Assignment 12 - Playing Moneyball in the NBA
- How many observations do we have in the training dataset?
The training dataset has 835 observations, with 20 variables.
- Is there any chance that a team winning 38 games can make it to the playoffs? Why?
According to the training dataset, the 8 teams that won 38 games made it to the playoffs 7 times. I believe 7/8 (about 87.5%) is a reasonable chance of making it to playoffs.
- What is the number of wins that can guarantee for any team a presence in the playoffs based on historical data?
According to the training dataset, only 4 of the 15 teams that won 37 games made it to playoffs, while all 10 of the teams that made 39 points made it to playoffs. It seems that after winning 38 games, the chances of making it to playoffs at least once are reasonably confident.
- Can you determine (visually) if there is any relationship between the points difference (PTSdiff) and the number of wins (W)?Explain.
In my opinion, there seems to be a positive linear relationship between the points diffeerence (PTSdiff) and the number of wins (W). When observing the plot made with the code below (#check for linear relationship), we can see that the a negative point difference correlates with a lower amount of wins, while a higher point difference correlates with a higher amount of wins.
- 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?
As shown below, PTSdiff has a Pr of under (<) 2e-16. With a 0.05 significance level, this predictor would be considered statistically significant. We would reject the null hypothesis and accept that there is a positive relationship between PTSdiff and W.
- 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?
The p-value of BLK shown in the code below the Q&A is 0.5256, which is greater than a 0.05 significance level. This means that BLK is not statistically significant.
- What has been the maximum number of points in a season?
max(NBA$PTS)[1] 10371- What is the meaning of the RMSE(Root mean squared error) in the PointsReg model? Are you satisfied with this value?
RMSE in the context of the PointsReg model is about 185 ( 184.4049), with an adjusted R-squared of 0.8981. This means that our model is including about 89.81% of the variance in points scored. Because our RMSE is over 100 or so, I believe this model is showing a satisfactory value, though there is always the chance that a different model may provide us an even better result.
- How well did your predictions work on the testing dataset? Report the new R2 and RMSE.
Our new R2 of 0.8127142 and RMSE of 196.3723 compare relatively well to the prior amounts of 0.8981 and 184.4049. In general, I would say that our predictive model worked well on the testing dataset.
CODING BLOCKS:
# VIDEO 1
# Read in the data
NBA = read.csv("NBA_train.csv")
str(NBA)'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 ...# VIDEO 2
# How many wins to make the playoffs?
table(NBA$W, NBA$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 1# Compute Points Difference
NBA$PTSdiff = NBA$PTS - NBA$oppPTS# Check for linear relationship
plot(NBA$PTSdiff, NBA$W)
# Linear regression model for wins
WinsReg = lm(W ~ PTSdiff, data=NBA)
summary(WinsReg)
Call:
lm(formula = W ~ PTSdiff, data = NBA)
Residuals:
Min 1Q Median 3Q Max
-9.7393 -2.1018 -0.0672 2.0265 10.6026
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.100e+01 1.059e-01 387.0 <2e-16 ***
PTSdiff 3.259e-02 2.793e-04 116.7 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.061 on 833 degrees of freedom
Multiple R-squared: 0.9423, Adjusted R-squared: 0.9423
F-statistic: 1.361e+04 on 1 and 833 DF, p-value: < 2.2e-16# VIDEO 3
# Linear regression model for points scored
PointsReg = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + TOV + STL + BLK, data=NBA)
summary(PointsReg)
Call:
lm(formula = PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + TOV +
STL + BLK, data = NBA)
Residuals:
Min 1Q Median 3Q Max
-527.40 -119.83 7.83 120.67 564.71
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.051e+03 2.035e+02 -10.078 <2e-16 ***
X2PA 1.043e+00 2.957e-02 35.274 <2e-16 ***
X3PA 1.259e+00 3.843e-02 32.747 <2e-16 ***
FTA 1.128e+00 3.373e-02 33.440 <2e-16 ***
AST 8.858e-01 4.396e-02 20.150 <2e-16 ***
ORB -9.554e-01 7.792e-02 -12.261 <2e-16 ***
DRB 3.883e-02 6.157e-02 0.631 0.5285
TOV -2.475e-02 6.118e-02 -0.405 0.6859
STL -1.992e-01 9.181e-02 -2.169 0.0303 *
BLK -5.576e-02 8.782e-02 -0.635 0.5256
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 185.5 on 825 degrees of freedom
Multiple R-squared: 0.8992, Adjusted R-squared: 0.8981
F-statistic: 817.3 on 9 and 825 DF, p-value: < 2.2e-16# Sum of Squared Errors
PointsReg$residuals 1 2 3 4 5 6 7 8 9 10
38.5722713 142.8720040 -92.8957180 -8.3913473 -258.4705615 171.4608325 150.4081623 169.3811429 40.7756197 -75.3256614
11 12 13 14 15 16 17 18 19 20
444.9088743 94.3864704 -205.6809050 113.5969040 64.1993998 -76.5711999 249.4888007 28.0363236 329.4487991 96.3248342
21 22 23 24 25 26 27 28 29 30
349.2067913 -284.3765225 196.1611379 198.2493104 445.4100295 93.8946072 -316.2962802 -166.1909668 -5.8446359 211.2301997
31 32 33 34 35 36 37 38 39 40
155.7426615 -23.9248929 -77.9070033 218.9449693 164.1368602 -177.6479438 66.9205988 162.7892553 23.5961895 93.9839603
41 42 43 44 45 46 47 48 49 50
185.7015113 -50.2507837 -90.1181969 139.6866673 -231.1772776 111.2200135 185.9069491 210.6753018 -47.9420913 -257.8213675
51 52 53 54 55 56 57 58 59 60
225.7399197 70.4925628 432.6468031 187.4169561 -34.3947653 112.9305359 334.4717296 222.4169937 17.6755711 165.4512882
61 62 63 64 65 66 67 68 69 70
207.9970351 56.8277093 214.6051983 -23.0235142 341.7509536 -48.3807695 304.9203623 -36.7878762 -31.0357805 61.8847883
71 72 73 74 75 76 77 78 79 80
-153.0322403 121.7423324 -61.1581185 -47.9906548 -120.3599484 245.7621368 -264.3876116 161.1110819 87.3192423 426.2098591
81 82 83 84 85 86 87 88 89 90
-4.7790973 126.8613801 -97.5009340 329.9773912 -16.2338716 7.8513505 191.9280982 87.0090318 -142.5397602 -216.2264974
91 92 93 94 95 96 97 98 99 100
-199.6293933 71.0810742 257.3751407 -227.1203824 -61.4866232 71.3329444 -233.2637272 -34.7860771 84.9503466 108.6553543
101 102 103 104 105 106 107 108 109 110
-84.8168235 -90.0423121 341.2144522 52.8507112 47.8978397 181.0574099 160.7203318 237.0174702 314.9609845 51.9650831
111 112 113 114 115 116 117 118 119 120
300.2035074 -148.0931149 -13.3592416 -161.6184704 82.1172789 277.6080699 233.4334153 -225.7299932 69.0259972 37.3407430
121 122 123 124 125 126 127 128 129 130
18.2709681 121.8125335 217.9464858 -74.8210467 36.2611001 356.2366230 439.4127892 111.0266627 72.1377278 -6.1141295
131 132 133 134 135 136 137 138 139 140
331.6249450 -158.3642350 94.9048994 151.3242943 -284.7768411 -184.0287416 -103.9972773 54.1758237 139.3176593 125.3796164
141 142 143 144 145 146 147 148 149 150
-71.4407602 83.4742245 -131.6383234 -33.5752771 98.9460909 -59.8760139 -116.6711077 -110.4055752 290.8888709 38.5758792
151 152 153 154 155 156 157 158 159 160
-6.8265554 -284.8106013 149.5419209 -185.9270381 -13.5712897 -90.2301662 21.0080300 14.5295957 -346.4091267 -54.7198161
161 162 163 164 165 166 167 168 169 170
87.6823846 203.7903006 -30.7131853 -153.9699795 194.6791232 -357.4466727 133.8696823 -21.6271760 -220.4987354 -153.7269937
171 172 173 174 175 176 177 178 179 180
-383.7168614 212.2104185 -100.3118791 -30.5085767 -57.7910608 205.9463003 -124.1358862 -61.2169391 -93.9538879 -135.6180284
181 182 183 184 185 186 187 188 189 190
69.1245169 -435.5355494 -47.8153585 115.1051439 222.5411686 104.6516380 7.8335700 178.0759383 -185.3383423 122.0537263
191 192 193 194 195 196 197 198 199 200
-29.4729351 27.1344203 189.2078833 -429.5919872 57.2397301 -170.2701567 -14.0836520 21.0147294 49.6548689 -127.4633821
201 202 203 204 205 206 207 208 209 210
-87.4084020 -77.6940715 -155.2913076 8.4930328 -232.7210528 35.3384277 151.1394532 119.4563308 -416.3088878 134.8599211
211 212 213 214 215 216 217 218 219 220
33.3825347 48.4541197 -269.8021487 214.9045443 88.1318416 -24.0318730 188.2281015 -249.1537666 157.9872056 -146.6803006
221 222 223 224 225 226 227 228 229 230
72.9077663 31.1747176 337.2185582 69.7227713 -2.7440511 -55.2845827 -84.6255409 -151.4858821 234.7432200 -165.3909069
231 232 233 234 235 236 237 238 239 240
-172.9288404 386.6402387 34.4884530 -368.0387956 304.8349400 -173.0591889 168.9365987 -327.6509605 95.0370278 -75.5698743
241 242 243 244 245 246 247 248 249 250
-74.9702316 290.0371682 -21.8628806 72.5362398 -144.3565453 -44.7765529 -155.4752429 -114.0232742 82.8841506 -306.5759686
251 252 253 254 255 256 257 258 259 260
256.9630856 75.4312937 -108.9852622 -160.6985087 -1.0708625 389.4834173 48.4039145 -173.2376267 102.4859575 564.7127452
261 262 263 264 265 266 267 268 269 270
-135.6781765 435.5847710 -238.8763852 93.4120332 -346.4790813 84.2266238 124.2627684 157.9013909 90.9742388 -319.7738668
271 272 273 274 275 276 277 278 279 280
111.6330940 -136.0189613 179.6895020 -139.8481361 -60.2214721 21.1448936 -102.4930752 87.4261255 -2.2833983 -33.1839059
281 282 283 284 285 286 287 288 289 290
-313.4181662 -9.7903234 365.0041757 -170.9089658 -203.2682115 -59.0783300 344.4592952 -177.2934555 278.4424923 31.1539516
291 292 293 294 295 296 297 298 299 300
-19.4217087 146.9309508 49.6437593 323.4485389 47.1034178 3.9718411 -111.0589062 -40.0036081 187.1994351 134.5701059
301 302 303 304 305 306 307 308 309 310
-130.3795390 227.3624370 16.4481298 -91.2556101 215.9887998 70.7747666 50.5357552 -86.7616664 66.3006293 348.5847817
311 312 313 314 315 316 317 318 319 320
69.7928527 -144.9174008 48.2485248 262.5189212 -11.0182067 276.2567984 40.2609782 -235.0009787 91.8230888 -36.7029055
321 322 323 324 325 326 327 328 329 330
66.1862316 127.1446887 34.6306466 -89.1508242 -38.0350890 74.6959695 -24.6713632 -139.6322463 120.5781319 -256.3194253
331 332 333 334 335 336 337 338 339 340
35.3325803 -238.1863124 204.2701943 -231.4333870 -242.0178081 27.3589769 442.7697537 -90.3428846 -252.6536092 31.2460678
341 342 343 344 345 346 347 348 349 350
-24.0030042 -113.6697991 74.2030422 -63.3601223 13.1314540 -58.4065092 16.5093336 -26.4233092 -49.9197611 102.5295504
351 352 353 354 355 356 357 358 359 360
-276.0762358 -171.2605451 235.4118705 -295.3696087 -259.1915277 -209.8493128 -60.3803252 40.8738668 -162.3559100 -3.1584146
361 362 363 364 365 366 367 368 369 370
-252.6683460 -359.6072976 219.8480950 107.9177034 -228.4285961 77.5838841 77.6092501 176.9728823 21.0277939 225.7947949
371 372 373 374 375 376 377 378 379 380
90.6177409 -95.0387148 243.8004275 63.7765295 -135.7112041 127.9942080 208.5134149 -226.2507886 -27.4427262 215.5791874
381 382 383 384 385 386 387 388 389 390
70.0554598 -220.3324085 -252.5213694 -117.0224660 36.9146043 188.5932206 -12.6241171 24.1401960 39.4113815 130.8261623
391 392 393 394 395 396 397 398 399 400
194.8028770 140.1603242 100.4917058 367.8120506 -77.1138759 190.1907177 430.4505906 243.1092461 -220.7690501 -135.3500281
401 402 403 404 405 406 407 408 409 410
182.9169784 58.1314347 -10.3705665 134.0505987 333.4363828 110.9704334 37.1431301 188.8559358 -88.4445131 -165.3268990
411 412 413 414 415 416 417 418 419 420
148.8624801 -4.7914163 -114.6045335 -90.1562962 -65.1353805 9.9207366 -20.2393315 147.7163583 153.4474395 95.5889698
421 422 423 424 425 426 427 428 429 430
-329.6439893 323.3019593 345.3838501 -148.5288812 166.9648145 277.3541861 162.6383840 -78.9033000 -176.7932426 365.3962572
431 432 433 434 435 436 437 438 439 440
132.7242544 85.6582953 -19.3417988 95.4767236 -102.8199452 111.8183778 299.2808339 -124.0889739 -37.3805041 118.5055640
441 442 443 444 445 446 447 448 449 450
38.2173450 -122.8141423 -84.3447659 154.5643586 42.6355711 54.7178397 102.9846564 32.6861086 112.7943954 -163.3563028
451 452 453 454 455 456 457 458 459 460
150.7521084 217.5877806 -96.7133626 13.7243484 -33.1690450 -112.2550008 -15.7083565 -224.4198990 18.2593593 -393.0403979
461 462 463 464 465 466 467 468 469 470
49.2945267 52.0947949 43.2496203 -149.1223107 75.6856970 170.8878792 -257.6364448 51.6854016 11.8121415 -176.9048352
471 472 473 474 475 476 477 478 479 480
-149.5317630 -64.1990241 -71.3105611 -317.9190063 -65.8451642 97.8497015 -103.1692986 3.0848318 -104.6823532 -234.7534874
481 482 483 484 485 486 487 488 489 490
50.5295490 -75.4835788 -526.1468848 -393.9784124 -360.8366411 116.7193515 -321.3756304 -28.1090479 -508.3250405 -39.9958738
491 492 493 494 495 496 497 498 499 500
67.9854387 -97.4641720 -268.8364479 -26.0249946 188.1881640 -127.9366821 -86.3440758 133.8144538 29.4480488 -292.9821609
501 502 503 504 505 506 507 508 509 510
-124.9408024 101.3655240 -186.5181083 -63.5389375 -212.2015589 -323.1476886 -125.6610320 56.9083106 -39.0559074 -1.9339391
511 512 513 514 515 516 517 518 519 520
-319.9727619 -433.1243358 -431.1346590 -95.8909016 120.6089792 -409.7409083 -352.9341830 -527.3988939 110.6694955 -193.5043557
521 522 523 524 525 526 527 528 529 530
-92.6385367 -143.5858243 -189.7838251 172.1977457 -80.8020663 -342.9141699 124.8700974 -226.9524006 -73.5173798 -388.4868649
531 532 533 534 535 536 537 538 539 540
82.9536394 -96.7444961 -114.0835553 60.0566113 -332.3804023 -175.5276633 -338.7116370 -148.1422366 -45.2258816 -270.5159099
541 542 543 544 545 546 547 548 549 550
-159.8389177 -420.4637398 -133.0466450 183.8988039 -267.0297916 -5.2562902 -228.0471046 -11.6818058 -255.6786897 -7.7244412
551 552 553 554 555 556 557 558 559 560
-115.5357863 -298.4118693 -122.2961876 90.2924072 111.3930340 -245.4519945 -164.6445508 -29.3651223 -41.9781581 33.4260937
561 562 563 564 565 566 567 568 569 570
15.1663563 -29.4557965 44.0659204 247.9836928 -57.4318280 -238.6989443 -8.7249850 30.9454288 -343.6175905 -207.4418486
571 572 573 574 575 576 577 578 579 580
-306.4223254 157.4538406 -502.4785715 -126.1415717 48.8616098 143.9835801 -344.7694076 -116.5012114 -142.7898454 -127.9612584
581 582 583 584 585 586 587 588 589 590
-226.7659179 67.1679765 -94.0443422 -326.2414346 -84.6517620 4.5942017 -89.9757406 -97.0958454 -34.6927947 40.9701699
591 592 593 594 595 596 597 598 599 600
-88.3066869 126.5679875 -128.7529512 -166.6757304 -208.2444446 -105.4053449 -69.9961388 -104.0297252 -475.1678378 -290.6421238
601 602 603 604 605 606 607 608 609 610
195.4801727 -116.0865727 -136.0505114 -118.3811054 125.8235124 -145.2484421 -144.5655628 -435.6270621 -230.6201428 -112.7403208
611 612 613 614 615 616 617 618 619 620
-243.8883351 13.9124625 -392.1393056 -233.5727670 88.6125994 -203.7574893 -207.3393547 36.7326516 71.7237279 -110.6124268
621 622 623 624 625 626 627 628 629 630
-151.5524839 95.2365977 -227.3589026 -98.5962165 -210.8715081 -53.6787512 33.2644764 -380.2334407 -217.0512157 -135.7283167
631 632 633 634 635 636 637 638 639 640
208.5947156 -198.2473902 -147.6362401 -282.5390059 -55.4726214 3.0618526 -118.7764165 -15.9756605 1.5396468 2.2068206
641 642 643 644 645 646 647 648 649 650
-78.5559489 20.5194552 -376.9064555 -367.5790965 78.4730898 88.0528050 -178.9859105 283.6342652 18.0639226 1.4275017
651 652 653 654 655 656 657 658 659 660
-22.1910648 334.1581029 -44.6704981 -166.2133428 -112.8182784 175.7515262 60.9355144 -331.2815975 -175.1322112 34.9727118
661 662 663 664 665 666 667 668 669 670
430.8913232 -260.7815266 -99.5985786 -306.5331420 -144.2463445 -71.9561309 40.4095734 -9.9170555 9.7141807 72.8730721
671 672 673 674 675 676 677 678 679 680
-61.2840291 -51.9936086 -452.8596863 -81.9437393 69.2906290 254.7395766 -22.9459505 215.8931262 -16.9537293 -107.9068394
681 682 683 684 685 686 687 688 689 690
202.3017464 287.5765859 180.7757394 -305.5932029 56.2240459 4.5320328 -44.0648823 -278.0391307 -13.3280981 -112.7276708
691 692 693 694 695 696 697 698 699 700
422.1750569 -131.0023955 51.4971549 -86.9745423 28.8396258 -107.9302127 -55.3683153 -16.7225380 60.3453436 3.3520616
701 702 703 704 705 706 707 708 709 710
140.9429255 -17.9219329 -296.8381962 136.2394242 106.7244264 168.2861008 26.7860625 339.8954937 187.8922770 -202.6392008
711 712 713 714 715 716 717 718 719 720
148.7995083 268.8921528 0.6597544 -119.2916116 -23.0549542 -28.1758366 206.7679556 -138.5838793 -210.7824121 -29.6626073
721 722 723 724 725 726 727 728 729 730
210.3268820 -212.8798945 88.1962039 129.1032851 11.9530477 -166.3796048 -372.3297260 67.5130804 1.7122210 -179.0745146
731 732 733 734 735 736 737 738 739 740
-28.4404659 151.2765881 -425.3360446 344.3671825 -47.2592021 136.9801455 63.4427397 203.2044716 27.7908779 251.4279736
741 742 743 744 745 746 747 748 749 750
84.5817590 -155.6577645 150.3787715 138.7921016 198.4699948 101.8590582 345.8144412 35.1336113 169.1641149 354.9998851
751 752 753 754 755 756 757 758 759 760
251.7571721 47.8412497 77.9677328 66.2799291 216.7990909 155.1577399 -131.2437994 230.2449071 218.7156645 116.0349148
761 762 763 764 765 766 767 768 769 770
-78.5937100 -23.1321308 99.7713990 280.2227149 40.8527845 19.4188914 72.9388151 120.7266716 439.1035137 456.0100354
771 772 773 774 775 776 777 778 779 780
47.3239201 186.1096824 31.7505381 -54.0912550 73.0035369 234.4761589 27.9146721 -21.6493313 -75.0167664 148.4251726
781 782 783 784 785 786 787 788 789 790
106.3308316 76.0196340 37.3592068 56.5562663 -41.8917486 -200.7598142 -55.5159544 109.1518868 321.3239680 219.8866600
791 792 793 794 795 796 797 798 799 800
-73.6034103 3.1961900 -171.1408177 190.8979178 101.1845265 253.1734885 263.7840087 199.5924560 463.8379676 219.1540922
801 802 803 804 805 806 807 808 809 810
52.3032317 140.7498122 195.8267787 -55.3103142 153.8564182 61.1275837 92.8158603 -108.8302808 73.3423661 -360.6001538
811 812 813 814 815 816 817 818 819 820
134.1518035 73.3435884 141.0017271 272.8259956 -33.1611977 19.7818711 -149.9998706 190.0065593 261.3992751 308.7602526
821 822 823 824 825 826 827 828 829 830
-135.4172110 108.2677094 -171.3410196 102.4439076 156.0829202 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 SSE = sum(PointsReg$residuals^2)
SSE[1] 28394314# Root mean squared error
RMSE = sqrt(SSE/nrow(NBA))
RMSE[1] 184.4049# Average number of points in a season
mean(NBA$PTS)[1] 8370.24# Remove insignifcant variables
summary(PointsReg)
Call:
lm(formula = PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + TOV +
STL + BLK, data = NBA)
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-16PointsReg4 = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + STL, data=NBA)
summary(PointsReg4)
Call:
lm(formula = PTS ~ X2PA + X3PA + FTA + AST + ORB + STL, data = NBA)
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$residuals^2)
RMSE_4 = sqrt(SSE_4/nrow(NBA))
SSE_4[1] 28421465RMSE_4[1] 184.493# VIDEO 4
# Read in test set
NBA_test = read.csv("NBA_test.csv")# Make predictions on test set
PointsPredictions = predict(PointsReg4, newdata=NBA_test)# Compute out-of-sample R^2
SSE = sum((PointsPredictions - NBA_test$PTS)^2)
SST = sum((mean(NBA$PTS) - NBA_test$PTS)^2)
R2 = 1 - SSE/SST
R2[1] 0.8127142# Compute the RMSE
RMSE = sqrt(SSE/nrow(NBA_test))
RMSE [1] 196.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