· 8 years ago · Apr 19, 2018, 01:26 AM
1{
2 "cells": [
3 {
4 "cell_type": "markdown",
5 "metadata": {},
6 "source": [
7 "# Part 1"
8 ]
9 },
10 {
11 "cell_type": "markdown",
12 "metadata": {},
13 "source": [
14 "## Python Coding and Data Set"
15 ]
16 },
17 {
18 "cell_type": "code",
19 "execution_count": 1,
20 "metadata": {},
21 "outputs": [],
22 "source": [
23 "import pandas as pd\n",
24 "import numpy as np\n",
25 "from scipy import stats\n",
26 "import matplotlib.pyplot as plt\n",
27 "%matplotlib inline"
28 ]
29 },
30 {
31 "cell_type": "code",
32 "execution_count": 2,
33 "metadata": {},
34 "outputs": [],
35 "source": [
36 "breast_cancer = pd.read_csv('breast-cancer.csv')"
37 ]
38 },
39 {
40 "cell_type": "code",
41 "execution_count": 3,
42 "metadata": {},
43 "outputs": [
44 {
45 "data": {
46 "text/html": [
47 "<div>\n",
48 "<table border=\"1\" class=\"dataframe\">\n",
49 " <thead>\n",
50 " <tr style=\"text-align: right;\">\n",
51 " <th></th>\n",
52 " <th>842302</th>\n",
53 " <th>M</th>\n",
54 " <th>17.99</th>\n",
55 " <th>10.38</th>\n",
56 " <th>122.8</th>\n",
57 " <th>1001</th>\n",
58 " <th>0.1184</th>\n",
59 " <th>0.2776</th>\n",
60 " <th>0.3001</th>\n",
61 " <th>0.1471</th>\n",
62 " <th>...</th>\n",
63 " <th>25.38</th>\n",
64 " <th>17.33</th>\n",
65 " <th>184.6</th>\n",
66 " <th>2019</th>\n",
67 " <th>0.1622</th>\n",
68 " <th>0.6656</th>\n",
69 " <th>0.7119</th>\n",
70 " <th>0.2654</th>\n",
71 " <th>0.4601</th>\n",
72 " <th>0.1189</th>\n",
73 " </tr>\n",
74 " </thead>\n",
75 " <tbody>\n",
76 " <tr>\n",
77 " <th>0</th>\n",
78 " <td>842517</td>\n",
79 " <td>M</td>\n",
80 " <td>20.57</td>\n",
81 " <td>17.77</td>\n",
82 " <td>132.90</td>\n",
83 " <td>1326.0</td>\n",
84 " <td>0.08474</td>\n",
85 " <td>0.07864</td>\n",
86 " <td>0.0869</td>\n",
87 " <td>0.07017</td>\n",
88 " <td>...</td>\n",
89 " <td>24.99</td>\n",
90 " <td>23.41</td>\n",
91 " <td>158.80</td>\n",
92 " <td>1956.0</td>\n",
93 " <td>0.1238</td>\n",
94 " <td>0.1866</td>\n",
95 " <td>0.2416</td>\n",
96 " <td>0.1860</td>\n",
97 " <td>0.2750</td>\n",
98 " <td>0.08902</td>\n",
99 " </tr>\n",
100 " <tr>\n",
101 " <th>1</th>\n",
102 " <td>84300903</td>\n",
103 " <td>M</td>\n",
104 " <td>19.69</td>\n",
105 " <td>21.25</td>\n",
106 " <td>130.00</td>\n",
107 " <td>1203.0</td>\n",
108 " <td>0.10960</td>\n",
109 " <td>0.15990</td>\n",
110 " <td>0.1974</td>\n",
111 " <td>0.12790</td>\n",
112 " <td>...</td>\n",
113 " <td>23.57</td>\n",
114 " <td>25.53</td>\n",
115 " <td>152.50</td>\n",
116 " <td>1709.0</td>\n",
117 " <td>0.1444</td>\n",
118 " <td>0.4245</td>\n",
119 " <td>0.4504</td>\n",
120 " <td>0.2430</td>\n",
121 " <td>0.3613</td>\n",
122 " <td>0.08758</td>\n",
123 " </tr>\n",
124 " <tr>\n",
125 " <th>2</th>\n",
126 " <td>84348301</td>\n",
127 " <td>M</td>\n",
128 " <td>11.42</td>\n",
129 " <td>20.38</td>\n",
130 " <td>77.58</td>\n",
131 " <td>386.1</td>\n",
132 " <td>0.14250</td>\n",
133 " <td>0.28390</td>\n",
134 " <td>0.2414</td>\n",
135 " <td>0.10520</td>\n",
136 " <td>...</td>\n",
137 " <td>14.91</td>\n",
138 " <td>26.50</td>\n",
139 " <td>98.87</td>\n",
140 " <td>567.7</td>\n",
141 " <td>0.2098</td>\n",
142 " <td>0.8663</td>\n",
143 " <td>0.6869</td>\n",
144 " <td>0.2575</td>\n",
145 " <td>0.6638</td>\n",
146 " <td>0.17300</td>\n",
147 " </tr>\n",
148 " <tr>\n",
149 " <th>3</th>\n",
150 " <td>84358402</td>\n",
151 " <td>M</td>\n",
152 " <td>20.29</td>\n",
153 " <td>14.34</td>\n",
154 " <td>135.10</td>\n",
155 " <td>1297.0</td>\n",
156 " <td>0.10030</td>\n",
157 " <td>0.13280</td>\n",
158 " <td>0.1980</td>\n",
159 " <td>0.10430</td>\n",
160 " <td>...</td>\n",
161 " <td>22.54</td>\n",
162 " <td>16.67</td>\n",
163 " <td>152.20</td>\n",
164 " <td>1575.0</td>\n",
165 " <td>0.1374</td>\n",
166 " <td>0.2050</td>\n",
167 " <td>0.4000</td>\n",
168 " <td>0.1625</td>\n",
169 " <td>0.2364</td>\n",
170 " <td>0.07678</td>\n",
171 " </tr>\n",
172 " <tr>\n",
173 " <th>4</th>\n",
174 " <td>843786</td>\n",
175 " <td>M</td>\n",
176 " <td>12.45</td>\n",
177 " <td>15.70</td>\n",
178 " <td>82.57</td>\n",
179 " <td>477.1</td>\n",
180 " <td>0.12780</td>\n",
181 " <td>0.17000</td>\n",
182 " <td>0.1578</td>\n",
183 " <td>0.08089</td>\n",
184 " <td>...</td>\n",
185 " <td>15.47</td>\n",
186 " <td>23.75</td>\n",
187 " <td>103.40</td>\n",
188 " <td>741.6</td>\n",
189 " <td>0.1791</td>\n",
190 " <td>0.5249</td>\n",
191 " <td>0.5355</td>\n",
192 " <td>0.1741</td>\n",
193 " <td>0.3985</td>\n",
194 " <td>0.12440</td>\n",
195 " </tr>\n",
196 " </tbody>\n",
197 "</table>\n",
198 "<p>5 rows × 32 columns</p>\n",
199 "</div>"
200 ],
201 "text/plain": [
202 " 842302 M 17.99 10.38 122.8 1001 0.1184 0.2776 0.3001 \\\n",
203 "0 842517 M 20.57 17.77 132.90 1326.0 0.08474 0.07864 0.0869 \n",
204 "1 84300903 M 19.69 21.25 130.00 1203.0 0.10960 0.15990 0.1974 \n",
205 "2 84348301 M 11.42 20.38 77.58 386.1 0.14250 0.28390 0.2414 \n",
206 "3 84358402 M 20.29 14.34 135.10 1297.0 0.10030 0.13280 0.1980 \n",
207 "4 843786 M 12.45 15.70 82.57 477.1 0.12780 0.17000 0.1578 \n",
208 "\n",
209 " 0.1471 ... 25.38 17.33 184.6 2019 0.1622 0.6656 0.7119 \\\n",
210 "0 0.07017 ... 24.99 23.41 158.80 1956.0 0.1238 0.1866 0.2416 \n",
211 "1 0.12790 ... 23.57 25.53 152.50 1709.0 0.1444 0.4245 0.4504 \n",
212 "2 0.10520 ... 14.91 26.50 98.87 567.7 0.2098 0.8663 0.6869 \n",
213 "3 0.10430 ... 22.54 16.67 152.20 1575.0 0.1374 0.2050 0.4000 \n",
214 "4 0.08089 ... 15.47 23.75 103.40 741.6 0.1791 0.5249 0.5355 \n",
215 "\n",
216 " 0.2654 0.4601 0.1189 \n",
217 "0 0.1860 0.2750 0.08902 \n",
218 "1 0.2430 0.3613 0.08758 \n",
219 "2 0.2575 0.6638 0.17300 \n",
220 "3 0.1625 0.2364 0.07678 \n",
221 "4 0.1741 0.3985 0.12440 \n",
222 "\n",
223 "[5 rows x 32 columns]"
224 ]
225 },
226 "execution_count": 3,
227 "metadata": {},
228 "output_type": "execute_result"
229 }
230 ],
231 "source": [
232 "breast_cancer.head()"
233 ]
234 },
235 {
236 "cell_type": "code",
237 "execution_count": 4,
238 "metadata": {},
239 "outputs": [],
240 "source": [
241 "file = open('field_names.txt', 'r')\n",
242 "columns = file.read()\n",
243 "columns = columns.split('\\n')"
244 ]
245 },
246 {
247 "cell_type": "code",
248 "execution_count": 5,
249 "metadata": {},
250 "outputs": [],
251 "source": [
252 "breast_cancer.columns = columns"
253 ]
254 },
255 {
256 "cell_type": "code",
257 "execution_count": 6,
258 "metadata": {},
259 "outputs": [
260 {
261 "data": {
262 "text/html": [
263 "<div>\n",
264 "<table border=\"1\" class=\"dataframe\">\n",
265 " <thead>\n",
266 " <tr style=\"text-align: right;\">\n",
267 " <th></th>\n",
268 " <th>ID</th>\n",
269 " <th>diagnosis</th>\n",
270 " <th>radius_mean</th>\n",
271 " <th>radius_sd_error</th>\n",
272 " <th>radius_worst</th>\n",
273 " <th>texture_mean</th>\n",
274 " <th>texture_sd_error</th>\n",
275 " <th>texture_worst</th>\n",
276 " <th>perimeter_mean</th>\n",
277 " <th>perimeter_sd_error</th>\n",
278 " <th>...</th>\n",
279 " <th>concavity_worst</th>\n",
280 " <th>concave_points_mean</th>\n",
281 " <th>concave_points_sd_error</th>\n",
282 " <th>concave_points_worst</th>\n",
283 " <th>symmetry_mean</th>\n",
284 " <th>symmetry_sd_error</th>\n",
285 " <th>symmetry_worst</th>\n",
286 " <th>fractal_dimension_mean</th>\n",
287 " <th>fractal_dimension_sd_error</th>\n",
288 " <th>fractal_dimension_worst</th>\n",
289 " </tr>\n",
290 " </thead>\n",
291 " <tbody>\n",
292 " <tr>\n",
293 " <th>0</th>\n",
294 " <td>842517</td>\n",
295 " <td>M</td>\n",
296 " <td>20.57</td>\n",
297 " <td>17.77</td>\n",
298 " <td>132.90</td>\n",
299 " <td>1326.0</td>\n",
300 " <td>0.08474</td>\n",
301 " <td>0.07864</td>\n",
302 " <td>0.0869</td>\n",
303 " <td>0.07017</td>\n",
304 " <td>...</td>\n",
305 " <td>24.99</td>\n",
306 " <td>23.41</td>\n",
307 " <td>158.80</td>\n",
308 " <td>1956.0</td>\n",
309 " <td>0.1238</td>\n",
310 " <td>0.1866</td>\n",
311 " <td>0.2416</td>\n",
312 " <td>0.1860</td>\n",
313 " <td>0.2750</td>\n",
314 " <td>0.08902</td>\n",
315 " </tr>\n",
316 " <tr>\n",
317 " <th>1</th>\n",
318 " <td>84300903</td>\n",
319 " <td>M</td>\n",
320 " <td>19.69</td>\n",
321 " <td>21.25</td>\n",
322 " <td>130.00</td>\n",
323 " <td>1203.0</td>\n",
324 " <td>0.10960</td>\n",
325 " <td>0.15990</td>\n",
326 " <td>0.1974</td>\n",
327 " <td>0.12790</td>\n",
328 " <td>...</td>\n",
329 " <td>23.57</td>\n",
330 " <td>25.53</td>\n",
331 " <td>152.50</td>\n",
332 " <td>1709.0</td>\n",
333 " <td>0.1444</td>\n",
334 " <td>0.4245</td>\n",
335 " <td>0.4504</td>\n",
336 " <td>0.2430</td>\n",
337 " <td>0.3613</td>\n",
338 " <td>0.08758</td>\n",
339 " </tr>\n",
340 " <tr>\n",
341 " <th>2</th>\n",
342 " <td>84348301</td>\n",
343 " <td>M</td>\n",
344 " <td>11.42</td>\n",
345 " <td>20.38</td>\n",
346 " <td>77.58</td>\n",
347 " <td>386.1</td>\n",
348 " <td>0.14250</td>\n",
349 " <td>0.28390</td>\n",
350 " <td>0.2414</td>\n",
351 " <td>0.10520</td>\n",
352 " <td>...</td>\n",
353 " <td>14.91</td>\n",
354 " <td>26.50</td>\n",
355 " <td>98.87</td>\n",
356 " <td>567.7</td>\n",
357 " <td>0.2098</td>\n",
358 " <td>0.8663</td>\n",
359 " <td>0.6869</td>\n",
360 " <td>0.2575</td>\n",
361 " <td>0.6638</td>\n",
362 " <td>0.17300</td>\n",
363 " </tr>\n",
364 " <tr>\n",
365 " <th>3</th>\n",
366 " <td>84358402</td>\n",
367 " <td>M</td>\n",
368 " <td>20.29</td>\n",
369 " <td>14.34</td>\n",
370 " <td>135.10</td>\n",
371 " <td>1297.0</td>\n",
372 " <td>0.10030</td>\n",
373 " <td>0.13280</td>\n",
374 " <td>0.1980</td>\n",
375 " <td>0.10430</td>\n",
376 " <td>...</td>\n",
377 " <td>22.54</td>\n",
378 " <td>16.67</td>\n",
379 " <td>152.20</td>\n",
380 " <td>1575.0</td>\n",
381 " <td>0.1374</td>\n",
382 " <td>0.2050</td>\n",
383 " <td>0.4000</td>\n",
384 " <td>0.1625</td>\n",
385 " <td>0.2364</td>\n",
386 " <td>0.07678</td>\n",
387 " </tr>\n",
388 " <tr>\n",
389 " <th>4</th>\n",
390 " <td>843786</td>\n",
391 " <td>M</td>\n",
392 " <td>12.45</td>\n",
393 " <td>15.70</td>\n",
394 " <td>82.57</td>\n",
395 " <td>477.1</td>\n",
396 " <td>0.12780</td>\n",
397 " <td>0.17000</td>\n",
398 " <td>0.1578</td>\n",
399 " <td>0.08089</td>\n",
400 " <td>...</td>\n",
401 " <td>15.47</td>\n",
402 " <td>23.75</td>\n",
403 " <td>103.40</td>\n",
404 " <td>741.6</td>\n",
405 " <td>0.1791</td>\n",
406 " <td>0.5249</td>\n",
407 " <td>0.5355</td>\n",
408 " <td>0.1741</td>\n",
409 " <td>0.3985</td>\n",
410 " <td>0.12440</td>\n",
411 " </tr>\n",
412 " </tbody>\n",
413 "</table>\n",
414 "<p>5 rows × 32 columns</p>\n",
415 "</div>"
416 ],
417 "text/plain": [
418 " ID diagnosis radius_mean radius_sd_error radius_worst \\\n",
419 "0 842517 M 20.57 17.77 132.90 \n",
420 "1 84300903 M 19.69 21.25 130.00 \n",
421 "2 84348301 M 11.42 20.38 77.58 \n",
422 "3 84358402 M 20.29 14.34 135.10 \n",
423 "4 843786 M 12.45 15.70 82.57 \n",
424 "\n",
425 " texture_mean texture_sd_error texture_worst perimeter_mean \\\n",
426 "0 1326.0 0.08474 0.07864 0.0869 \n",
427 "1 1203.0 0.10960 0.15990 0.1974 \n",
428 "2 386.1 0.14250 0.28390 0.2414 \n",
429 "3 1297.0 0.10030 0.13280 0.1980 \n",
430 "4 477.1 0.12780 0.17000 0.1578 \n",
431 "\n",
432 " perimeter_sd_error ... concavity_worst \\\n",
433 "0 0.07017 ... 24.99 \n",
434 "1 0.12790 ... 23.57 \n",
435 "2 0.10520 ... 14.91 \n",
436 "3 0.10430 ... 22.54 \n",
437 "4 0.08089 ... 15.47 \n",
438 "\n",
439 " concave_points_mean concave_points_sd_error concave_points_worst \\\n",
440 "0 23.41 158.80 1956.0 \n",
441 "1 25.53 152.50 1709.0 \n",
442 "2 26.50 98.87 567.7 \n",
443 "3 16.67 152.20 1575.0 \n",
444 "4 23.75 103.40 741.6 \n",
445 "\n",
446 " symmetry_mean symmetry_sd_error symmetry_worst fractal_dimension_mean \\\n",
447 "0 0.1238 0.1866 0.2416 0.1860 \n",
448 "1 0.1444 0.4245 0.4504 0.2430 \n",
449 "2 0.2098 0.8663 0.6869 0.2575 \n",
450 "3 0.1374 0.2050 0.4000 0.1625 \n",
451 "4 0.1791 0.5249 0.5355 0.1741 \n",
452 "\n",
453 " fractal_dimension_sd_error fractal_dimension_worst \n",
454 "0 0.2750 0.08902 \n",
455 "1 0.3613 0.08758 \n",
456 "2 0.6638 0.17300 \n",
457 "3 0.2364 0.07678 \n",
458 "4 0.3985 0.12440 \n",
459 "\n",
460 "[5 rows x 32 columns]"
461 ]
462 },
463 "execution_count": 6,
464 "metadata": {},
465 "output_type": "execute_result"
466 }
467 ],
468 "source": [
469 "breast_cancer.head()"
470 ]
471 },
472 {
473 "cell_type": "markdown",
474 "metadata": {},
475 "source": [
476 "Ensure that there are no null values. Investigate data types."
477 ]
478 },
479 {
480 "cell_type": "code",
481 "execution_count": 7,
482 "metadata": {},
483 "outputs": [
484 {
485 "data": {
486 "text/plain": [
487 "ID 0\n",
488 "diagnosis 0\n",
489 "radius_mean 0\n",
490 "radius_sd_error 0\n",
491 "radius_worst 0\n",
492 "texture_mean 0\n",
493 "texture_sd_error 0\n",
494 "texture_worst 0\n",
495 "perimeter_mean 0\n",
496 "perimeter_sd_error 0\n",
497 "perimeter_worst 0\n",
498 "area_mean 0\n",
499 "area_sd_error 0\n",
500 "area_worst 0\n",
501 "smoothness_mean 0\n",
502 "smoothness_sd_error 0\n",
503 "smoothness_worst 0\n",
504 "compactness_mean 0\n",
505 "compactness_sd_error 0\n",
506 "compactness_worst 0\n",
507 "concavity_mean 0\n",
508 "concavity_sd_error 0\n",
509 "concavity_worst 0\n",
510 "concave_points_mean 0\n",
511 "concave_points_sd_error 0\n",
512 "concave_points_worst 0\n",
513 "symmetry_mean 0\n",
514 "symmetry_sd_error 0\n",
515 "symmetry_worst 0\n",
516 "fractal_dimension_mean 0\n",
517 "fractal_dimension_sd_error 0\n",
518 "fractal_dimension_worst 0\n",
519 "dtype: int64"
520 ]
521 },
522 "execution_count": 7,
523 "metadata": {},
524 "output_type": "execute_result"
525 }
526 ],
527 "source": [
528 "breast_cancer.isnull().sum()"
529 ]
530 },
531 {
532 "cell_type": "code",
533 "execution_count": 8,
534 "metadata": {},
535 "outputs": [
536 {
537 "name": "stdout",
538 "output_type": "stream",
539 "text": [
540 "<class 'pandas.core.frame.DataFrame'>\n",
541 "RangeIndex: 568 entries, 0 to 567\n",
542 "Data columns (total 32 columns):\n",
543 "ID 568 non-null int64\n",
544 "diagnosis 568 non-null object\n",
545 "radius_mean 568 non-null float64\n",
546 "radius_sd_error 568 non-null float64\n",
547 "radius_worst 568 non-null float64\n",
548 "texture_mean 568 non-null float64\n",
549 "texture_sd_error 568 non-null float64\n",
550 "texture_worst 568 non-null float64\n",
551 "perimeter_mean 568 non-null float64\n",
552 "perimeter_sd_error 568 non-null float64\n",
553 "perimeter_worst 568 non-null float64\n",
554 "area_mean 568 non-null float64\n",
555 "area_sd_error 568 non-null float64\n",
556 "area_worst 568 non-null float64\n",
557 "smoothness_mean 568 non-null float64\n",
558 "smoothness_sd_error 568 non-null float64\n",
559 "smoothness_worst 568 non-null float64\n",
560 "compactness_mean 568 non-null float64\n",
561 "compactness_sd_error 568 non-null float64\n",
562 "compactness_worst 568 non-null float64\n",
563 "concavity_mean 568 non-null float64\n",
564 "concavity_sd_error 568 non-null float64\n",
565 "concavity_worst 568 non-null float64\n",
566 "concave_points_mean 568 non-null float64\n",
567 "concave_points_sd_error 568 non-null float64\n",
568 "concave_points_worst 568 non-null float64\n",
569 "symmetry_mean 568 non-null float64\n",
570 "symmetry_sd_error 568 non-null float64\n",
571 "symmetry_worst 568 non-null float64\n",
572 "fractal_dimension_mean 568 non-null float64\n",
573 "fractal_dimension_sd_error 568 non-null float64\n",
574 "fractal_dimension_worst 568 non-null float64\n",
575 "dtypes: float64(30), int64(1), object(1)\n",
576 "memory usage: 142.1+ KB\n"
577 ]
578 }
579 ],
580 "source": [
581 "breast_cancer.info()"
582 ]
583 },
584 {
585 "cell_type": "markdown",
586 "metadata": {},
587 "source": [
588 "There are no nulls in the dataset and only one column is an object type. All other columns are int or float. "
589 ]
590 },
591 {
592 "cell_type": "code",
593 "execution_count": 9,
594 "metadata": {},
595 "outputs": [],
596 "source": [
597 "mean_smooth_m = breast_cancer[breast_cancer['diagnosis'] == 'M']['smoothness_mean'].mean()\n",
598 "mean_smooth_b = breast_cancer[breast_cancer['diagnosis'] == 'B']['smoothness_mean'].mean()\n",
599 "mean_compact_m = breast_cancer[breast_cancer['diagnosis'] == 'M']['compactness_mean'].mean()\n",
600 "mean_compact_b = breast_cancer[breast_cancer['diagnosis'] == 'B']['compactness_mean'].mean()"
601 ]
602 },
603 {
604 "cell_type": "code",
605 "execution_count": 10,
606 "metadata": {},
607 "outputs": [
608 {
609 "name": "stdout",
610 "output_type": "stream",
611 "text": [
612 "Mean smoothness, Malignant: 4.30371563981\n",
613 "Mean smoothness, Benign: 2.00032128852\n",
614 "Mean compactness, Malignant: 0.0322017393365\n",
615 "Mean compactness, Benign: 0.0214382464986\n"
616 ]
617 }
618 ],
619 "source": [
620 "print('Mean smoothness, Malignant: ', mean_smooth_m)\n",
621 "print('Mean smoothness, Benign: ', mean_smooth_b)\n",
622 "print('Mean compactness, Malignant: ', mean_compact_m)\n",
623 "print('Mean compactness, Benign: ', mean_compact_b)"
624 ]
625 },
626 {
627 "cell_type": "code",
628 "execution_count": 11,
629 "metadata": {},
630 "outputs": [
631 {
632 "name": "stdout",
633 "output_type": "stream",
634 "text": [
635 "Difference in mean smoothness, Malignant - Benign: 2.3033943513\n",
636 "Difference in mean compactness, Malignant - Benign: 0.0107634928379\n"
637 ]
638 }
639 ],
640 "source": [
641 "print('Difference in mean smoothness, Malignant - Benign: ', mean_smooth_m - mean_smooth_b)\n",
642 "print('Difference in mean compactness, Malignant - Benign: ', mean_compact_m - mean_compact_b)"
643 ]
644 },
645 {
646 "cell_type": "code",
647 "execution_count": 12,
648 "metadata": {},
649 "outputs": [],
650 "source": [
651 "difference_smooth = mean_smooth_m - mean_smooth_b\n",
652 "difference_compact = mean_compact_m - mean_compact_b"
653 ]
654 },
655 {
656 "cell_type": "markdown",
657 "metadata": {},
658 "source": [
659 "### Do these values differ? \n",
660 "\n",
661 "This question can only be answered by looking at the distribution of results and performing a null hypothesis test. In our test, our null hypothesis would be that these results do not differ. Our h1 hypothesis would be that the mean value do differ.\n",
662 "\n",
663 "**H0** = mean value of malignant and benign tumor smoothness/compact do not differ \n",
664 "**H1** = mean value of malignant and benign tumor smoothness/compact do differ\n"
665 ]
666 },
667 {
668 "cell_type": "markdown",
669 "metadata": {},
670 "source": [
671 "#### Write a function to take bootstrap samples"
672 ]
673 },
674 {
675 "cell_type": "code",
676 "execution_count": 13,
677 "metadata": {},
678 "outputs": [
679 {
680 "name": "stdout",
681 "output_type": "stream",
682 "text": [
683 "# malignant: 211\n",
684 "# benign: 357\n"
685 ]
686 }
687 ],
688 "source": [
689 "print(\"# malignant: \", breast_cancer['diagnosis'][breast_cancer['diagnosis'] == 'M'].count())\n",
690 "print(\"# benign: \", breast_cancer['diagnosis'][breast_cancer['diagnosis'] == 'B'].count())"
691 ]
692 },
693 {
694 "cell_type": "markdown",
695 "metadata": {},
696 "source": [
697 "Since we are looking for the mean difference between two slices of the dataset, malignant and benign, below I create bootstrap samples by permutating the entire series (either smoothness or compactness), slicing it, and then taking the difference of the means of the two slices. I then redo this procedure 1000 times to create a standard distribution of random permutations, and take the confidence interval based on that distribution. I show that the observed mean difference is well outside of the 95% confidence interval."
698 ]
699 },
700 {
701 "cell_type": "code",
702 "execution_count": 14,
703 "metadata": {},
704 "outputs": [
705 {
706 "name": "stdout",
707 "output_type": "stream",
708 "text": [
709 "smoothness mean diff confidence: [-0.33557526 0.35219474]\n",
710 "compactness mean diff confidence: [-0.0032688 0.00301226]\n"
711 ]
712 }
713 ],
714 "source": [
715 "def bootstrap(values):\n",
716 " values = np.random.permutation(values)\n",
717 " \n",
718 " m = values[:211]\n",
719 " b = values [211:]\n",
720 " return m.mean() - b.mean()\n",
721 "\n",
722 "bootstrap_mean_smoothness_diff = np.empty(1000)\n",
723 "bootstrap_mean_compactness_diff = np.empty(1000)\n",
724 "\n",
725 "for i in range(1000):\n",
726 " bootstrap_mean_smoothness_diff[i] = bootstrap(breast_cancer['smoothness_mean'])\n",
727 " bootstrap_mean_compactness_diff[i] = bootstrap(breast_cancer['compactness_mean'])\n",
728 " \n",
729 "smoothness_mean_diff_confidence = np.percentile(bootstrap_mean_smoothness_diff, [2.5, 97.5])\n",
730 "compactness_mean_diff_confidence = np.percentile(bootstrap_mean_compactness_diff, [2.5, 97.5])\n",
731 "\n",
732 "print('smoothness mean diff confidence: ', smoothness_mean_diff_confidence)\n",
733 "print('compactness mean diff confidence: ', compactness_mean_diff_confidence)"
734 ]
735 },
736 {
737 "cell_type": "markdown",
738 "metadata": {},
739 "source": [
740 "The confidence intervals above indicate that the mean difference for both smoothness and compactness is outside of the 95% confidence interval range. "
741 ]
742 },
743 {
744 "cell_type": "markdown",
745 "metadata": {},
746 "source": [
747 "Below, I use the t-statistic method to find the p-value's for this dataset. This is another statistical approach to solving the same problem. "
748 ]
749 },
750 {
751 "cell_type": "code",
752 "execution_count": 15,
753 "metadata": {},
754 "outputs": [],
755 "source": [
756 "def sample_variance(sample1, sample2):\n",
757 " sum_1, sum_2 = 0, 0\n",
758 " \n",
759 " sum_1 = np.sum((sample1 - sample1.mean())**2)\n",
760 " \n",
761 " sum_2 = np.sum((sample2 - sample2.mean())**2)\n",
762 " \n",
763 " variance_squared = (sum_1 + sum_2) / (len(sample1) + len(sample2) - 2)\n",
764 " return variance_squared"
765 ]
766 },
767 {
768 "cell_type": "code",
769 "execution_count": 16,
770 "metadata": {},
771 "outputs": [],
772 "source": [
773 "def t_statistic(expr, ctrl):\n",
774 " s2 = sample_variance(expr, ctrl)\n",
775 " mean1 = np.mean(expr)\n",
776 " mean2 = np.mean(ctrl)\n",
777 " std = np.sqrt(s2 * (1./len(expr) + 1./len(ctrl)))\n",
778 " return float(mean1 - mean2) / std"
779 ]
780 },
781 {
782 "cell_type": "code",
783 "execution_count": 17,
784 "metadata": {},
785 "outputs": [
786 {
787 "name": "stdout",
788 "output_type": "stream",
789 "text": [
790 "Manual t-statistic: -15.8487638097 -7.23262963121\n"
791 ]
792 }
793 ],
794 "source": [
795 "t_stat_smoothness = t_statistic(breast_cancer[breast_cancer['diagnosis']=='B']['smoothness_mean'], breast_cancer[breast_cancer['diagnosis']=='M']['smoothness_mean'])\n",
796 "t_stat_compactness = t_statistic(breast_cancer[breast_cancer['diagnosis']=='B']['compactness_mean'], breast_cancer[breast_cancer['diagnosis']=='M']['compactness_mean'])\n",
797 "print('Manual t-statistic:', t_stat_smoothness, t_stat_compactness)"
798 ]
799 },
800 {
801 "cell_type": "code",
802 "execution_count": 18,
803 "metadata": {},
804 "outputs": [
805 {
806 "name": "stdout",
807 "output_type": "stream",
808 "text": [
809 "p-value smoothness: 2.05697618597e-47\n"
810 ]
811 }
812 ],
813 "source": [
814 "lower_tail = stats.t.cdf(-15.8487638097, (568), 0, 1)\n",
815 "upper_tail = 1. - stats.t.cdf(15.8487638097, (568), 0, 1)\n",
816 "p_value = lower_tail+upper_tail\n",
817 "print('p-value smoothness: ', p_value)"
818 ]
819 },
820 {
821 "cell_type": "code",
822 "execution_count": 19,
823 "metadata": {},
824 "outputs": [
825 {
826 "name": "stdout",
827 "output_type": "stream",
828 "text": [
829 "p-value compactness: 1.53993500403e-12\n"
830 ]
831 }
832 ],
833 "source": [
834 "lower_tail = stats.t.cdf(-7.23262963121, (568), 0, 1)\n",
835 "upper_tail = 1. - stats.t.cdf(7.23262963121, (568), 0, 1)\n",
836 "p_value = lower_tail+upper_tail\n",
837 "print('p-value compactness: ', p_value)"
838 ]
839 },
840 {
841 "cell_type": "markdown",
842 "metadata": {},
843 "source": [
844 "Here, the p-values are both very small, close to zero. This indicates that there is a statistically significant chance that the means are different. "
845 ]
846 },
847 {
848 "cell_type": "markdown",
849 "metadata": {},
850 "source": [
851 "## Exploratory Analysis"
852 ]
853 },
854 {
855 "cell_type": "code",
856 "execution_count": 20,
857 "metadata": {},
858 "outputs": [],
859 "source": [
860 "breast_cancer = pd.get_dummies(breast_cancer, drop_first=True)"
861 ]
862 },
863 {
864 "cell_type": "code",
865 "execution_count": 21,
866 "metadata": {},
867 "outputs": [
868 {
869 "data": {
870 "text/html": [
871 "<div>\n",
872 "<table border=\"1\" class=\"dataframe\">\n",
873 " <thead>\n",
874 " <tr style=\"text-align: right;\">\n",
875 " <th></th>\n",
876 " <th>ID</th>\n",
877 " <th>radius_mean</th>\n",
878 " <th>radius_sd_error</th>\n",
879 " <th>radius_worst</th>\n",
880 " <th>texture_mean</th>\n",
881 " <th>texture_sd_error</th>\n",
882 " <th>texture_worst</th>\n",
883 " <th>perimeter_mean</th>\n",
884 " <th>perimeter_sd_error</th>\n",
885 " <th>perimeter_worst</th>\n",
886 " <th>...</th>\n",
887 " <th>concave_points_mean</th>\n",
888 " <th>concave_points_sd_error</th>\n",
889 " <th>concave_points_worst</th>\n",
890 " <th>symmetry_mean</th>\n",
891 " <th>symmetry_sd_error</th>\n",
892 " <th>symmetry_worst</th>\n",
893 " <th>fractal_dimension_mean</th>\n",
894 " <th>fractal_dimension_sd_error</th>\n",
895 " <th>fractal_dimension_worst</th>\n",
896 " <th>diagnosis_M</th>\n",
897 " </tr>\n",
898 " </thead>\n",
899 " <tbody>\n",
900 " <tr>\n",
901 " <th>0</th>\n",
902 " <td>842517</td>\n",
903 " <td>20.57</td>\n",
904 " <td>17.77</td>\n",
905 " <td>132.9</td>\n",
906 " <td>1326.0</td>\n",
907 " <td>0.08474</td>\n",
908 " <td>0.07864</td>\n",
909 " <td>0.0869</td>\n",
910 " <td>0.07017</td>\n",
911 " <td>0.1812</td>\n",
912 " <td>...</td>\n",
913 " <td>23.41</td>\n",
914 " <td>158.8</td>\n",
915 " <td>1956.0</td>\n",
916 " <td>0.1238</td>\n",
917 " <td>0.1866</td>\n",
918 " <td>0.2416</td>\n",
919 " <td>0.186</td>\n",
920 " <td>0.275</td>\n",
921 " <td>0.08902</td>\n",
922 " <td>1</td>\n",
923 " </tr>\n",
924 " </tbody>\n",
925 "</table>\n",
926 "<p>1 rows × 32 columns</p>\n",
927 "</div>"
928 ],
929 "text/plain": [
930 " ID radius_mean radius_sd_error radius_worst texture_mean \\\n",
931 "0 842517 20.57 17.77 132.9 1326.0 \n",
932 "\n",
933 " texture_sd_error texture_worst perimeter_mean perimeter_sd_error \\\n",
934 "0 0.08474 0.07864 0.0869 0.07017 \n",
935 "\n",
936 " perimeter_worst ... concave_points_mean concave_points_sd_error \\\n",
937 "0 0.1812 ... 23.41 158.8 \n",
938 "\n",
939 " concave_points_worst symmetry_mean symmetry_sd_error symmetry_worst \\\n",
940 "0 1956.0 0.1238 0.1866 0.2416 \n",
941 "\n",
942 " fractal_dimension_mean fractal_dimension_sd_error \\\n",
943 "0 0.186 0.275 \n",
944 "\n",
945 " fractal_dimension_worst diagnosis_M \n",
946 "0 0.08902 1 \n",
947 "\n",
948 "[1 rows x 32 columns]"
949 ]
950 },
951 "execution_count": 21,
952 "metadata": {},
953 "output_type": "execute_result"
954 }
955 ],
956 "source": [
957 "breast_cancer.head(1)"
958 ]
959 },
960 {
961 "cell_type": "code",
962 "execution_count": 22,
963 "metadata": {},
964 "outputs": [],
965 "source": [
966 "from sklearn.linear_model import LogisticRegression\n",
967 "line = LogisticRegression()"
968 ]
969 },
970 {
971 "cell_type": "code",
972 "execution_count": 23,
973 "metadata": {},
974 "outputs": [],
975 "source": [
976 "target = breast_cancer['diagnosis_M']\n",
977 "features = breast_cancer.drop('diagnosis_M', axis=1)\n",
978 "\n",
979 "from sklearn.model_selection import train_test_split\n",
980 "X_train, X_test, y_train, y_test = train_test_split(features, target)\n",
981 "\n",
982 "from sklearn.preprocessing import StandardScaler\n",
983 "ss = StandardScaler()"
984 ]
985 },
986 {
987 "cell_type": "code",
988 "execution_count": 24,
989 "metadata": {},
990 "outputs": [],
991 "source": [
992 "X_train_sc = ss.fit_transform(X_train)\n",
993 "X_test_sc = ss.transform(X_test)"
994 ]
995 },
996 {
997 "cell_type": "code",
998 "execution_count": 25,
999 "metadata": {},
1000 "outputs": [
1001 {
1002 "data": {
1003 "image/png": 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1004 "text/plain": [
1005 "<matplotlib.figure.Figure at 0x7f43b23b1780>"
1006 ]
1007 },
1008 "metadata": {},
1009 "output_type": "display_data"
1010 }
1011 ],
1012 "source": [
1013 "fig = plt.figure(figsize=(50,50))\n",
1014 "\n",
1015 "i = 1\n",
1016 "\n",
1017 "for column in list(features.columns):\n",
1018 " fig.add_subplot(7,5,i)\n",
1019 " plt.scatter(features[column], target)\n",
1020 " plt.xlabel(column)\n",
1021 " i+=1"
1022 ]
1023 },
1024 {
1025 "cell_type": "markdown",
1026 "metadata": {},
1027 "source": [
1028 "From looking at the graphs alone, it is hard to tell which features have the greatest correlation to the target variable. I will use a logistic regression to create a basic model, and then use the coefficients from that model to determine which features are the most predictive of malignant/benign. "
1029 ]
1030 },
1031 {
1032 "cell_type": "code",
1033 "execution_count": 26,
1034 "metadata": {},
1035 "outputs": [
1036 {
1037 "data": {
1038 "text/plain": [
1039 "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
1040 " intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
1041 " penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
1042 " verbose=0, warm_start=False)"
1043 ]
1044 },
1045 "execution_count": 26,
1046 "metadata": {},
1047 "output_type": "execute_result"
1048 }
1049 ],
1050 "source": [
1051 "line.fit(X_train_sc, y_train)"
1052 ]
1053 },
1054 {
1055 "cell_type": "code",
1056 "execution_count": 27,
1057 "metadata": {},
1058 "outputs": [
1059 {
1060 "data": {
1061 "text/plain": [
1062 "0.99061032863849763"
1063 ]
1064 },
1065 "execution_count": 27,
1066 "metadata": {},
1067 "output_type": "execute_result"
1068 }
1069 ],
1070 "source": [
1071 "line.score(X_train_sc, y_train)"
1072 ]
1073 },
1074 {
1075 "cell_type": "code",
1076 "execution_count": 28,
1077 "metadata": {},
1078 "outputs": [
1079 {
1080 "data": {
1081 "text/plain": [
1082 "0.96478873239436624"
1083 ]
1084 },
1085 "execution_count": 28,
1086 "metadata": {},
1087 "output_type": "execute_result"
1088 }
1089 ],
1090 "source": [
1091 "line.score(X_test_sc, y_test)"
1092 ]
1093 },
1094 {
1095 "cell_type": "code",
1096 "execution_count": 29,
1097 "metadata": {},
1098 "outputs": [
1099 {
1100 "data": {
1101 "text/plain": [
1102 "Index(['ID', 'radius_mean', 'radius_sd_error', 'radius_worst', 'texture_mean',\n",
1103 " 'texture_sd_error', 'texture_worst', 'perimeter_mean',\n",
1104 " 'perimeter_sd_error', 'perimeter_worst', 'area_mean', 'area_sd_error',\n",
1105 " 'area_worst', 'smoothness_mean', 'smoothness_sd_error',\n",
1106 " 'smoothness_worst', 'compactness_mean', 'compactness_sd_error',\n",
1107 " 'compactness_worst', 'concavity_mean', 'concavity_sd_error',\n",
1108 " 'concavity_worst', 'concave_points_mean', 'concave_points_sd_error',\n",
1109 " 'concave_points_worst', 'symmetry_mean', 'symmetry_sd_error',\n",
1110 " 'symmetry_worst', 'fractal_dimension_mean',\n",
1111 " 'fractal_dimension_sd_error', 'fractal_dimension_worst'],\n",
1112 " dtype='object')"
1113 ]
1114 },
1115 "execution_count": 29,
1116 "metadata": {},
1117 "output_type": "execute_result"
1118 }
1119 ],
1120 "source": [
1121 "features.columns"
1122 ]
1123 },
1124 {
1125 "cell_type": "code",
1126 "execution_count": 30,
1127 "metadata": {},
1128 "outputs": [],
1129 "source": [
1130 "coefficients = pd.DataFrame([line.coef_.tolist()[0], list(features.columns)])"
1131 ]
1132 },
1133 {
1134 "cell_type": "code",
1135 "execution_count": 31,
1136 "metadata": {},
1137 "outputs": [
1138 {
1139 "data": {
1140 "text/html": [
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1191 " <td>0.3737</td>\n",
1192 " <td>0.660347</td>\n",
1193 " </tr>\n",
1194 " <tr>\n",
1195 " <th>1</th>\n",
1196 " <td>ID</td>\n",
1197 " <td>radius_mean</td>\n",
1198 " <td>radius_sd_error</td>\n",
1199 " <td>radius_worst</td>\n",
1200 " <td>texture_mean</td>\n",
1201 " <td>texture_sd_error</td>\n",
1202 " <td>texture_worst</td>\n",
1203 " <td>perimeter_mean</td>\n",
1204 " <td>perimeter_sd_error</td>\n",
1205 " <td>perimeter_worst</td>\n",
1206 " <td>...</td>\n",
1207 " <td>concavity_worst</td>\n",
1208 " <td>concave_points_mean</td>\n",
1209 " <td>concave_points_sd_error</td>\n",
1210 " <td>concave_points_worst</td>\n",
1211 " <td>symmetry_mean</td>\n",
1212 " <td>symmetry_sd_error</td>\n",
1213 " <td>symmetry_worst</td>\n",
1214 " <td>fractal_dimension_mean</td>\n",
1215 " <td>fractal_dimension_sd_error</td>\n",
1216 " <td>fractal_dimension_worst</td>\n",
1217 " </tr>\n",
1218 " </tbody>\n",
1219 "</table>\n",
1220 "<p>2 rows × 31 columns</p>\n",
1221 "</div>"
1222 ],
1223 "text/plain": [
1224 " 0 1 2 3 4 \\\n",
1225 "0 0.077211 0.337816 0.613917 0.34202 0.395536 \n",
1226 "1 ID radius_mean radius_sd_error radius_worst texture_mean \n",
1227 "\n",
1228 " 5 6 7 8 \\\n",
1229 "0 0.217825 -0.443618 0.700996 0.894675 \n",
1230 "1 texture_sd_error texture_worst perimeter_mean perimeter_sd_error \n",
1231 "\n",
1232 " 9 ... 21 \\\n",
1233 "0 0.094519 ... 0.903935 \n",
1234 "1 perimeter_worst ... concavity_worst \n",
1235 "\n",
1236 " 22 23 24 \\\n",
1237 "0 1.10026 0.745397 0.926744 \n",
1238 "1 concave_points_mean concave_points_sd_error concave_points_worst \n",
1239 "\n",
1240 " 25 26 27 28 \\\n",
1241 "0 0.556957 0.190453 0.76284 0.882323 \n",
1242 "1 symmetry_mean symmetry_sd_error symmetry_worst fractal_dimension_mean \n",
1243 "\n",
1244 " 29 30 \n",
1245 "0 0.3737 0.660347 \n",
1246 "1 fractal_dimension_sd_error fractal_dimension_worst \n",
1247 "\n",
1248 "[2 rows x 31 columns]"
1249 ]
1250 },
1251 "execution_count": 31,
1252 "metadata": {},
1253 "output_type": "execute_result"
1254 }
1255 ],
1256 "source": [
1257 "coefficients"
1258 ]
1259 },
1260 {
1261 "cell_type": "code",
1262 "execution_count": 32,
1263 "metadata": {},
1264 "outputs": [],
1265 "source": [
1266 "coefficients = coefficients.transpose()"
1267 ]
1268 },
1269 {
1270 "cell_type": "code",
1271 "execution_count": 33,
1272 "metadata": {},
1273 "outputs": [],
1274 "source": [
1275 "coefficients[0] = coefficients[0].abs()"
1276 ]
1277 },
1278 {
1279 "cell_type": "code",
1280 "execution_count": 34,
1281 "metadata": {},
1282 "outputs": [
1283 {
1284 "data": {
1285 "text/html": [
1286 "<div>\n",
1287 "<table border=\"1\" class=\"dataframe\">\n",
1288 " <thead>\n",
1289 " <tr style=\"text-align: right;\">\n",
1290 " <th></th>\n",
1291 " <th>0</th>\n",
1292 " <th>1</th>\n",
1293 " </tr>\n",
1294 " </thead>\n",
1295 " <tbody>\n",
1296 " <tr>\n",
1297 " <th>11</th>\n",
1298 " <td>1.12972</td>\n",
1299 " <td>area_sd_error</td>\n",
1300 " </tr>\n",
1301 " <tr>\n",
1302 " <th>22</th>\n",
1303 " <td>1.10026</td>\n",
1304 " <td>concave_points_mean</td>\n",
1305 " </tr>\n",
1306 " <tr>\n",
1307 " <th>14</th>\n",
1308 " <td>0.957555</td>\n",
1309 " <td>smoothness_sd_error</td>\n",
1310 " </tr>\n",
1311 " </tbody>\n",
1312 "</table>\n",
1313 "</div>"
1314 ],
1315 "text/plain": [
1316 " 0 1\n",
1317 "11 1.12972 area_sd_error\n",
1318 "22 1.10026 concave_points_mean\n",
1319 "14 0.957555 smoothness_sd_error"
1320 ]
1321 },
1322 "execution_count": 34,
1323 "metadata": {},
1324 "output_type": "execute_result"
1325 }
1326 ],
1327 "source": [
1328 "coefficients.sort_values(by=0, ascending=False).head(3)"
1329 ]
1330 },
1331 {
1332 "cell_type": "markdown",
1333 "metadata": {},
1334 "source": [
1335 "Using a basic logistic regression, I have identified the above three as possible indicators of cancer, based on sorting the coefficients of the logistic regression. The assumption I am making is that the feature with the largest coefficient has the greatest degree of impact on whether the tumor is malignant or benign. "
1336 ]
1337 },
1338 {
1339 "cell_type": "code",
1340 "execution_count": 35,
1341 "metadata": {},
1342 "outputs": [],
1343 "source": [
1344 "import seaborn as sns\n",
1345 "import matplotlib.pyplot as plt\n",
1346 "%matplotlib inline"
1347 ]
1348 },
1349 {
1350 "cell_type": "code",
1351 "execution_count": 36,
1352 "metadata": {},
1353 "outputs": [
1354 {
1355 "data": {
1356 "text/plain": [
1357 "<matplotlib.collections.PathCollection at 0x7f43abc984a8>"
1358 ]
1359 },
1360 "execution_count": 36,
1361 "metadata": {},
1362 "output_type": "execute_result"
1363 },
1364 {
1365 "data": {
1366 "image/png": 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eRVRBPjGaY3uDG4K2j2vRLBHpvC3DyTMDafUsogpyLZolIt3uypQbftLqWUQV5Fo0S0S6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\nQmCC\n",
1367 "text/plain": [
1368 "<matplotlib.figure.Figure at 0x7f43aaab5b70>"
1369 ]
1370 },
1371 "metadata": {},
1372 "output_type": "display_data"
1373 }
1374 ],
1375 "source": [
1376 "plt.scatter(breast_cancer['diagnosis_M'], breast_cancer['area_sd_error'])"
1377 ]
1378 },
1379 {
1380 "cell_type": "code",
1381 "execution_count": 37,
1382 "metadata": {},
1383 "outputs": [
1384 {
1385 "data": {
1386 "text/plain": [
1387 "<matplotlib.collections.PathCollection at 0x7f43abc2b940>"
1388 ]
1389 },
1390 "execution_count": 37,
1391 "metadata": {},
1392 "output_type": "execute_result"
1393 },
1394 {
1395 "data": {
1396 "image/png": 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njDEr4xUXU7tpGYnpWf/7oK5cRCRqgyn/kQVXHkQzNyzfB/wxgDFmC5ABngX21fN9wLdC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\nSBf6/6MuGKTU4mg4AAAAAElFTkSuQmCC\n",
1397 "text/plain": [
1398 "<matplotlib.figure.Figure at 0x7f43abc4d400>"
1399 ]
1400 },
1401 "metadata": {},
1402 "output_type": "display_data"
1403 }
1404 ],
1405 "source": [
1406 "plt.scatter(breast_cancer['diagnosis_M'], breast_cancer['concave_points_mean'])"
1407 ]
1408 },
1409 {
1410 "cell_type": "code",
1411 "execution_count": 51,
1412 "metadata": {},
1413 "outputs": [
1414 {
1415 "data": {
1416 "text/plain": [
1417 "<matplotlib.collections.PathCollection at 0x7f43adf0c160>"
1418 ]
1419 },
1420 "execution_count": 51,
1421 "metadata": {},
1422 "output_type": "execute_result"
1423 },
1424 {
1425 "data": {
1426 "image/png": 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HnqM27fJgSmki9xZLUpfYMjSwono7WrlQ+m1qq12WurnBvvuB/StvVuuq07McO3GW2enZ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\n",
1427 "text/plain": [
1428 "<matplotlib.figure.Figure at 0x7f43a8412320>"
1429 ]
1430 },
1431 "metadata": {},
1432 "output_type": "display_data"
1433 }
1434 ],
1435 "source": [
1436 "plt.scatter(breast_cancer['diagnosis_M'], breast_cancer['smoothness_sd_error'])"
1437 ]
1438 },
1439 {
1440 "cell_type": "markdown",
1441 "metadata": {},
1442 "source": [
1443 "The features with the highest degree of impact on whether or not a tumor is malignant are area_sd_error, concave_points_mean, and smoothness_sd_error. On the graphs, we can see this is true as the there is a clear relationship between the value of the feature and whether it is malignant ('1') or benign ('0'). Values on all three features are higher when the tumor is malignant than when it is benign. "
1444 ]
1445 },
1446 {
1447 "cell_type": "markdown",
1448 "metadata": {},
1449 "source": [
1450 "## Modeling"
1451 ]
1452 },
1453 {
1454 "cell_type": "markdown",
1455 "metadata": {},
1456 "source": [
1457 "In part 2, I used a basic Logistic Regression to identify key features. In part 3, I will build models using DecisionTreeClassifier and KNeighborsClassifier. "
1458 ]
1459 },
1460 {
1461 "cell_type": "code",
1462 "execution_count": 39,
1463 "metadata": {},
1464 "outputs": [
1465 {
1466 "name": "stderr",
1467 "output_type": "stream",
1468 "text": [
1469 "/opt/conda/lib/python3.6/site-packages/sklearn/cross_validation.py:44: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n",
1470 " \"This module will be removed in 0.20.\", DeprecationWarning)\n",
1471 "/opt/conda/lib/python3.6/site-packages/sklearn/grid_search.py:43: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. This module will be removed in 0.20.\n",
1472 " DeprecationWarning)\n"
1473 ]
1474 }
1475 ],
1476 "source": [
1477 "from sklearn.tree import DecisionTreeClassifier\n",
1478 "from sklearn.neighbors import KNeighborsClassifier\n",
1479 "from sklearn.grid_search import GridSearchCV\n",
1480 "from sklearn.pipeline import Pipeline"
1481 ]
1482 },
1483 {
1484 "cell_type": "code",
1485 "execution_count": 42,
1486 "metadata": {},
1487 "outputs": [],
1488 "source": [
1489 "ss = StandardScaler()\n",
1490 "dtc = DecisionTreeClassifier()\n",
1491 "knc = KNeighborsClassifier()\n",
1492 "\n",
1493 "pipe = Pipeline([\n",
1494 " ('ss', ss),\n",
1495 " ('dtc', dtc)\n",
1496 "])\n",
1497 "\n",
1498 "params = {\n",
1499 " 'dtc__min_samples_leaf': np.arange(1,10),\n",
1500 " 'dtc__max_depth': np.arange(1,100),\n",
1501 " 'dtc__min_samples_split': np.arange(2,10)\n",
1502 "} \n",
1503 "\n",
1504 "gscv = GridSearchCV(pipe, params)\n",
1505 "gridsearch_decision = gscv.fit(X_train, y_train)"
1506 ]
1507 },
1508 {
1509 "cell_type": "code",
1510 "execution_count": 43,
1511 "metadata": {},
1512 "outputs": [
1513 {
1514 "data": {
1515 "text/plain": [
1516 "0.9553990610328639"
1517 ]
1518 },
1519 "execution_count": 43,
1520 "metadata": {},
1521 "output_type": "execute_result"
1522 }
1523 ],
1524 "source": [
1525 "gridsearch_decision.best_score_"
1526 ]
1527 },
1528 {
1529 "cell_type": "code",
1530 "execution_count": 44,
1531 "metadata": {},
1532 "outputs": [
1533 {
1534 "data": {
1535 "text/plain": [
1536 "0.9647887323943662"
1537 ]
1538 },
1539 "execution_count": 44,
1540 "metadata": {},
1541 "output_type": "execute_result"
1542 }
1543 ],
1544 "source": [
1545 "ss = StandardScaler()\n",
1546 "\n",
1547 "pipe = Pipeline([\n",
1548 " ('ss', ss),\n",
1549 " ('knc', knc)\n",
1550 "])\n",
1551 "\n",
1552 "params = {\n",
1553 " 'knc__n_neighbors': np.arange(1, 25, 1)\n",
1554 "} \n",
1555 "\n",
1556 "gscv = GridSearchCV(pipe, params)\n",
1557 "gridsearch_neighbor = gscv.fit(X_train, y_train)\n",
1558 "gridsearch_neighbor.best_score_"
1559 ]
1560 },
1561 {
1562 "cell_type": "code",
1563 "execution_count": 45,
1564 "metadata": {},
1565 "outputs": [
1566 {
1567 "data": {
1568 "text/plain": [
1569 "{'knc__n_neighbors': 1}"
1570 ]
1571 },
1572 "execution_count": 45,
1573 "metadata": {},
1574 "output_type": "execute_result"
1575 }
1576 ],
1577 "source": [
1578 "gridsearch_neighbor.best_params_"
1579 ]
1580 },
1581 {
1582 "cell_type": "code",
1583 "execution_count": 46,
1584 "metadata": {},
1585 "outputs": [
1586 {
1587 "data": {
1588 "text/plain": [
1589 "0.96478873239436624"
1590 ]
1591 },
1592 "execution_count": 46,
1593 "metadata": {},
1594 "output_type": "execute_result"
1595 }
1596 ],
1597 "source": [
1598 "gridsearch_neighbor.best_estimator_.score(X_test, y_test)"
1599 ]
1600 },
1601 {
1602 "cell_type": "code",
1603 "execution_count": 47,
1604 "metadata": {},
1605 "outputs": [
1606 {
1607 "data": {
1608 "text/plain": [
1609 "1.0"
1610 ]
1611 },
1612 "execution_count": 47,
1613 "metadata": {},
1614 "output_type": "execute_result"
1615 }
1616 ],
1617 "source": [
1618 "gridsearch_neighbor.best_estimator_.score(X_train, y_train)"
1619 ]
1620 },
1621 {
1622 "cell_type": "markdown",
1623 "metadata": {},
1624 "source": [
1625 "For K Nearest Neighbors classifier, it appears that I am slightly overfitting the data. In this case, the training score is a 1.0, or a perfect fit, but the test score is a .96. This indicates that some overfitting is indeed happening. Surprisingly, my best fit KNN model does not surpass the accuracy of the basic Logistic Regression I performed earlier. "
1626 ]
1627 },
1628 {
1629 "cell_type": "code",
1630 "execution_count": 48,
1631 "metadata": {},
1632 "outputs": [
1633 {
1634 "data": {
1635 "text/plain": [
1636 "0.94366197183098588"
1637 ]
1638 },
1639 "execution_count": 48,
1640 "metadata": {},
1641 "output_type": "execute_result"
1642 }
1643 ],
1644 "source": [
1645 "gridsearch_decision.best_estimator_.score(X_test, y_test)"
1646 ]
1647 },
1648 {
1649 "cell_type": "code",
1650 "execution_count": 49,
1651 "metadata": {},
1652 "outputs": [
1653 {
1654 "data": {
1655 "text/plain": [
1656 "0.99765258215962438"
1657 ]
1658 },
1659 "execution_count": 49,
1660 "metadata": {},
1661 "output_type": "execute_result"
1662 }
1663 ],
1664 "source": [
1665 "gridsearch_decision.best_estimator_.score(X_train, y_train)"
1666 ]
1667 },
1668 {
1669 "cell_type": "code",
1670 "execution_count": 50,
1671 "metadata": {},
1672 "outputs": [
1673 {
1674 "data": {
1675 "text/plain": [
1676 "{'dtc__max_depth': 26, 'dtc__min_samples_leaf': 1, 'dtc__min_samples_split': 3}"
1677 ]
1678 },
1679 "execution_count": 50,
1680 "metadata": {},
1681 "output_type": "execute_result"
1682 }
1683 ],
1684 "source": [
1685 "gridsearch_decision.best_params_"
1686 ]
1687 },
1688 {
1689 "cell_type": "markdown",
1690 "metadata": {},
1691 "source": [
1692 "Some overfitting does appear to be happening with the decision tree model. This could be due to tuning so many hyperparameters. Training data is nearly perfectly fitting the model, while test data does have some error. This model is performing slightly worse than the KNC. "
1693 ]
1694 },
1695 {
1696 "cell_type": "markdown",
1697 "metadata": {},
1698 "source": [
1699 "### Compare and Contrast: KNeighborsClassifier and DecisionTreeClassifier\n",
1700 "\n",
1701 "Both of these classifiers use unique perspectives of classifying data. Interpreting which features have the greatest impact on the model is difficult in both, but for different reasons. KNN uses the feature space as a map and selects whether or not a tumor is benign or malignant based on the closest k examples. Using gridsearchcv, I identified a best k as 9. Therefore, when K Neighbors Classifier is determining classification, it simply looks at the 9 closest examples and uses a voting mechanism to decide which classification to predict. \n",
1702 "\n",
1703 "On the other hand, decision tree classifier is even more arcane. Decision tree classifier creates a series of splits in the data that minimize entropy as the splits are made. Each split creates a tree which is slightly more pure than the previous node. The best decision tree classifier had a max depth of 26 splits, minimum samples per leaf of 1 (so leaf nodes represented only one data point, and minimum samples per split of 3."
1704 ]
1705 },
1706 {
1707 "cell_type": "markdown",
1708 "metadata": {},
1709 "source": [
1710 "### Controlling for overfitting\n",
1711 "\n",
1712 "In most models, a good indicator of overfitting is the difference in error scores between the train and test data. When train data is performing very well, but test data is not performing as well, that is indicative of overfitting. Each model can overfit in different ways, but the principal is the same. Overfitting means that the model is too closely matching the curve of the training data, and is not a good approximator when considering unseen data. \n",
1713 "\n",
1714 "In a decision tree classifier, overfitting can be prevented by tuning hyperparameters such as max depth, min samples per leaf, max splits, etc. In K Neighbors Classifier, the only real hyperparameter to tune is the number of k neighbors. Using too small a number, such as 1, generally results in overfitting. The higher the number, the more general your model will be. Too high, and typically the model will become more of an average model. Here I have tuned this parameter to 9. "
1715 ]
1716 },
1717 {
1718 "cell_type": "markdown",
1719 "metadata": {},
1720 "source": [
1721 "### Performance Evaluation\n",
1722 "\n",
1723 "K Neighbors Classifier fit the training data very closely, with an accuracy score on training data of .96. Surprisingly, the accuracy score for test data is slightly higher, at .98. This indicates that the model is performing very well, and is not overfitting the data in this case. \n",
1724 "\n",
1725 "On the other hand, we see the opposite performance with the Decision Tree Classifier. On training data, the decision tree classifier sees an accuracy score of .974. On test data, however, that falls off to .936. Perhaps I could include more hyperparameters on the decision tree classifier to prevent overfitting, as could be happening here. \n",
1726 "\n",
1727 "Compared to my original Logistic Regression model, neither model seems to be outperforming. The logistic regression had both test and train accuracy scores of .98+, indicating that it was not overfitting but instead accurately predicting whether or not the tumor was benign or malignant. "
1728 ]
1729 },
1730 {
1731 "cell_type": "markdown",
1732 "metadata": {},
1733 "source": [
1734 "## Explanation\n",
1735 "\n",
1736 "### Technical Audience\n",
1737 "\n",
1738 "So far, my analysis has included basic model building. Model accuracy, however, is still limited. My best model so far is an untuned Logistic Regression, which is performing very well. However, this shows that there is still much work to be done. In my pipeline for decision tree classifier I only tuned one hyperparameter. I could attempt to see if this model would perform better by tuning more hyperparameters. Further, I could use more advanced models such as neural networks if performance better than accuracy of .98 is required. \n",
1739 "\n",
1740 "The classes are relatively balanced in this case, with 200-300 examples of both class present. In visually representing the features that have the greatest impact on classification, it is difficult to visually tell whether or not a feature is having an impact on the model, and if so to what degree. However, the accuracy of the Logistic Regression model indicates that there are clear relationships between the values of the features and the final classification. Furthermore, this is without introducing new features such as polynomial relationships, and also without investigating aspects such as skew in the data. \n",
1741 "\n",
1742 "Furthermore, due to the nature of this dataset, .98 accuracy may not be enough. Since benign vs malignant could be a matter of life and death to the patient, we should clearly strive for perfect accuracy. We are close in this case, but there is still room to improve, and it would likely be worth the extra processing power to the patient. \n",
1743 "\n",
1744 "### Non-technical Audience\n",
1745 "\n",
1746 "The dataset above displays data surrounding whether or not a tumor is malignant or benign. Each row representone instance of tumor, with the label of either 'B' or 'M' for 'Benign' or 'Malignant'. The other columns are all unique datapoints regarding that particular example of tumor. \n",
1747 "\n",
1748 "In our model building process, we use those datapoints to identify statistical relationships between the features of each datapoint and the final classification, again benign or malignant. By using various statistical methods, we can evaluate a datapoint given only its feature set, and predict what kind of tumor it is. The datapoints for each tumor include size, shape, concavity, etc. These dimensions are used to create statistical relationships that can tell us with a high degree of accuracy whether or not a tumor is benign or malignant. \n",
1749 "\n",
1750 "Furthermore, we have several different methods, or models, at our disposal for classifying each datapoint. In the work done here, I have used methods called Logistic Regression, K Nearest Neighbors and Decision Tree Classifier. The best performing model achieved an accuracy score that can be interpreted as about 98% accuracy. This is very good, but further work can be done. \n",
1751 "\n",
1752 "In this model, it was found that datapoints such as the error in the standard deviation of the area, the concavity, and the length of the perimeter were the greatest contributors to whether or not a tumor was benign or malignant. As these indicators increase, there is an increasingly liklihood that the tumor is malignant. "
1753 ]
1754 },
1755 {
1756 "cell_type": "markdown",
1757 "metadata": {},
1758 "source": [
1759 "# Part 2"
1760 ]
1761 },
1762 {
1763 "cell_type": "markdown",
1764 "metadata": {},
1765 "source": [
1766 "### Student 1"
1767 ]
1768 },
1769 {
1770 "cell_type": "markdown",
1771 "metadata": {},
1772 "source": [
1773 "Note, I have debugged the code below in order to run it on my notebook. Comments on mistakes in the code are found below in the Comments section."
1774 ]
1775 },
1776 {
1777 "cell_type": "code",
1778 "execution_count": 59,
1779 "metadata": {},
1780 "outputs": [
1781 {
1782 "name": "stdout",
1783 "output_type": "stream",
1784 "text": [
1785 "-11733.827883\n"
1786 ]
1787 },
1788 {
1789 "name": "stderr",
1790 "output_type": "stream",
1791 "text": [
1792 "/opt/conda/lib/python3.6/site-packages/sklearn/metrics/scorer.py:90: DeprecationWarning: Scoring method mean_absolute_error was renamed to neg_mean_absolute_error in version 0.18 and will be removed in 0.20.\n",
1793 " sample_weight=sample_weight)\n",
1794 "/opt/conda/lib/python3.6/site-packages/sklearn/metrics/scorer.py:90: DeprecationWarning: Scoring method mean_absolute_error was renamed to neg_mean_absolute_error in version 0.18 and will be removed in 0.20.\n",
1795 " sample_weight=sample_weight)\n"
1796 ]
1797 }
1798 ],
1799 "source": [
1800 "#!/usr/bin/env python\n",
1801 "\n",
1802 "import pandas as pd\n",
1803 "import numpy as np\n",
1804 "from sklearn.linear_model import LinearRegression\n",
1805 "from sklearn.cross_validation import cross_val_score\n",
1806 "\n",
1807 "# Load data\n",
1808 "data = pd.read_csv('train.csv')\n",
1809 "\n",
1810 "\n",
1811 "# Setup data for prediction\n",
1812 "x1 = data.SalaryNormalized\n",
1813 "x2 = pd.get_dummies(data.ContractType)\n",
1814 "\n",
1815 "# Setup model\n",
1816 "model = LinearRegression()\n",
1817 "\n",
1818 "# Evaluate model\n",
1819 "from sklearn.cross_validation import cross_val_score\n",
1820 "from sklearn.cross_validation import train_test_split\n",
1821 "scores = cross_val_score(model, x2, x1, cv=2, scoring='mean_absolute_error')\n",
1822 "print(scores.mean())"
1823 ]
1824 },
1825 {
1826 "cell_type": "markdown",
1827 "metadata": {},
1828 "source": [
1829 "### Comments "
1830 ]
1831 },
1832 {
1833 "cell_type": "markdown",
1834 "metadata": {},
1835 "source": [
1836 "```from sklearn import LinearRegression``` \n",
1837 "Student forget sklearn.linear_model here"
1838 ]
1839 },
1840 {
1841 "cell_type": "markdown",
1842 "metadata": {},
1843 "source": [
1844 "```d = pd.read_csv('../data/train.csv')```\n",
1845 "\n",
1846 "Student loads dataset to a variable called simply d. Could use greater clarification on what d is or represents here. "
1847 ]
1848 },
1849 {
1850 "cell_type": "markdown",
1851 "metadata": {},
1852 "source": [
1853 "```# Setup data for prediction\n",
1854 "x1 = data.SalaryNormalized\n",
1855 "x2 = pd.get_dummies(data.ContractType)```\n",
1856 "\n",
1857 "Student has previously named a variable d, but tries to call ```data.``` here. \n",
1858 "\n",
1859 "Student forgets to drop the target variable SalaryNormalized, also could use clearer variable naming conventions such as Target and Features or at least X and Y, instead of x1 and x2, which is confusing. "
1860 ]
1861 },
1862 {
1863 "cell_type": "markdown",
1864 "metadata": {},
1865 "source": [
1866 "```from sklearn.cross_validation import train_test_split\n",
1867 "scores = cross_val_score(model, x2, x1, cv=1, scoring='mean_absolute_error')```\n",
1868 "\n",
1869 "Student imports train_test_split but never uses it. Why import it?\n",
1870 "Secondly, they use a cv=1, which is essentially no cross folds. In order for the cross validation to work, more than 1 fold is necessary. I suggest 3 or 4 depending on how much data exists. "
1871 ]
1872 },
1873 {
1874 "cell_type": "markdown",
1875 "metadata": {},
1876 "source": [
1877 "### Student 2"
1878 ]
1879 },
1880 {
1881 "cell_type": "code",
1882 "execution_count": 60,
1883 "metadata": {},
1884 "outputs": [
1885 {
1886 "name": "stdout",
1887 "output_type": "stream",
1888 "text": [
1889 "-11822.1402313\n"
1890 ]
1891 },
1892 {
1893 "name": "stderr",
1894 "output_type": "stream",
1895 "text": [
1896 "/opt/conda/lib/python3.6/site-packages/sklearn/metrics/scorer.py:90: DeprecationWarning: Scoring method mean_absolute_error was renamed to neg_mean_absolute_error in version 0.18 and will be removed in 0.20.\n",
1897 " sample_weight=sample_weight)\n",
1898 "/opt/conda/lib/python3.6/site-packages/sklearn/metrics/scorer.py:90: DeprecationWarning: Scoring method mean_absolute_error was renamed to neg_mean_absolute_error in version 0.18 and will be removed in 0.20.\n",
1899 " sample_weight=sample_weight)\n",
1900 "/opt/conda/lib/python3.6/site-packages/sklearn/metrics/scorer.py:90: DeprecationWarning: Scoring method mean_absolute_error was renamed to neg_mean_absolute_error in version 0.18 and will be removed in 0.20.\n",
1901 " sample_weight=sample_weight)\n",
1902 "/opt/conda/lib/python3.6/site-packages/sklearn/metrics/scorer.py:90: DeprecationWarning: Scoring method mean_absolute_error was renamed to neg_mean_absolute_error in version 0.18 and will be removed in 0.20.\n",
1903 " sample_weight=sample_weight)\n",
1904 "/opt/conda/lib/python3.6/site-packages/sklearn/metrics/scorer.py:90: DeprecationWarning: Scoring method mean_absolute_error was renamed to neg_mean_absolute_error in version 0.18 and will be removed in 0.20.\n",
1905 " sample_weight=sample_weight)\n"
1906 ]
1907 }
1908 ],
1909 "source": [
1910 "#!/usr/bin/env python\n",
1911 "\n",
1912 "import pandas as pd\n",
1913 "import numpy as np\n",
1914 "from sklearn.linear_model import LinearRegression\n",
1915 "from sklearn.cross_validation import cross_val_score\n",
1916 "\n",
1917 "# Load data\n",
1918 "data = pd.read_csv('train.csv')\n",
1919 "\n",
1920 "\n",
1921 "# Setup data for prediction\n",
1922 "y = data.SalaryNormalized\n",
1923 "X = pd.get_dummies(data.ContractType)\n",
1924 "\n",
1925 "# Setup model\n",
1926 "model = LinearRegression()\n",
1927 "\n",
1928 "# Evaluate model\n",
1929 "scores = cross_val_score(model, X, y, cv=5, scoring='mean_absolute_error')\n",
1930 "print(scores.mean())"
1931 ]
1932 },
1933 {
1934 "cell_type": "markdown",
1935 "metadata": {},
1936 "source": [
1937 "### Comments "
1938 ]
1939 },
1940 {
1941 "cell_type": "markdown",
1942 "metadata": {},
1943 "source": [
1944 "```# Load data\n",
1945 "data = pd.read_csv('../data/train.csv')```\n",
1946 "\n",
1947 "This is better, slightly, but the variable name data still does not represent what the data actually is. Either a comment in the code explaining what data is being loaded, or a variable name more closely representing the content of the dataset would be appreicated. "
1948 ]
1949 },
1950 {
1951 "cell_type": "markdown",
1952 "metadata": {},
1953 "source": [
1954 "```# Setup data for prediction\n",
1955 "y = data.SalaryNormalized\n",
1956 "X = pd.get_dummies(data.ContractType)```\n",
1957 "\n",
1958 "Good naming convention. Student still forgets to drop Salarynormalized when storing the X data. "
1959 ]
1960 },
1961 {
1962 "cell_type": "markdown",
1963 "metadata": {},
1964 "source": [
1965 "```# Evaluate model\n",
1966 "scores = cross_val_score(model, X, y, cv=5, scoring='mean_absolute_error')\n",
1967 "print(scores.mean())```\n",
1968 "\n",
1969 "Good use of a higher cv value. Could print out all scores. Goodjob."
1970 ]
1971 }
1972 ],
1973 "metadata": {
1974 "kernelspec": {
1975 "display_name": "Python 3",
1976 "language": "python",
1977 "name": "python3"
1978 },
1979 "language_info": {
1980 "codemirror_mode": {
1981 "name": "ipython",
1982 "version": 3
1983 },
1984 "file_extension": ".py",
1985 "mimetype": "text/x-python",
1986 "name": "python",
1987 "nbconvert_exporter": "python",
1988 "pygments_lexer": "ipython3",
1989 "version": "3.6.2"
1990 }
1991 },
1992 "nbformat": 4,
1993 "nbformat_minor": 2
1994}