8	Low
121	219.94	49.04	88.04	357.02	53.14	10	High
122	243.27	43.37	46.87	333.51	50.57	12	Medium
123	127.29	15.79	43.29	186.37	40.79	6	Medium
124	116.71	22.71	45.61	185.03	39.61	6	Medium
125	164.88	13.88	19.78	198.54	42.58	6	Low
126	262.58	17.18	17.38	297.14	43.38	8	Medium
127	266.08	59.28	53.38	378.74	55.98	12	High
128	65.45	33.95	27.55	126.95	38.55	3	High
129	301.6	22.2	44.1	367.9	44.7	6	High
130	144.47	19.27	58.37	222.11	42.77	6	High
131	194.62	50.42	47.22	292.26	50.02	10	Medium
132	207.64	28.34	15.54	251.52	43.14	6	Low
133	23.65	18.55	11.45	53.65	30.45	3	Low
134	117.7	54.7	60.5	232.9	46.8	10	Low
135	175.6	14.5	36.3	226.4	43.6	7	High
136	35.19	47.79	54.89	137.87	38.49	5	Medium
137	154.93	29.03	44.03	227.99	43.83	7	Low
138	195.48	28.48	39.88	263.84	45.08	10	Low
139	111.9	49.4	61.7	223	47.2	7	High
140	186.35	47.05	16.45	249.85	48.55	8	Low
141	141.28	26.18	15.68	183.14	43.68	7	Low
142	258.01	14.31	94.51	366.83	43.11	9	Low
143	38.87	45.97	28.77	113.61	36.67	4	Medium
144	227.91	13.71	26.71	268.33	41.01	10	Low
145	239.81	35.41	68.21	343.43	49.21	10	Low
146	306.77	20.47	15.07	342.31	45.17	10	Medium
147	185.03	28.83	54.13	267.99	42.73	7	Low
148	44.13	32.03	27.73	103.89	39.83	4	Medium
149	188.43	14.53	19.03	221.99	39.43	7	Low
150	247.75	16.15	24.65	288.55	44.55	7	Low
151	300.5	59.9	51.6	412	58.3	9	High
152	193.4	18.4	44.6	256.4	42.6	9	Low
153	298.3	11.3	31.5	341.1	41.1	10	High
154	188.07	19.87	26.27	234.21	42.77	6	High
155	179.4	12.8	17.3	209.5	41	9	Low
156	239.07	13.37	34.17	286.61	40.47	10	Medium
157	79.21	16.11	38.91	134.23	39.41	4	Low
158	307.43	50.23	77.83	435.49	53.73	11	Low
159	275.04	29.94	37.44	342.42	46.54	9	Low
160	225.79	53.29	26.59	305.67	51.09	10	Medium
161	160.79	10.79	34.09	205.67	39.29	4	Medium
162	216.67	41.67	29.97	288.31	50.57	12	Medium
163	308.42	23.72	12.32	344.46	46.02	9	Low
164	43.46	24.26	34.36	102.08	39.16	6	Medium
165	64.96	53.96	17.46	136.38	43.96	9	High
166	97.69	20.39	14.39	132.47	39.79	7	High
167	36.95	11.25	37.55	85.75	33.35	7	Low
168	188.45	51.05	11.45	250.95	48.95	9	Low
169	174.07	47.37	16.57	238.01	49.37	12	High
170	59.86	12.76	21.66	94.28	36.96	4	Low
171	117.91	16.01	18.01	151.93	41.11	7	Low
172	308.78	54.58	77.58	440.94	58.38	10	Medium

3) For this assignment, you need to use Smarket dataset which is available with ISLR library.

Support Vector Machine:

a. Using tune() function try different values for gamma and cost. Use the training data from part (1) (Consider that Direction shows the classes), (You can consider the code below).

tune.out=tune(svm, y~., data=dat, kernel="radial", ranges=list(cost=c(0.1,1,10,100,1000),gamma=c(0.5,1,2,3,4)))

b. After obtaining the optimized parameters gamma and cost from part .a, fit a support vector machine with radial kernel for the training data from part (1).

c. Find the support vectors and find their corresponding alpha values. (Make sure that they should be non-zero).

Need help with the R code