Activity 12
basketball_train = read.csv("C:/Users/duway/Downloads/NBA_train.csv")
str(basketball_train)'data.frame': 835 obs. of 20 variables:
$ SeasonEnd: int 1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 ...
$ Team : chr "Atlanta Hawks" "Boston Celtics" "Chicago Bulls" "Cleveland Cavaliers" ...
$ Playoffs : int 1 1 0 0 0 0 0 1 0 1 ...
$ W : int 50 61 30 37 30 16 24 41 37 47 ...
$ PTS : int 8573 9303 8813 9360 8878 8933 8493 9084 9119 8860 ...
$ oppPTS : int 8334 8664 9035 9332 9240 9609 8853 9070 9176 8603 ...
$ FG : int 3261 3617 3362 3811 3462 3643 3527 3599 3639 3582 ...
$ FGA : int 7027 7387 6943 8041 7470 7596 7318 7496 7689 7489 ...
$ X2P : int 3248 3455 3292 3775 3379 3586 3500 3495 3551 3557 ...
$ X2PA : int 6952 6965 6668 7854 7215 7377 7197 7117 7375 7375 ...
$ X3P : int 13 162 70 36 83 57 27 104 88 25 ...
$ X3PA : int 75 422 275 187 255 219 121 379 314 114 ...
$ FT : int 2038 1907 2019 1702 1871 1590 1412 1782 1753 1671 ...
$ FTA : int 2645 2449 2592 2205 2539 2149 1914 2326 2333 2250 ...
$ ORB : int 1369 1227 1115 1307 1311 1226 1155 1394 1398 1187 ...
$ DRB : int 2406 2457 2465 2381 2524 2415 2437 2217 2326 2429 ...
$ AST : int 1913 2198 2152 2108 2079 1950 2028 2149 2148 2123 ...
$ STL : int 782 809 704 764 746 783 779 782 900 863 ...
$ BLK : int 539 308 392 342 404 562 339 373 530 356 ...
$ TOV : int 1495 1539 1684 1370 1533 1742 1492 1565 1517 1439 ...How many observations do we have in the training dataset?
dim(basketball_train)[1] 835 20we have 835 rows(observations) and 20 columns in the training dataset
Is there any chance that a team winning 38 games can make it to the playoffs? Why?
# How many wins to make the playoffs?
table(basketball_train$W, basketball_train$Playoffs)
0 1
11 2 0
12 2 0
13 2 0
14 2 0
15 10 0
16 2 0
17 11 0
18 5 0
19 10 0
20 10 0
21 12 0
22 11 0
23 11 0
24 18 0
25 11 0
26 17 0
27 10 0
28 18 0
29 12 0
30 19 1
31 15 1
32 12 0
33 17 0
34 16 0
35 13 3
36 17 4
37 15 4
38 8 7
39 10 10
40 9 13
41 11 26
42 8 29
43 2 18
44 2 27
45 3 22
46 1 15
47 0 28
48 1 14
49 0 17
50 0 32
51 0 12
52 0 20
53 0 17
54 0 18
55 0 24
56 0 16
57 0 23
58 0 13
59 0 14
60 0 8
61 0 10
62 0 13
63 0 7
64 0 3
65 0 3
66 0 2
67 0 4
69 0 1
72 0 1A team winning 38 games based on historical data made it to the postseason 7 times.
What is the number of wins that can guarantee for any team a presence in the playoffs based on historical data?
#What is the number of wins that can guarantee for any team a presence in the playoffs based on historical data?
table(basketball_train$W, basketball_train$Playoffs)
0 1
11 2 0
12 2 0
13 2 0
14 2 0
15 10 0
16 2 0
17 11 0
18 5 0
19 10 0
20 10 0
21 12 0
22 11 0
23 11 0
24 18 0
25 11 0
26 17 0
27 10 0
28 18 0
29 12 0
30 19 1
31 15 1
32 12 0
33 17 0
34 16 0
35 13 3
36 17 4
37 15 4
38 8 7
39 10 10
40 9 13
41 11 26
42 8 29
43 2 18
44 2 27
45 3 22
46 1 15
47 0 28
48 1 14
49 0 17
50 0 32
51 0 12
52 0 20
53 0 17
54 0 18
55 0 24
56 0 16
57 0 23
58 0 13
59 0 14
60 0 8
61 0 10
62 0 13
63 0 7
64 0 3
65 0 3
66 0 2
67 0 4
69 0 1
72 0 1A Team needs to win at least 47 games to guarantee a playoff spot.
Can you determine (visually) if there is any relationship between the points difference (PTSdiff) and the number of wins (W)?Explain.
# compute points difference
basketball_train$PTSdiff = basketball_train$PTS - basketball_train$oppPTS
plot(basketball_train$PTSdiff, basketball_train$W, xlab = "Points Difference", ylab = "Wins", main = "Points Difference vs Wins")
There is a positive linear relationship between points difference and the number of wins. The more points a team scores compared to their opponent, the more wins they are likely to have.
Here we want to determine what aspects of the game affect the number of wins of a team(WingsReg model). Is the predictor variable points difference (PTSdiff) significant at a 5% significance level?
# Fit a linear regression model
WingsReg = lm(W ~ PTSdiff, data = basketball_train)
summary(WingsReg)
Call:
lm(formula = W ~ PTSdiff, data = basketball_train)
Residuals:
Min 1Q Median 3Q Max
-9.7393 -2.1018 -0.0672 2.0265 10.6026
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.100e+01 1.059e-01 387.0 <2e-16 ***
PTSdiff 3.259e-02 2.793e-04 116.7 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.061 on 833 degrees of freedom
Multiple R-squared: 0.9423, Adjusted R-squared: 0.9423
F-statistic: 1.361e+04 on 1 and 833 DF, p-value: < 2.2e-16The p-value for PTSdiff is less than 0.05, indicating that it is a significant predictor of the number of wins at a 5% significance level.
We also built a linear model to predict the number of points as a function of some aspects of the game. Is the number of blocks (BLK) significant at a 5% significance level?
# Linear regression model for points scored
PointsReg = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + TOV + STL + BLK, data=basketball_train)
summary(PointsReg)
Call:
lm(formula = PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + TOV +
STL + BLK, data = basketball_train)
Residuals:
Min 1Q Median 3Q Max
-527.40 -119.83 7.83 120.67 564.71
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.051e+03 2.035e+02 -10.078 <2e-16 ***
X2PA 1.043e+00 2.957e-02 35.274 <2e-16 ***
X3PA 1.259e+00 3.843e-02 32.747 <2e-16 ***
FTA 1.128e+00 3.373e-02 33.440 <2e-16 ***
AST 8.858e-01 4.396e-02 20.150 <2e-16 ***
ORB -9.554e-01 7.792e-02 -12.261 <2e-16 ***
DRB 3.883e-02 6.157e-02 0.631 0.5285
TOV -2.475e-02 6.118e-02 -0.405 0.6859
STL -1.992e-01 9.181e-02 -2.169 0.0303 *
BLK -5.576e-02 8.782e-02 -0.635 0.5256
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 185.5 on 825 degrees of freedom
Multiple R-squared: 0.8992, Adjusted R-squared: 0.8981
F-statistic: 817.3 on 9 and 825 DF, p-value: < 2.2e-16According to the summary of the PointsReg model, the p-value for BLK is not asignificant predictor of points scored at a 5% significance level. The p-value is greater than 0.05, indicating that the number of blocks does not have a statistically significant effect on the number of points scored.
What has been the maximum number of points in a season?
max(basketball_train$PTS)[1] 10371The maximum number of points in a season is 10371.
What is the meaning of the RMSE(Root mean squared error) in the PointsReg model? Are you satisfied with this value? # the RMSE is a measure of how well the model predicts the number of points scored. It represents the average distance between the predicted and actual values. A lower RMSE indicates a better fit of the model to the data.
#What is the meaning of the RMSE(Root mean squared error) in the PointsReg model? Are you satisfied with this value?
PointsReg = lm(PTS ~ BLK, data = basketball_train)
PointsReg
Call:
lm(formula = PTS ~ BLK, data = basketball_train)
Coefficients:
(Intercept) BLK
7919.434 1.074 How well did your predictions work on the testing dataset? Report the new R2 and RMSE.
# Sum of Squared Errors
PointsReg$residuals 1 2 3 4 5
38.5722713 142.8720040 -92.8957180 -8.3913473 -258.4705615
6 7 8 9 10
171.4608325 150.4081623 169.3811429 40.7756197 -75.3256614
11 12 13 14 15
444.9088743 94.3864704 -205.6809050 113.5969040 64.1993998
16 17 18 19 20
-76.5711999 249.4888007 28.0363236 329.4487991 96.3248342
21 22 23 24 25
349.2067913 -284.3765225 196.1611379 198.2493104 445.4100295
26 27 28 29 30
93.8946072 -316.2962802 -166.1909668 -5.8446359 211.2301997
31 32 33 34 35
155.7426615 -23.9248929 -77.9070033 218.9449693 164.1368602
36 37 38 39 40
-177.6479438 66.9205988 162.7892553 23.5961895 93.9839603
41 42 43 44 45
185.7015113 -50.2507837 -90.1181969 139.6866673 -231.1772776
46 47 48 49 50
111.2200135 185.9069491 210.6753018 -47.9420913 -257.8213675
51 52 53 54 55
225.7399197 70.4925628 432.6468031 187.4169561 -34.3947653
56 57 58 59 60
112.9305359 334.4717296 222.4169937 17.6755711 165.4512882
61 62 63 64 65
207.9970351 56.8277093 214.6051983 -23.0235142 341.7509536
66 67 68 69 70
-48.3807695 304.9203623 -36.7878762 -31.0357805 61.8847883
71 72 73 74 75
-153.0322403 121.7423324 -61.1581185 -47.9906548 -120.3599484
76 77 78 79 80
245.7621368 -264.3876116 161.1110819 87.3192423 426.2098591
81 82 83 84 85
-4.7790973 126.8613801 -97.5009340 329.9773912 -16.2338716
86 87 88 89 90
7.8513505 191.9280982 87.0090318 -142.5397602 -216.2264974
91 92 93 94 95
-199.6293933 71.0810742 257.3751407 -227.1203824 -61.4866232
96 97 98 99 100
71.3329444 -233.2637272 -34.7860771 84.9503466 108.6553543
101 102 103 104 105
-84.8168235 -90.0423121 341.2144522 52.8507112 47.8978397
106 107 108 109 110
181.0574099 160.7203318 237.0174702 314.9609845 51.9650831
111 112 113 114 115
300.2035074 -148.0931149 -13.3592416 -161.6184704 82.1172789
116 117 118 119 120
277.6080699 233.4334153 -225.7299932 69.0259972 37.3407430
121 122 123 124 125
18.2709681 121.8125335 217.9464858 -74.8210467 36.2611001
126 127 128 129 130
356.2366230 439.4127892 111.0266627 72.1377278 -6.1141295
131 132 133 134 135
331.6249450 -158.3642350 94.9048994 151.3242943 -284.7768411
136 137 138 139 140
-184.0287416 -103.9972773 54.1758237 139.3176593 125.3796164
141 142 143 144 145
-71.4407602 83.4742245 -131.6383234 -33.5752771 98.9460909
146 147 148 149 150
-59.8760139 -116.6711077 -110.4055752 290.8888709 38.5758792
151 152 153 154 155
-6.8265554 -284.8106013 149.5419209 -185.9270381 -13.5712897
156 157 158 159 160
-90.2301662 21.0080300 14.5295957 -346.4091267 -54.7198161
161 162 163 164 165
87.6823846 203.7903006 -30.7131853 -153.9699795 194.6791232
166 167 168 169 170
-357.4466727 133.8696823 -21.6271760 -220.4987354 -153.7269937
171 172 173 174 175
-383.7168614 212.2104185 -100.3118791 -30.5085767 -57.7910608
176 177 178 179 180
205.9463003 -124.1358862 -61.2169391 -93.9538879 -135.6180284
181 182 183 184 185
69.1245169 -435.5355494 -47.8153585 115.1051439 222.5411686
186 187 188 189 190
104.6516380 7.8335700 178.0759383 -185.3383423 122.0537263
191 192 193 194 195
-29.4729351 27.1344203 189.2078833 -429.5919872 57.2397301
196 197 198 199 200
-170.2701567 -14.0836520 21.0147294 49.6548689 -127.4633821
201 202 203 204 205
-87.4084020 -77.6940715 -155.2913076 8.4930328 -232.7210528
206 207 208 209 210
35.3384277 151.1394532 119.4563308 -416.3088878 134.8599211
211 212 213 214 215
33.3825347 48.4541197 -269.8021487 214.9045443 88.1318416
216 217 218 219 220
-24.0318730 188.2281015 -249.1537666 157.9872056 -146.6803006
221 222 223 224 225
72.9077663 31.1747176 337.2185582 69.7227713 -2.7440511
226 227 228 229 230
-55.2845827 -84.6255409 -151.4858821 234.7432200 -165.3909069
231 232 233 234 235
-172.9288404 386.6402387 34.4884530 -368.0387956 304.8349400
236 237 238 239 240
-173.0591889 168.9365987 -327.6509605 95.0370278 -75.5698743
241 242 243 244 245
-74.9702316 290.0371682 -21.8628806 72.5362398 -144.3565453
246 247 248 249 250
-44.7765529 -155.4752429 -114.0232742 82.8841506 -306.5759686
251 252 253 254 255
256.9630856 75.4312937 -108.9852622 -160.6985087 -1.0708625
256 257 258 259 260
389.4834173 48.4039145 -173.2376267 102.4859575 564.7127452
261 262 263 264 265
-135.6781765 435.5847710 -238.8763852 93.4120332 -346.4790813
266 267 268 269 270
84.2266238 124.2627684 157.9013909 90.9742388 -319.7738668
271 272 273 274 275
111.6330940 -136.0189613 179.6895020 -139.8481361 -60.2214721
276 277 278 279 280
21.1448936 -102.4930752 87.4261255 -2.2833983 -33.1839059
281 282 283 284 285
-313.4181662 -9.7903234 365.0041757 -170.9089658 -203.2682115
286 287 288 289 290
-59.0783300 344.4592952 -177.2934555 278.4424923 31.1539516
291 292 293 294 295
-19.4217087 146.9309508 49.6437593 323.4485389 47.1034178
296 297 298 299 300
3.9718411 -111.0589062 -40.0036081 187.1994351 134.5701059
301 302 303 304 305
-130.3795390 227.3624370 16.4481298 -91.2556101 215.9887998
306 307 308 309 310
70.7747666 50.5357552 -86.7616664 66.3006293 348.5847817
311 312 313 314 315
69.7928527 -144.9174008 48.2485248 262.5189212 -11.0182067
316 317 318 319 320
276.2567984 40.2609782 -235.0009787 91.8230888 -36.7029055
321 322 323 324 325
66.1862316 127.1446887 34.6306466 -89.1508242 -38.0350890
326 327 328 329 330
74.6959695 -24.6713632 -139.6322463 120.5781319 -256.3194253
331 332 333 334 335
35.3325803 -238.1863124 204.2701943 -231.4333870 -242.0178081
336 337 338 339 340
27.3589769 442.7697537 -90.3428846 -252.6536092 31.2460678
341 342 343 344 345
-24.0030042 -113.6697991 74.2030422 -63.3601223 13.1314540
346 347 348 349 350
-58.4065092 16.5093336 -26.4233092 -49.9197611 102.5295504
351 352 353 354 355
-276.0762358 -171.2605451 235.4118705 -295.3696087 -259.1915277
356 357 358 359 360
-209.8493128 -60.3803252 40.8738668 -162.3559100 -3.1584146
361 362 363 364 365
-252.6683460 -359.6072976 219.8480950 107.9177034 -228.4285961
366 367 368 369 370
77.5838841 77.6092501 176.9728823 21.0277939 225.7947949
371 372 373 374 375
90.6177409 -95.0387148 243.8004275 63.7765295 -135.7112041
376 377 378 379 380
127.9942080 208.5134149 -226.2507886 -27.4427262 215.5791874
381 382 383 384 385
70.0554598 -220.3324085 -252.5213694 -117.0224660 36.9146043
386 387 388 389 390
188.5932206 -12.6241171 24.1401960 39.4113815 130.8261623
391 392 393 394 395
194.8028770 140.1603242 100.4917058 367.8120506 -77.1138759
396 397 398 399 400
190.1907177 430.4505906 243.1092461 -220.7690501 -135.3500281
401 402 403 404 405
182.9169784 58.1314347 -10.3705665 134.0505987 333.4363828
406 407 408 409 410
110.9704334 37.1431301 188.8559358 -88.4445131 -165.3268990
411 412 413 414 415
148.8624801 -4.7914163 -114.6045335 -90.1562962 -65.1353805
416 417 418 419 420
9.9207366 -20.2393315 147.7163583 153.4474395 95.5889698
421 422 423 424 425
-329.6439893 323.3019593 345.3838501 -148.5288812 166.9648145
426 427 428 429 430
277.3541861 162.6383840 -78.9033000 -176.7932426 365.3962572
431 432 433 434 435
132.7242544 85.6582953 -19.3417988 95.4767236 -102.8199452
436 437 438 439 440
111.8183778 299.2808339 -124.0889739 -37.3805041 118.5055640
441 442 443 444 445
38.2173450 -122.8141423 -84.3447659 154.5643586 42.6355711
446 447 448 449 450
54.7178397 102.9846564 32.6861086 112.7943954 -163.3563028
451 452 453 454 455
150.7521084 217.5877806 -96.7133626 13.7243484 -33.1690450
456 457 458 459 460
-112.2550008 -15.7083565 -224.4198990 18.2593593 -393.0403979
461 462 463 464 465
49.2945267 52.0947949 43.2496203 -149.1223107 75.6856970
466 467 468 469 470
170.8878792 -257.6364448 51.6854016 11.8121415 -176.9048352
471 472 473 474 475
-149.5317630 -64.1990241 -71.3105611 -317.9190063 -65.8451642
476 477 478 479 480
97.8497015 -103.1692986 3.0848318 -104.6823532 -234.7534874
481 482 483 484 485
50.5295490 -75.4835788 -526.1468848 -393.9784124 -360.8366411
486 487 488 489 490
116.7193515 -321.3756304 -28.1090479 -508.3250405 -39.9958738
491 492 493 494 495
67.9854387 -97.4641720 -268.8364479 -26.0249946 188.1881640
496 497 498 499 500
-127.9366821 -86.3440758 133.8144538 29.4480488 -292.9821609
501 502 503 504 505
-124.9408024 101.3655240 -186.5181083 -63.5389375 -212.2015589
506 507 508 509 510
-323.1476886 -125.6610320 56.9083106 -39.0559074 -1.9339391
511 512 513 514 515
-319.9727619 -433.1243358 -431.1346590 -95.8909016 120.6089792
516 517 518 519 520
-409.7409083 -352.9341830 -527.3988939 110.6694955 -193.5043557
521 522 523 524 525
-92.6385367 -143.5858243 -189.7838251 172.1977457 -80.8020663
526 527 528 529 530
-342.9141699 124.8700974 -226.9524006 -73.5173798 -388.4868649
531 532 533 534 535
82.9536394 -96.7444961 -114.0835553 60.0566113 -332.3804023
536 537 538 539 540
-175.5276633 -338.7116370 -148.1422366 -45.2258816 -270.5159099
541 542 543 544 545
-159.8389177 -420.4637398 -133.0466450 183.8988039 -267.0297916
546 547 548 549 550
-5.2562902 -228.0471046 -11.6818058 -255.6786897 -7.7244412
551 552 553 554 555
-115.5357863 -298.4118693 -122.2961876 90.2924072 111.3930340
556 557 558 559 560
-245.4519945 -164.6445508 -29.3651223 -41.9781581 33.4260937
561 562 563 564 565
15.1663563 -29.4557965 44.0659204 247.9836928 -57.4318280
566 567 568 569 570
-238.6989443 -8.7249850 30.9454288 -343.6175905 -207.4418486
571 572 573 574 575
-306.4223254 157.4538406 -502.4785715 -126.1415717 48.8616098
576 577 578 579 580
143.9835801 -344.7694076 -116.5012114 -142.7898454 -127.9612584
581 582 583 584 585
-226.7659179 67.1679765 -94.0443422 -326.2414346 -84.6517620
586 587 588 589 590
4.5942017 -89.9757406 -97.0958454 -34.6927947 40.9701699
591 592 593 594 595
-88.3066869 126.5679875 -128.7529512 -166.6757304 -208.2444446
596 597 598 599 600
-105.4053449 -69.9961388 -104.0297252 -475.1678378 -290.6421238
601 602 603 604 605
195.4801727 -116.0865727 -136.0505114 -118.3811054 125.8235124
606 607 608 609 610
-145.2484421 -144.5655628 -435.6270621 -230.6201428 -112.7403208
611 612 613 614 615
-243.8883351 13.9124625 -392.1393056 -233.5727670 88.6125994
616 617 618 619 620
-203.7574893 -207.3393547 36.7326516 71.7237279 -110.6124268
621 622 623 624 625
-151.5524839 95.2365977 -227.3589026 -98.5962165 -210.8715081
626 627 628 629 630
-53.6787512 33.2644764 -380.2334407 -217.0512157 -135.7283167
631 632 633 634 635
208.5947156 -198.2473902 -147.6362401 -282.5390059 -55.4726214
636 637 638 639 640
3.0618526 -118.7764165 -15.9756605 1.5396468 2.2068206
641 642 643 644 645
-78.5559489 20.5194552 -376.9064555 -367.5790965 78.4730898
646 647 648 649 650
88.0528050 -178.9859105 283.6342652 18.0639226 1.4275017
651 652 653 654 655
-22.1910648 334.1581029 -44.6704981 -166.2133428 -112.8182784
656 657 658 659 660
175.7515262 60.9355144 -331.2815975 -175.1322112 34.9727118
661 662 663 664 665
430.8913232 -260.7815266 -99.5985786 -306.5331420 -144.2463445
666 667 668 669 670
-71.9561309 40.4095734 -9.9170555 9.7141807 72.8730721
671 672 673 674 675
-61.2840291 -51.9936086 -452.8596863 -81.9437393 69.2906290
676 677 678 679 680
254.7395766 -22.9459505 215.8931262 -16.9537293 -107.9068394
681 682 683 684 685
202.3017464 287.5765859 180.7757394 -305.5932029 56.2240459
686 687 688 689 690
4.5320328 -44.0648823 -278.0391307 -13.3280981 -112.7276708
691 692 693 694 695
422.1750569 -131.0023955 51.4971549 -86.9745423 28.8396258
696 697 698 699 700
-107.9302127 -55.3683153 -16.7225380 60.3453436 3.3520616
701 702 703 704 705
140.9429255 -17.9219329 -296.8381962 136.2394242 106.7244264
706 707 708 709 710
168.2861008 26.7860625 339.8954937 187.8922770 -202.6392008
711 712 713 714 715
148.7995083 268.8921528 0.6597544 -119.2916116 -23.0549542
716 717 718 719 720
-28.1758366 206.7679556 -138.5838793 -210.7824121 -29.6626073
721 722 723 724 725
210.3268820 -212.8798945 88.1962039 129.1032851 11.9530477
726 727 728 729 730
-166.3796048 -372.3297260 67.5130804 1.7122210 -179.0745146
731 732 733 734 735
-28.4404659 151.2765881 -425.3360446 344.3671825 -47.2592021
736 737 738 739 740
136.9801455 63.4427397 203.2044716 27.7908779 251.4279736
741 742 743 744 745
84.5817590 -155.6577645 150.3787715 138.7921016 198.4699948
746 747 748 749 750
101.8590582 345.8144412 35.1336113 169.1641149 354.9998851
751 752 753 754 755
251.7571721 47.8412497 77.9677328 66.2799291 216.7990909
756 757 758 759 760
155.1577399 -131.2437994 230.2449071 218.7156645 116.0349148
761 762 763 764 765
-78.5937100 -23.1321308 99.7713990 280.2227149 40.8527845
766 767 768 769 770
19.4188914 72.9388151 120.7266716 439.1035137 456.0100354
771 772 773 774 775
47.3239201 186.1096824 31.7505381 -54.0912550 73.0035369
776 777 778 779 780
234.4761589 27.9146721 -21.6493313 -75.0167664 148.4251726
781 782 783 784 785
106.3308316 76.0196340 37.3592068 56.5562663 -41.8917486
786 787 788 789 790
-200.7598142 -55.5159544 109.1518868 321.3239680 219.8866600
791 792 793 794 795
-73.6034103 3.1961900 -171.1408177 190.8979178 101.1845265
796 797 798 799 800
253.1734885 263.7840087 199.5924560 463.8379676 219.1540922
801 802 803 804 805
52.3032317 140.7498122 195.8267787 -55.3103142 153.8564182
806 807 808 809 810
61.1275837 92.8158603 -108.8302808 73.3423661 -360.6001538
811 812 813 814 815
134.1518035 73.3435884 141.0017271 272.8259956 -33.1611977
816 817 818 819 820
19.7818711 -149.9998706 190.0065593 261.3992751 308.7602526
821 822 823 824 825
-135.4172110 108.2677094 -171.3410196 102.4439076 156.0829202
826 827 828 829 830
210.0521687 109.4908936 -20.5354175 59.2845716 175.9235274
831 832 833 834 835
30.6531825 262.6728011 70.0671862 -17.5789419 -8.3393046 # Sum of Squared Errors
SSE = sum(PointsReg$residuals^2)
SSE[1] 28394314# Root Mean Squared Error
RMSE = sqrt(SSE / nrow(basketball_train))
RMSE[1] 184.4049# Average number of points in a season
mean(basketball_train$PTS)[1] 8370.24# Remove insignifcant variables
summary(PointsReg)
Call:
lm(formula = PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + TOV +
STL + BLK, data = basketball_train)
Residuals:
Min 1Q Median 3Q Max
-527.40 -119.83 7.83 120.67 564.71
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.051e+03 2.035e+02 -10.078 <2e-16 ***
X2PA 1.043e+00 2.957e-02 35.274 <2e-16 ***
X3PA 1.259e+00 3.843e-02 32.747 <2e-16 ***
FTA 1.128e+00 3.373e-02 33.440 <2e-16 ***
AST 8.858e-01 4.396e-02 20.150 <2e-16 ***
ORB -9.554e-01 7.792e-02 -12.261 <2e-16 ***
DRB 3.883e-02 6.157e-02 0.631 0.5285
TOV -2.475e-02 6.118e-02 -0.405 0.6859
STL -1.992e-01 9.181e-02 -2.169 0.0303 *
BLK -5.576e-02 8.782e-02 -0.635 0.5256
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 185.5 on 825 degrees of freedom
Multiple R-squared: 0.8992, Adjusted R-squared: 0.8981
F-statistic: 817.3 on 9 and 825 DF, p-value: < 2.2e-16PointsReg2 = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + STL + BLK, data=basketball_train)
summary(PointsReg2)
Call:
lm(formula = PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + STL +
BLK, data = basketball_train)
Residuals:
Min 1Q Median 3Q Max
-526.79 -121.09 6.37 120.74 565.94
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.077e+03 1.931e+02 -10.755 <2e-16 ***
X2PA 1.044e+00 2.951e-02 35.366 <2e-16 ***
X3PA 1.263e+00 3.703e-02 34.099 <2e-16 ***
FTA 1.125e+00 3.308e-02 34.023 <2e-16 ***
AST 8.861e-01 4.393e-02 20.173 <2e-16 ***
ORB -9.581e-01 7.758e-02 -12.350 <2e-16 ***
DRB 3.892e-02 6.154e-02 0.632 0.5273
STL -2.068e-01 8.984e-02 -2.301 0.0216 *
BLK -5.863e-02 8.749e-02 -0.670 0.5029
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 185.4 on 826 degrees of freedom
Multiple R-squared: 0.8991, Adjusted R-squared: 0.8982
F-statistic: 920.4 on 8 and 826 DF, p-value: < 2.2e-16PointsReg3 = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + STL + BLK, data=basketball_train)
summary(PointsReg3)
Call:
lm(formula = PTS ~ X2PA + X3PA + FTA + AST + ORB + STL + BLK,
data = basketball_train)
Residuals:
Min 1Q Median 3Q Max
-523.79 -121.64 6.07 120.81 573.64
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.015e+03 1.670e+02 -12.068 < 2e-16 ***
X2PA 1.048e+00 2.852e-02 36.753 < 2e-16 ***
X3PA 1.271e+00 3.475e-02 36.568 < 2e-16 ***
FTA 1.128e+00 3.270e-02 34.506 < 2e-16 ***
AST 8.909e-01 4.326e-02 20.597 < 2e-16 ***
ORB -9.702e-01 7.519e-02 -12.903 < 2e-16 ***
STL -2.276e-01 8.356e-02 -2.724 0.00659 **
BLK -3.882e-02 8.165e-02 -0.475 0.63462
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 185.4 on 827 degrees of freedom
Multiple R-squared: 0.8991, Adjusted R-squared: 0.8982
F-statistic: 1053 on 7 and 827 DF, p-value: < 2.2e-16PointsReg4 = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + STL, data=basketball_train)
summary(PointsReg4)
Call:
lm(formula = PTS ~ X2PA + X3PA + FTA + AST + ORB + STL, data = basketball_train)
Residuals:
Min 1Q Median 3Q Max
-523.33 -122.02 6.93 120.68 568.26
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.033e+03 1.629e+02 -12.475 < 2e-16 ***
X2PA 1.050e+00 2.829e-02 37.117 < 2e-16 ***
X3PA 1.273e+00 3.441e-02 37.001 < 2e-16 ***
FTA 1.127e+00 3.260e-02 34.581 < 2e-16 ***
AST 8.884e-01 4.292e-02 20.701 < 2e-16 ***
ORB -9.743e-01 7.465e-02 -13.051 < 2e-16 ***
STL -2.268e-01 8.350e-02 -2.717 0.00673 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 185.3 on 828 degrees of freedom
Multiple R-squared: 0.8991, Adjusted R-squared: 0.8983
F-statistic: 1229 on 6 and 828 DF, p-value: < 2.2e-16# Compute SSE and RMSE for new model
SSE_4 = sum(PointsReg4$residuals^2)
RMSE_4 = sqrt(SSE_4/nrow(basketball_train))
SSE_4[1] 28421465RMSE_4[1] 184.493
basketball_test = read.csv("C:/Users/duway/Downloads/NBA_test.csv")# Make predictions on test set
PointsPredictions = predict(PointsReg4, newdata=basketball_test)# Compute out-of-sample R^2
SSE = sum((PointsPredictions - basketball_test$PTS)^2)
SST = sum((mean(basketball_train$PTS) - basketball_test$PTS)^2)
R2 = 1 - SSE/SST
R2[1] 0.81271420.812 means the features we have chosen explain 81.2% of the variance in the test dataset. This is a good value, indicating that the model is able to explain a significant portion of the variability in the number of points scored.
# Compute the RMSE
RMSE = sqrt(SSE/nrow(basketball_test))
RMSE [1] 196.3723based on the RMSE value 196 means that the prediction value is off by 196 in terms of points scored every season this RMSE is a very good model to work with.
Activity 13
Our data shows that a team with 49 wins has never missed the playoffs. What is the expected points difference for a team to make it to the postseason? Use the lecture solution file and more specifically the WingsReg model.
# Fit a linear regression model
WingsReg = lm(W ~ PTSdiff, data = basketball_train)
summary(WingsReg)
Call:
lm(formula = W ~ PTSdiff, data = basketball_train)
Residuals:
Min 1Q Median 3Q Max
-9.7393 -2.1018 -0.0672 2.0265 10.6026
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.100e+01 1.059e-01 387.0 <2e-16 ***
PTSdiff 3.259e-02 2.793e-04 116.7 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.061 on 833 degrees of freedom
Multiple R-squared: 0.9423, Adjusted R-squared: 0.9423
F-statistic: 1.361e+04 on 1 and 833 DF, p-value: < 2.2e-16# Calculate expected points difference for a team with 49 wins
WingsReg = lm(W ~ PTSdiff, data = basketball_train)
PTSdiff = (49 - WingsReg$coefficients[1]) / WingsReg$coefficients[2]
PTSdiff(Intercept)
245.5017 #49=41+0.326*(x)
x_1= (49-41)/0.0326
x_1[1] 245.3988The expected points difference for a team to make it to the postseason is 245.39 points. This means that a team with 49 wins is expected to have a points difference of 245.39 points in order to make it to the playoffs.
---
title: "Activity 12"
output: html_notebook
---


```{r}
basketball_train = read.csv("C:/Users/duway/Downloads/NBA_train.csv")

```


```{r}
str(basketball_train)
```


How many observations do we have in the training dataset?
```{r}
dim(basketball_train)

```
# we have 835 rows(observations) and 20 columns in the training dataset

Is there any chance that a team winning 38 games can make it to the
playoffs? Why? 
```{r}
# How many wins to make the playoffs?
table(basketball_train$W, basketball_train$Playoffs)
```

# A team winning 38 games based on historical data made it to the postseason 7 times.   

What is the number of wins that can guarantee for any team a presence in the playoffs based on historical data?
```{r}
#What is the number of wins that can guarantee for any team a presence in the playoffs based on historical data?
table(basketball_train$W, basketball_train$Playoffs)
```

# A Team needs to win at least 47 games to guarantee a playoff spot. 


```{r}
```

Can you determine (visually) if there is any relationship between the points difference (PTSdiff) and the number of wins (W)?Explain.
```{r}
# compute points difference
basketball_train$PTSdiff = basketball_train$PTS - basketball_train$oppPTS
plot(basketball_train$PTSdiff, basketball_train$W, xlab = "Points Difference", ylab = "Wins", main = "Points Difference vs Wins")

```

# There is a positive linear relationship between points difference and the number of wins. The more points a team scores compared to their opponent, the more wins they are likely to have. 


Here we want to determine what aspects of the game affect the number of wins of a team(WingsReg model). Is the predictor variable points difference (PTSdiff) significant at a 5% significance level?
```{r}
# Fit a linear regression model
WingsReg = lm(W ~ PTSdiff, data = basketball_train)
summary(WingsReg)
```
# The p-value for PTSdiff is less than 0.05, indicating that it is a significant predictor of the number of wins at a 5% significance level. 

We also built a linear model to predict the number of points as a function of some aspects of the game. Is the number of blocks (BLK) significant at a 5% significance level?
```{r}
# Linear regression model for points scored
PointsReg = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + TOV + STL + BLK, data=basketball_train)
summary(PointsReg)

```
# According to the summary of the PointsReg model, the p-value for BLK is not asignificant predictor of points scored at a 5% significance level. The p-value is greater than 0.05, indicating that the number of blocks does not have a statistically significant effect on the number of points scored.




What has been the maximum number of points in a season?
```{r}
max(basketball_train$PTS)

```
# The maximum number of points in a season is 10371.


What is the meaning of the RMSE(Root mean squared error) in the PointsReg model? Are you satisfied with this value?
# the RMSE is a measure of how well the model predicts the number of points scored. It represents the average distance between the predicted and actual values. A lower RMSE indicates a better fit of the model to the data. 
```{r}

PointsReg = lm(PTS ~ BLK, data = basketball_train)
PointsReg
  
```

How well did your predictions work on the testing dataset? Report the new R2 and RMSE.
```{r}
# Sum of Squared Errors
PointsReg$residuals
```


```{r}
# Sum of Squared Errors
SSE = sum(PointsReg$residuals^2)
SSE

```

```{r}
# Root Mean Squared Error

RMSE = sqrt(SSE / nrow(basketball_train))
RMSE
```

```{r}
# Average number of points in a season
mean(basketball_train$PTS)
```

```{r}
# Remove insignifcant variables
summary(PointsReg)
```
```{r}
PointsReg2 = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + STL + BLK, data=basketball_train)
summary(PointsReg2)
```

```{r}
PointsReg3 = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + STL + BLK, data=basketball_train)
summary(PointsReg3)
```


```{r}
PointsReg4 = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + STL, data=basketball_train)
summary(PointsReg4)
```


```{r}
# Compute SSE and RMSE for new model
SSE_4 = sum(PointsReg4$residuals^2)
RMSE_4 = sqrt(SSE_4/nrow(basketball_train))
SSE_4
```

```{r}
RMSE_4
```







```{r}

basketball_test = read.csv("C:/Users/duway/Downloads/NBA_test.csv")
```


```{r}
# Make predictions on test set
PointsPredictions = predict(PointsReg4, newdata=basketball_test)
```


```{r}
# Compute out-of-sample R^2
SSE = sum((PointsPredictions - basketball_test$PTS)^2)
SST = sum((mean(basketball_train$PTS) - basketball_test$PTS)^2)
R2 = 1 - SSE/SST
R2
```
# 0.812 means the features we have chosen explain 81.2% of the variance in the test dataset. This is a good value, indicating that the model is able to explain a significant portion of the variability in the number of points scored.


```{r}
# Compute the RMSE
RMSE = sqrt(SSE/nrow(basketball_test))
RMSE 
```
# based on the RMSE value 196 means that the prediction value is off by 196 in terms of points scored every season this RMSE is a very good model to work with.







# Activity 13

# Our data shows that a team with 49 wins has never missed the playoffs. What is the expected points difference for a team to make it to the postseason? Use the lecture solution file and more specifically the WingsReg model.


```{r}
# Fit a linear regression model
WingsReg = lm(W ~ PTSdiff, data = basketball_train)
summary(WingsReg)
```



```{r}
# Calculate expected points difference for a team with 49 wins
 
WingsReg = lm(W ~ PTSdiff, data = basketball_train)
PTSdiff = (49 - WingsReg$coefficients[1]) / WingsReg$coefficients[2]
PTSdiff
#49=41+0.326*(x)
x_1= (49-41)/0.0326
x_1
```

# The expected points difference for a team to make it to the postseason is 245.39 points. This means that a team with 49 wins is expected to have a points difference of 245.39 points in order to make it to the playoffs.















