INTRODUCTION OF SMARKET

   smarket is one of the data of ISLR Package.smarket dataset has 1250 observations and 9 variables.
  ** year-The year that the obseravtion wa recorded.
   lag1-percantage return for previous day.
   lag2-percentage return for past 2 days
   lag3-percentage returns for past 3 days
   lag4-percentage returns for pasts 4 days
   lag5-percentage returns for pasts 5 days
   volume-number of shares traded
   direction-it indicates up and down of the market **
   
'data.frame':   1250 obs. of  9 variables:
 $ Year     : num  2001 2001 2001 2001 2001 ...
 $ Lag1     : num  0.381 0.959 1.032 -0.623 0.614 ...
 $ Lag2     : num  -0.192 0.381 0.959 1.032 -0.623 ...
 $ Lag3     : num  -2.624 -0.192 0.381 0.959 1.032 ...
 $ Lag4     : num  -1.055 -2.624 -0.192 0.381 0.959 ...
 $ Lag5     : num  5.01 -1.055 -2.624 -0.192 0.381 ...
 $ Volume   : num  1.19 1.3 1.41 1.28 1.21 ...
 $ Today    : num  0.959 1.032 -0.623 0.614 0.213 ...
 $ Direction: Factor w/ 2 levels "Down","Up": 2 2 1 2 2 2 1 2 2 2 ...

How many elements are positive and negative in Lag1


Attaching package: 'dplyr'
The following objects are masked from 'package:stats':

    filter, lag
The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union
  category   n
1 Negative 601
2 Positive 648
3     Zero   1

What is the top 20% of volume traded ?

     80% 
1.704914 

How many days market direction is UP/DOWN?

[1] 0.0385

State the number of cases per year?

# A tibble: 5 × 2
   Year new_case
  <dbl>    <int>
1  2001      242
2  2002      252
3  2003      252
4  2004      252
5  2005      252

How many days market direction is UP/DOWN?

# A tibble: 2 × 2
# Groups:   Direction [2]
  Direction     n
  <fct>     <int>
1 Down        602
2 Up          648

Create datset which has only 2001 data ?

    Year   Lag1   Lag2   Lag3   Lag4   Lag5  Volume  Today Direction
1   2001  0.381 -0.192 -2.624 -1.055  5.010 1.19130  0.959        Up
2   2001  0.959  0.381 -0.192 -2.624 -1.055 1.29650  1.032        Up
3   2001  1.032  0.959  0.381 -0.192 -2.624 1.41120 -0.623      Down
4   2001 -0.623  1.032  0.959  0.381 -0.192 1.27600  0.614        Up
5   2001  0.614 -0.623  1.032  0.959  0.381 1.20570  0.213        Up
6   2001  0.213  0.614 -0.623  1.032  0.959 1.34910  1.392        Up
7   2001  1.392  0.213  0.614 -0.623  1.032 1.44500 -0.403      Down
8   2001 -0.403  1.392  0.213  0.614 -0.623 1.40780  0.027        Up
9   2001  0.027 -0.403  1.392  0.213  0.614 1.16400  1.303        Up
10  2001  1.303  0.027 -0.403  1.392  0.213 1.23260  0.287        Up
11  2001  0.287  1.303  0.027 -0.403  1.392 1.30900 -0.498      Down
12  2001 -0.498  0.287  1.303  0.027 -0.403 1.25800 -0.189      Down
13  2001 -0.189 -0.498  0.287  1.303  0.027 1.09800  0.680        Up
14  2001  0.680 -0.189 -0.498  0.287  1.303 1.05310  0.701        Up
15  2001  0.701  0.680 -0.189 -0.498  0.287 1.14980 -0.562      Down
16  2001 -0.562  0.701  0.680 -0.189 -0.498 1.29530  0.546        Up
17  2001  0.546 -0.562  0.701  0.680 -0.189 1.11880 -1.747      Down
18  2001 -1.747  0.546 -0.562  0.701  0.680 1.04840  0.359        Up
19  2001  0.359 -1.747  0.546 -0.562  0.701 1.01300 -0.151      Down
20  2001 -0.151  0.359 -1.747  0.546 -0.562 1.05960 -0.841      Down
21  2001 -0.841 -0.151  0.359 -1.747  0.546 1.15830 -0.623      Down
22  2001 -0.623 -0.841 -0.151  0.359 -1.747 1.10720 -1.334      Down
23  2001 -1.334 -0.623 -0.841 -0.151  0.359 1.07550  1.183        Up
24  2001  1.183 -1.334 -0.623 -0.841 -0.151 1.03910 -0.865      Down
25  2001 -0.865  1.183 -1.334 -0.623 -0.841 1.07520 -0.218      Down
26  2001 -0.218 -0.865  1.183 -1.334 -0.623 1.15030  0.812        Up
27  2001  0.812 -0.218 -0.865  1.183 -1.334 1.15370 -1.891      Down
28  2001 -1.891  0.812 -0.218 -0.865  1.183 1.25720 -1.736      Down
29  2001 -1.736 -1.891  0.812 -0.218 -0.865 1.11220 -1.851      Down
30  2001 -1.851 -1.736 -1.891  0.812 -0.218 1.20850 -0.195      Down
31  2001 -0.195 -1.851 -1.736 -1.891  0.812 1.36590 -0.556      Down
32  2001 -0.556 -0.195 -1.851 -1.736 -1.891 1.23130  1.749        Up
33  2001  1.749 -0.556 -0.195 -1.851 -1.736 1.13080 -0.766      Down
34  2001 -0.766  1.749 -0.556 -0.195 -1.851 1.11410 -1.431      Down
35  2001 -1.431 -0.766  1.749 -0.556 -0.195 1.22530  0.104        Up
36  2001  0.104 -1.431 -0.766  1.749 -0.556 1.29490 -0.568      Down
37  2001 -0.568  0.104 -1.431 -0.766  1.749 1.29400  0.586        Up
38  2001  0.586 -0.568  0.104 -1.431 -0.766 0.92920  0.998        Up
39  2001  0.998  0.586 -0.568  0.104 -1.431 1.09180  0.645        Up
40  2001  0.645  0.998  0.586 -0.568  0.104 1.13220  0.226        Up
41  2001  0.226  0.645  0.998  0.586 -0.568 1.11410 -2.476      Down
42  2001 -2.476  0.226  0.645  0.998  0.586 1.08590 -4.318      Down
43  2001 -4.318 -2.476  0.226  0.645  0.998 1.22900  1.483        Up
44  2001  1.483 -4.318 -2.476  0.226  0.645 1.36090 -2.584      Down
45  2001 -2.584  1.483 -4.318 -2.476  0.226 1.39740  0.587        Up
46  2001  0.587 -2.584  1.483 -4.318 -2.476 1.25950 -1.962      Down
47  2001 -1.962  0.587 -2.584  1.483 -4.318 1.54356  1.763        Up
48  2001  1.763 -1.962  0.587 -2.584  1.483 1.12620 -2.408      Down
49  2001 -2.408  1.763 -1.962  0.587 -2.584 1.23590 -1.792      Down
50  2001 -1.792 -2.408  1.763 -1.962  0.587 1.34630 -0.406      Down
51  2001 -0.406 -1.792 -2.408  1.763 -1.962 1.72395  1.991        Up
52  2001  1.991 -0.406 -1.792 -2.408  1.763 1.36490  1.128        Up
53  2001  1.128  1.991 -0.406 -1.792 -2.408 1.11400  2.557        Up
54  2001  2.557  1.128  1.991 -0.406 -1.792 1.31420 -2.443      Down
55  2001 -2.443  2.557  1.128  1.991 -0.406 1.33340 -0.463      Down
56  2001 -0.463 -2.443  2.557  1.128  1.991 1.23450  1.078        Up
57  2001  1.078 -0.463 -2.443  2.557  1.128 1.28080 -1.246      Down
58  2001 -1.246  1.078 -0.463 -2.443  2.557 1.25490 -3.439      Down
59  2001 -3.439 -1.246  1.078 -0.463 -2.443 1.38610 -0.290      Down
60  2001 -0.290 -3.439 -1.246  1.078 -0.463 1.42559  4.368        Up
61  2001  4.368 -0.290 -3.439 -1.246  1.078 1.36800 -1.998      Down
62  2001 -1.998  4.368 -0.290 -3.439 -1.246 1.26680  0.812        Up
63  2001  0.812 -1.998  4.368 -0.290 -3.439 1.06280  2.707        Up
64  2001  2.707  0.812 -1.998  4.368 -0.290 1.34960 -0.213      Down
65  2001 -0.213  2.707  0.812 -1.998  4.368 1.29030  1.510        Up
66  2001  1.510 -0.213  2.707  0.812 -1.998 1.10200 -0.323      Down
67  2001 -0.323  1.510 -0.213  2.707  0.812 0.91390  1.028        Up
68  2001  1.028 -0.323  1.510 -0.213  2.707 1.10960  3.889        Up
69  2001  3.889  1.028 -0.323  1.510 -0.213 1.91890  1.254        Up
70  2001  1.254  3.889  1.028 -0.323  1.510 1.48680 -0.854      Down
71  2001 -0.854  1.254  3.889  1.028 -0.323 1.33870 -1.498      Down
72  2001 -1.498 -0.854  1.254  3.889  1.028 1.01260 -1.216      Down
73  2001 -1.216 -1.498 -0.854  1.254  3.889 1.21650  1.594        Up
74  2001  1.594 -1.216 -1.498 -0.854  1.254 1.20360  0.470        Up
75  2001  0.470  1.594 -1.216 -1.498 -0.854 1.34520  1.501        Up
76  2001  1.501  0.470  1.594 -1.216 -1.498 1.09130 -0.287      Down
77  2001 -0.287  1.501  0.470  1.594 -1.216 1.26680  1.359        Up
78  2001  1.359 -0.287  1.501  0.470  1.594 1.18130  0.078        Up
79  2001  0.078  1.359 -0.287  1.501  0.470 1.34220 -1.487      Down
80  2001 -1.487  0.078  1.359 -0.287  1.501 1.13790  1.444        Up
81  2001  1.444 -1.487  0.078  1.359 -0.287 1.08210 -0.245      Down
82  2001 -0.245  1.444 -1.487  0.078  1.359 0.94900 -0.183      Down
83  2001 -0.183 -0.245  1.444 -1.487  0.078 1.00630 -0.449      Down
84  2001 -0.449 -0.183 -0.245  1.444 -1.487 1.13240 -0.029      Down
85  2001 -0.029 -0.449 -0.183 -0.245  1.444 1.05670 -0.758      Down
86  2001 -0.758 -0.029 -0.449 -0.183 -0.245 0.90620  0.261        Up
87  2001  0.261 -0.758 -0.029 -0.449 -0.183 0.85820  0.042        Up
88  2001  0.042  0.261 -0.758 -0.029 -0.449 1.07180  2.845        Up
89  2001  2.845  0.042  0.261 -0.758 -0.029 1.40530  0.272        Up
90  2001  0.272  2.845  0.042  0.261 -0.758 1.35560  0.269        Up
91  2001  0.269  0.272  2.845  0.042  0.261 1.13080  1.615        Up
92  2001  1.615  0.269  0.272  2.845  0.042 1.17490 -0.263      Down
93  2001 -0.263  1.615  0.269  0.272  2.845 1.26040 -1.553      Down
94  2001 -1.553 -0.263  1.615  0.269  0.272 1.13480  0.320        Up
95  2001  0.320 -1.553 -0.263  1.615  0.269 1.10070 -1.182      Down
96  2001 -1.182  0.320 -1.553 -0.263  1.615 0.82810 -0.779      Down
97  2001 -0.779 -1.182  0.320 -1.553 -0.263 1.02600 -1.566      Down
98  2001 -1.566 -0.779 -1.182  0.320 -1.553 1.15860  0.620        Up
99  2001  0.620 -1.566 -0.779 -1.182  0.320 1.22660  0.386        Up
100 2001  0.386  0.620 -1.566 -0.779 -1.182 1.01500  0.511        Up
101 2001  0.511  0.386  0.620 -1.566 -0.779 0.83650  1.299        Up
102 2001  1.299  0.511  0.386  0.620 -1.566 1.11680 -1.055      Down
103 2001 -1.055  1.299  0.511  0.386  0.620 1.06190  0.546        Up
104 2001  0.546 -1.055  1.299  0.511  0.386 1.08960 -0.940      Down
105 2001 -0.940  0.546 -1.055  1.299  0.511 0.72620 -0.836      Down
106 2001 -0.836 -0.940  0.546 -1.055  1.299 0.87010  0.116        Up
107 2001  0.116 -0.836 -0.940  0.546 -1.055 1.13650 -1.135      Down
108 2001 -1.135  0.116 -0.836 -0.940  0.546 1.06360 -1.750      Down
109 2001 -1.750 -1.135  0.116 -0.836 -0.940 1.24290 -0.452      Down
110 2001 -0.452 -1.750 -1.135  0.116 -0.836 1.63555 -0.488      Down
111 2001 -0.488 -0.452 -1.750 -1.135  0.116 1.11160  0.343        Up
112 2001  0.343 -0.488 -0.452 -1.750 -1.135 1.18490  0.871        Up
113 2001  0.871  0.343 -0.488 -0.452 -1.750 1.35010  1.136        Up
114 2001  1.136  0.871  0.343 -0.488 -0.452 1.54682 -0.945      Down
115 2001 -0.945  1.136  0.871  0.343 -0.488 1.18920 -0.551      Down
116 2001 -0.551 -0.945  1.136  0.871  0.343 1.05010 -0.151      Down
117 2001 -0.151 -0.551 -0.945  1.136  0.871 1.19890 -0.468      Down
118 2001 -0.468 -0.151 -0.551 -0.945  1.136 1.16210  1.249        Up
119 2001  1.249 -0.468 -0.151 -0.551 -0.945 1.32730 -0.148      Down
120 2001 -0.148  1.249 -0.468 -0.151 -0.551 1.83236  1.008        Up
121 2001  1.008 -0.148  1.249 -0.468 -0.151 1.12830 -0.184      Down
122 2001 -0.184  1.008 -0.148  1.249 -0.468 0.62211 -1.232      Down
123 2001 -1.232 -0.184  1.008 -0.148  1.249 0.93490 -2.350      Down
124 2001 -2.350 -1.232 -0.184  1.008 -0.148 1.05670  0.688        Up
125 2001  0.688 -2.350 -1.232 -0.184  1.008 1.04570 -1.440      Down
126 2001 -1.440  0.688 -2.350 -1.232 -0.184 1.26380 -0.113      Down
127 2001 -0.113 -1.440  0.688 -2.350 -1.232 1.38410  2.369        Up
128 2001  2.369 -0.113 -1.440  0.688 -2.350 1.39400  0.624        Up
129 2001  0.624  2.369 -0.113 -1.440  0.688 1.12170 -1.088      Down
130 2001 -1.088  0.624  2.369 -0.113 -1.440 1.03980  0.997        Up
131 2001  0.997 -1.088  0.624  2.369 -0.113 1.23810 -0.554      Down
132 2001 -0.554  0.997 -1.088  0.624  2.369 1.31630  0.605        Up
133 2001  0.605 -0.554  0.997 -1.088  0.624 1.34350 -0.343      Down
134 2001 -0.343  0.605 -0.554  0.997 -1.088 1.17090 -1.637      Down
135 2001 -1.637 -0.343  0.605 -0.554  0.997 0.98690 -1.627      Down
136 2001 -1.627 -1.637 -0.343  0.605 -0.554 1.19870  1.608        Up
137 2001  1.608 -1.627 -1.637 -0.343  0.605 1.28070  1.045        Up
138 2001  1.045  1.608 -1.627 -1.637 -0.343 1.21390  0.240        Up
139 2001  0.240  1.045  1.608 -1.627 -1.637 1.01530 -0.108      Down
140 2001 -0.108  0.240  1.045  1.608 -1.627 0.90910  0.557        Up
141 2001  0.557 -0.108  0.240  1.045  1.608 1.12920  0.388        Up
142 2001  0.388  0.557 -0.108  0.240  1.045 1.34030  0.396        Up
143 2001  0.396  0.388  0.557 -0.108  0.240 1.21830 -0.524      Down
144 2001 -0.524  0.396  0.388  0.557 -0.108 0.93990 -1.142      Down
145 2001 -1.142 -0.524  0.396  0.388  0.557 0.81170  0.327        Up
146 2001  0.327 -1.142 -0.524  0.396  0.388 1.01200 -1.733      Down
147 2001 -1.733  0.327 -1.142 -0.524  0.396 1.12460 -0.008      Down
148 2001 -0.008 -1.733  0.327 -1.142 -0.524 1.10420  0.569        Up
149 2001  0.569 -0.008 -1.733  0.327 -1.142 0.96090  0.095        Up
150 2001  0.095  0.569 -0.008 -1.733  0.327 0.83760 -0.383      Down
151 2001 -0.383  0.095  0.569 -0.008 -1.733 0.96460 -0.734      Down
152 2001 -0.734 -0.383  0.095  0.569 -0.008 1.06560  0.309        Up
153 2001  0.309 -0.734 -0.383  0.095  0.569 1.05540 -1.666      Down
154 2001 -1.666  0.309 -0.734 -0.383  0.095 0.97430  0.812        Up
155 2001  0.812 -1.666  0.309 -0.734 -0.383 0.89710 -1.208      Down
156 2001 -1.208  0.812 -1.666  0.309 -0.734 1.04160  0.696        Up
157 2001  0.696 -1.208  0.812 -1.666  0.309 1.11080 -0.276      Down
158 2001 -0.276  0.696 -1.208  0.812 -1.666 0.98620  1.965        Up
159 2001  1.965 -0.276  0.696 -1.208  0.812 1.04360 -0.483      Down
160 2001 -0.483  1.965 -0.276  0.696 -1.208 0.84260 -1.501      Down
161 2001 -1.501 -0.483  1.965 -0.276  0.696 0.98710 -1.115      Down
162 2001 -1.115 -1.501 -0.483  1.965 -0.276 0.96370 -1.700      Down
163 2001 -1.700 -1.115 -1.501 -0.483  1.965 1.15700  0.403        Up
164 2001  0.403 -1.700 -1.115 -1.501 -0.483 0.92010 -0.056      Down
165 2001 -0.056  0.403 -1.700 -1.115 -1.501 1.17830 -0.106      Down
166 2001 -0.106 -0.056  0.403 -1.700 -1.115 1.38450 -2.239      Down
167 2001 -2.239 -0.106 -0.056  0.403 -1.700 1.35970 -1.864      Down
168 2001 -1.864 -2.239 -0.106 -0.056  0.403 1.42430  0.623        Up
169 2001  0.623 -1.864 -2.239 -0.106 -0.056 1.27660 -4.922      Down
170 2001 -4.922  0.623 -1.864 -2.239 -0.106 2.33083 -0.580      Down
171 2001 -0.580 -4.922  0.623 -1.864 -2.239 1.65041 -1.611      Down
172 2001 -1.611 -0.580 -4.922  0.623 -1.864 2.12055 -3.106      Down
173 2001 -3.106 -1.611 -0.580 -4.922  0.623 2.00480 -1.903      Down
174 2001 -1.903 -3.106 -1.611 -0.580 -4.922 2.31730  3.898        Up
175 2001  3.898 -1.903 -3.106 -1.611 -0.580 1.74660  0.879        Up
176 2001  0.879  3.898 -1.903 -3.106 -1.611 1.61380 -0.517      Down
177 2001 -0.517  0.879  3.898 -1.903 -3.106 1.51910  1.149        Up
178 2001  1.149 -0.517  0.879  3.898 -1.903 1.46700  2.192        Up
179 2001  2.192  1.149 -0.517  0.879  3.898 1.63150 -0.230      Down
180 2001 -0.230  2.192  1.149 -0.517  0.879 1.17560  1.231        Up
181 2001  1.231 -0.230  2.192  1.149 -0.517 1.28980  1.993        Up
182 2001  1.993  1.231 -0.230  2.192  1.149 1.65060 -0.247      Down
183 2001 -0.247  1.993  1.231 -0.230  2.192 1.60910  0.164        Up
184 2001  0.164 -0.247  1.993  1.231 -0.230 1.30170 -0.834      Down
185 2001 -0.834  0.164 -0.247  1.993  1.231 0.97900 -0.536      Down
186 2001 -0.536 -0.834  0.164 -0.247  1.993 1.22780  2.294        Up
187 2001  2.294 -0.536 -0.834  0.164 -0.247 1.31240  1.521        Up
188 2001  1.521  2.294 -0.536 -0.834  0.164 1.70458 -0.527      Down
189 2001 -0.527  1.521  2.294 -0.536 -0.834 1.33140 -0.153      Down
190 2001 -0.153 -0.527  1.521  2.294 -0.536 1.02470  0.694        Up
191 2001  0.694 -0.153 -0.527  1.521  2.294 1.21050 -1.863      Down
192 2001 -1.863  0.694 -0.153 -0.527  1.521 1.45220 -0.787      Down
193 2001 -0.787 -1.863  0.694 -0.153 -0.527 1.26290  0.456        Up
194 2001  0.456 -0.787 -1.863  0.694 -0.153 1.29490  1.530        Up
195 2001  1.530  0.456 -0.787 -1.863  0.694 1.10570 -0.470      Down
196 2001 -0.470  1.530  0.456 -0.787 -1.863 1.31730  0.039        Up
197 2001  0.039 -0.470  1.530  0.456 -0.787 1.33620  1.372        Up
198 2001  1.372  0.039 -0.470  1.530  0.456 1.36440  0.411        Up
199 2001  0.411  1.372  0.039 -0.470  1.530 1.24450 -2.382      Down
200 2001 -2.382  0.411  1.372  0.039 -0.470 1.10610 -1.717      Down
201 2001 -1.717 -2.382  0.411  1.372  0.039 1.29740 -0.001      Down
202 2001 -0.001 -1.717 -2.382  0.411  1.372 1.35250  2.295        Up
203 2001  2.295 -0.001 -1.717 -2.382  0.411 1.31740  0.286        Up
204 2001  0.286  2.295 -0.001 -1.717 -2.382 1.12190  1.439        Up
205 2001  1.439  0.286  2.295 -0.001 -1.717 1.26770  1.453        Up
206 2001  1.453  1.439  0.286  2.295 -0.001 1.35600 -0.273      Down
207 2001 -0.273  1.453  1.439  0.286  2.295 1.41130  0.246        Up
208 2001  0.246 -0.273  1.453  1.439  0.286 1.51750  0.158        Up
209 2001  0.158  0.246 -0.273  1.453  1.439 1.09380 -0.177      Down
210 2001 -0.177  0.158  0.246 -0.273  1.453 0.99160  1.856        Up
211 2001  1.856 -0.177  0.158  0.246 -0.273 1.37010  0.186        Up
212 2001  0.186  1.856 -0.177  0.158  0.246 1.44340  0.090        Up
213 2001  0.090  0.186  1.856 -0.177  0.158 1.45450 -0.314      Down
214 2001 -0.314  0.090  0.186  1.856 -0.177 1.33740  1.090        Up
215 2001  1.090 -0.314  0.090  0.186  1.856 1.31680 -0.730      Down
216 2001 -0.730  1.090 -0.314  0.090  0.186 1.33020 -0.493      Down
217 2001 -0.493 -0.730  1.090 -0.314  0.090 1.02930  1.171        Up
218 2001  1.171 -0.493 -0.730  1.090 -0.314 0.41030  0.615        Up
219 2001  0.615  1.171 -0.493 -0.730  1.090 1.12980 -0.684      Down
220 2001 -0.684  0.615  1.171 -0.493 -0.730 1.28800 -1.825      Down
221 2001 -1.825 -0.684  0.615  1.171 -0.493 1.42370  1.035        Up
222 2001  1.035 -1.825 -0.684  0.615  1.171 1.37570 -0.066      Down
223 2001 -0.066  1.035 -1.825 -0.684  0.615 1.34360 -0.838      Down
224 2001 -0.838 -0.066  1.035 -1.825 -0.684 1.20290  1.319        Up
225 2001  1.319 -0.838 -0.066  1.035 -1.825 1.31850  2.232        Up
226 2001  2.232  1.319 -0.838 -0.066  1.035 1.76530 -0.278      Down
227 2001 -0.278  2.232  1.319 -0.838 -0.066 1.48790 -0.753      Down
228 2001 -0.753 -0.278  2.232  1.319 -0.838 1.24820 -1.587      Down
229 2001 -1.587 -0.753 -0.278  2.232  1.319 1.21870 -0.278      Down
230 2001 -0.278 -1.587 -0.753 -0.278  2.232 1.36720  0.027        Up
231 2001  0.027 -0.278 -1.587 -0.753 -0.278 1.44970 -1.556      Down
232 2001 -1.556  0.027 -0.278 -1.587 -0.753 1.51150  0.331        Up
233 2001  0.331 -1.556  0.027 -0.278 -1.587 1.30680  1.003        Up
234 2001  1.003  0.331 -1.556  0.027 -0.278 1.26040  0.755        Up
235 2001  0.755  1.003  0.331 -1.556  0.027 1.35400  0.581        Up
236 2001  0.581  0.755  1.003  0.331 -1.556 1.48490 -0.838      Down
237 2001 -0.838  0.581  0.755  1.003  0.331 1.49050  0.435        Up
238 2001  0.435 -0.838  0.581  0.755  1.003 1.69400 -0.021      Down
239 2001 -0.021  0.435 -0.838  0.581  0.755 0.43967  0.412        Up
240 2001  0.412 -0.021  0.435 -0.838  0.581 0.79110  0.675        Up
241 2001  0.675  0.412 -0.021  0.435 -0.838 0.87630  0.336        Up
242 2001  0.336  0.675  0.412 -0.021  0.435 0.91740 -1.115      Down

What can you say about the distribution of lag1,lag3,lag5 ?

histograms for Lag1, Lag3, and Lag5

For Lag3

For Lag5

Discuss the distribution of percentage return for Today based on Direction of market?

# A tibble: 2 × 3
  Direction total percent
  <fct>     <dbl>   <dbl>
1 Down      -516. -13163.
2 Up         520.  13263.