CAP4936 In Class Activities 12, 13, 14
getwd()## [1] "/cloud/project"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 ...# View(NBA)
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# Activity 12
# A) 835 observations of 20 variables
# B) Yes, because a team winning 38 game made it to the playoffs 8 times and did not make it 7 times.
# C) 49 to 72 wins can guarantee for any team a presence in the playoffs based on historical data.
# D) There is a positive relationship between the points difference and the number of wins. As the points #difference increases, the number of wins increases. (See Scatterplot below).#scatterplot(NBA$W,NBA$Playoffs)# Compute Points Difference
NBA$PTSdiff = NBA$PTS - NBA$oppPTS plot(NBA$PTSdiff, NBA$W)
# Activity 12
# E) The predictor variable points difference is significant at a 5% significance level because p-value #according to the regression model below is at p-value: < 2.2e-16, which is significantly lower than 5%.
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-16lm(formula = W ~ PTSdiff, data = NBA)##
## Call:
## lm(formula = W ~ PTSdiff, data = NBA)
##
## Coefficients:
## (Intercept) PTSdiff
## 41.00000 0.03259# Linear regression model for points scored
# Activity 12
# F) According to to model run below where Block is one of the features. It appears Block is not significant at #5% significance level.
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-16summary(NBA$PTS)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 6901 7934 8312 8370 8784 10371# Activity 12
# G) The maximum number of points in a season is 10371.# Sum of Squarred Errors
PointsReg$residuals## 1 2 3 4 5 6
## 38.5722713 142.8720040 -92.8957180 -8.3913473 -258.4705615 171.4608325
## 7 8 9 10 11 12
## 150.4081623 169.3811429 40.7756197 -75.3256614 444.9088743 94.3864704
## 13 14 15 16 17 18
## -205.6809050 113.5969040 64.1993998 -76.5711999 249.4888007 28.0363236
## 19 20 21 22 23 24
## 329.4487991 96.3248342 349.2067913 -284.3765225 196.1611379 198.2493104
## 25 26 27 28 29 30
## 445.4100295 93.8946072 -316.2962802 -166.1909668 -5.8446359 211.2301997
## 31 32 33 34 35 36
## 155.7426615 -23.9248929 -77.9070033 218.9449693 164.1368602 -177.6479438
## 37 38 39 40 41 42
## 66.9205988 162.7892553 23.5961895 93.9839603 185.7015113 -50.2507837
## 43 44 45 46 47 48
## -90.1181969 139.6866673 -231.1772776 111.2200135 185.9069491 210.6753018
## 49 50 51 52 53 54
## -47.9420913 -257.8213675 225.7399197 70.4925628 432.6468031 187.4169561
## 55 56 57 58 59 60
## -34.3947653 112.9305359 334.4717296 222.4169937 17.6755711 165.4512882
## 61 62 63 64 65 66
## 207.9970351 56.8277093 214.6051983 -23.0235142 341.7509536 -48.3807695
## 67 68 69 70 71 72
## 304.9203623 -36.7878762 -31.0357805 61.8847883 -153.0322403 121.7423324
## 73 74 75 76 77 78
## -61.1581185 -47.9906548 -120.3599484 245.7621368 -264.3876116 161.1110819
## 79 80 81 82 83 84
## 87.3192423 426.2098591 -4.7790973 126.8613801 -97.5009340 329.9773912
## 85 86 87 88 89 90
## -16.2338716 7.8513505 191.9280982 87.0090318 -142.5397602 -216.2264974
## 91 92 93 94 95 96
## -199.6293933 71.0810742 257.3751407 -227.1203824 -61.4866232 71.3329444
## 97 98 99 100 101 102
## -233.2637272 -34.7860771 84.9503466 108.6553543 -84.8168235 -90.0423121
## 103 104 105 106 107 108
## 341.2144522 52.8507112 47.8978397 181.0574099 160.7203318 237.0174702
## 109 110 111 112 113 114
## 314.9609845 51.9650831 300.2035074 -148.0931149 -13.3592416 -161.6184704
## 115 116 117 118 119 120
## 82.1172789 277.6080699 233.4334153 -225.7299932 69.0259972 37.3407430
## 121 122 123 124 125 126
## 18.2709681 121.8125335 217.9464858 -74.8210467 36.2611001 356.2366230
## 127 128 129 130 131 132
## 439.4127892 111.0266627 72.1377278 -6.1141295 331.6249450 -158.3642350
## 133 134 135 136 137 138
## 94.9048994 151.3242943 -284.7768411 -184.0287416 -103.9972773 54.1758237
## 139 140 141 142 143 144
## 139.3176593 125.3796164 -71.4407602 83.4742245 -131.6383234 -33.5752771
## 145 146 147 148 149 150
## 98.9460909 -59.8760139 -116.6711077 -110.4055752 290.8888709 38.5758792
## 151 152 153 154 155 156
## -6.8265554 -284.8106013 149.5419209 -185.9270381 -13.5712897 -90.2301662
## 157 158 159 160 161 162
## 21.0080300 14.5295957 -346.4091267 -54.7198161 87.6823846 203.7903006
## 163 164 165 166 167 168
## -30.7131853 -153.9699795 194.6791232 -357.4466727 133.8696823 -21.6271760
## 169 170 171 172 173 174
## -220.4987354 -153.7269937 -383.7168614 212.2104185 -100.3118791 -30.5085767
## 175 176 177 178 179 180
## -57.7910608 205.9463003 -124.1358862 -61.2169391 -93.9538879 -135.6180284
## 181 182 183 184 185 186
## 69.1245169 -435.5355494 -47.8153585 115.1051439 222.5411686 104.6516380
## 187 188 189 190 191 192
## 7.8335700 178.0759383 -185.3383423 122.0537263 -29.4729351 27.1344203
## 193 194 195 196 197 198
## 189.2078833 -429.5919872 57.2397301 -170.2701567 -14.0836520 21.0147294
## 199 200 201 202 203 204
## 49.6548689 -127.4633821 -87.4084020 -77.6940715 -155.2913076 8.4930328
## 205 206 207 208 209 210
## -232.7210528 35.3384277 151.1394532 119.4563308 -416.3088878 134.8599211
## 211 212 213 214 215 216
## 33.3825347 48.4541197 -269.8021487 214.9045443 88.1318416 -24.0318730
## 217 218 219 220 221 222
## 188.2281015 -249.1537666 157.9872056 -146.6803006 72.9077663 31.1747176
## 223 224 225 226 227 228
## 337.2185582 69.7227713 -2.7440511 -55.2845827 -84.6255409 -151.4858821
## 229 230 231 232 233 234
## 234.7432200 -165.3909069 -172.9288404 386.6402387 34.4884530 -368.0387956
## 235 236 237 238 239 240
## 304.8349400 -173.0591889 168.9365987 -327.6509605 95.0370278 -75.5698743
## 241 242 243 244 245 246
## -74.9702316 290.0371682 -21.8628806 72.5362398 -144.3565453 -44.7765529
## 247 248 249 250 251 252
## -155.4752429 -114.0232742 82.8841506 -306.5759686 256.9630856 75.4312937
## 253 254 255 256 257 258
## -108.9852622 -160.6985087 -1.0708625 389.4834173 48.4039145 -173.2376267
## 259 260 261 262 263 264
## 102.4859575 564.7127452 -135.6781765 435.5847710 -238.8763852 93.4120332
## 265 266 267 268 269 270
## -346.4790813 84.2266238 124.2627684 157.9013909 90.9742388 -319.7738668
## 271 272 273 274 275 276
## 111.6330940 -136.0189613 179.6895020 -139.8481361 -60.2214721 21.1448936
## 277 278 279 280 281 282
## -102.4930752 87.4261255 -2.2833983 -33.1839059 -313.4181662 -9.7903234
## 283 284 285 286 287 288
## 365.0041757 -170.9089658 -203.2682115 -59.0783300 344.4592952 -177.2934555
## 289 290 291 292 293 294
## 278.4424923 31.1539516 -19.4217087 146.9309508 49.6437593 323.4485389
## 295 296 297 298 299 300
## 47.1034178 3.9718411 -111.0589062 -40.0036081 187.1994351 134.5701059
## 301 302 303 304 305 306
## -130.3795390 227.3624370 16.4481298 -91.2556101 215.9887998 70.7747666
## 307 308 309 310 311 312
## 50.5357552 -86.7616664 66.3006293 348.5847817 69.7928527 -144.9174008
## 313 314 315 316 317 318
## 48.2485248 262.5189212 -11.0182067 276.2567984 40.2609782 -235.0009787
## 319 320 321 322 323 324
## 91.8230888 -36.7029055 66.1862316 127.1446887 34.6306466 -89.1508242
## 325 326 327 328 329 330
## -38.0350890 74.6959695 -24.6713632 -139.6322463 120.5781319 -256.3194253
## 331 332 333 334 335 336
## 35.3325803 -238.1863124 204.2701943 -231.4333870 -242.0178081 27.3589769
## 337 338 339 340 341 342
## 442.7697537 -90.3428846 -252.6536092 31.2460678 -24.0030042 -113.6697991
## 343 344 345 346 347 348
## 74.2030422 -63.3601223 13.1314540 -58.4065092 16.5093336 -26.4233092
## 349 350 351 352 353 354
## -49.9197611 102.5295504 -276.0762358 -171.2605451 235.4118705 -295.3696087
## 355 356 357 358 359 360
## -259.1915277 -209.8493128 -60.3803252 40.8738668 -162.3559100 -3.1584146
## 361 362 363 364 365 366
## -252.6683460 -359.6072976 219.8480950 107.9177034 -228.4285961 77.5838841
## 367 368 369 370 371 372
## 77.6092501 176.9728823 21.0277939 225.7947949 90.6177409 -95.0387148
## 373 374 375 376 377 378
## 243.8004275 63.7765295 -135.7112041 127.9942080 208.5134149 -226.2507886
## 379 380 381 382 383 384
## -27.4427262 215.5791874 70.0554598 -220.3324085 -252.5213694 -117.0224660
## 385 386 387 388 389 390
## 36.9146043 188.5932206 -12.6241171 24.1401960 39.4113815 130.8261623
## 391 392 393 394 395 396
## 194.8028770 140.1603242 100.4917058 367.8120506 -77.1138759 190.1907177
## 397 398 399 400 401 402
## 430.4505906 243.1092461 -220.7690501 -135.3500281 182.9169784 58.1314347
## 403 404 405 406 407 408
## -10.3705665 134.0505987 333.4363828 110.9704334 37.1431301 188.8559358
## 409 410 411 412 413 414
## -88.4445131 -165.3268990 148.8624801 -4.7914163 -114.6045335 -90.1562962
## 415 416 417 418 419 420
## -65.1353805 9.9207366 -20.2393315 147.7163583 153.4474395 95.5889698
## 421 422 423 424 425 426
## -329.6439893 323.3019593 345.3838501 -148.5288812 166.9648145 277.3541861
## 427 428 429 430 431 432
## 162.6383840 -78.9033000 -176.7932426 365.3962572 132.7242544 85.6582953
## 433 434 435 436 437 438
## -19.3417988 95.4767236 -102.8199452 111.8183778 299.2808339 -124.0889739
## 439 440 441 442 443 444
## -37.3805041 118.5055640 38.2173450 -122.8141423 -84.3447659 154.5643586
## 445 446 447 448 449 450
## 42.6355711 54.7178397 102.9846564 32.6861086 112.7943954 -163.3563028
## 451 452 453 454 455 456
## 150.7521084 217.5877806 -96.7133626 13.7243484 -33.1690450 -112.2550008
## 457 458 459 460 461 462
## -15.7083565 -224.4198990 18.2593593 -393.0403979 49.2945267 52.0947949
## 463 464 465 466 467 468
## 43.2496203 -149.1223107 75.6856970 170.8878792 -257.6364448 51.6854016
## 469 470 471 472 473 474
## 11.8121415 -176.9048352 -149.5317630 -64.1990241 -71.3105611 -317.9190063
## 475 476 477 478 479 480
## -65.8451642 97.8497015 -103.1692986 3.0848318 -104.6823532 -234.7534874
## 481 482 483 484 485 486
## 50.5295490 -75.4835788 -526.1468848 -393.9784124 -360.8366411 116.7193515
## 487 488 489 490 491 492
## -321.3756304 -28.1090479 -508.3250405 -39.9958738 67.9854387 -97.4641720
## 493 494 495 496 497 498
## -268.8364479 -26.0249946 188.1881640 -127.9366821 -86.3440758 133.8144538
## 499 500 501 502 503 504
## 29.4480488 -292.9821609 -124.9408024 101.3655240 -186.5181083 -63.5389375
## 505 506 507 508 509 510
## -212.2015589 -323.1476886 -125.6610320 56.9083106 -39.0559074 -1.9339391
## 511 512 513 514 515 516
## -319.9727619 -433.1243358 -431.1346590 -95.8909016 120.6089792 -409.7409083
## 517 518 519 520 521 522
## -352.9341830 -527.3988939 110.6694955 -193.5043557 -92.6385367 -143.5858243
## 523 524 525 526 527 528
## -189.7838251 172.1977457 -80.8020663 -342.9141699 124.8700974 -226.9524006
## 529 530 531 532 533 534
## -73.5173798 -388.4868649 82.9536394 -96.7444961 -114.0835553 60.0566113
## 535 536 537 538 539 540
## -332.3804023 -175.5276633 -338.7116370 -148.1422366 -45.2258816 -270.5159099
## 541 542 543 544 545 546
## -159.8389177 -420.4637398 -133.0466450 183.8988039 -267.0297916 -5.2562902
## 547 548 549 550 551 552
## -228.0471046 -11.6818058 -255.6786897 -7.7244412 -115.5357863 -298.4118693
## 553 554 555 556 557 558
## -122.2961876 90.2924072 111.3930340 -245.4519945 -164.6445508 -29.3651223
## 559 560 561 562 563 564
## -41.9781581 33.4260937 15.1663563 -29.4557965 44.0659204 247.9836928
## 565 566 567 568 569 570
## -57.4318280 -238.6989443 -8.7249850 30.9454288 -343.6175905 -207.4418486
## 571 572 573 574 575 576
## -306.4223254 157.4538406 -502.4785715 -126.1415717 48.8616098 143.9835801
## 577 578 579 580 581 582
## -344.7694076 -116.5012114 -142.7898454 -127.9612584 -226.7659179 67.1679765
## 583 584 585 586 587 588
## -94.0443422 -326.2414346 -84.6517620 4.5942017 -89.9757406 -97.0958454
## 589 590 591 592 593 594
## -34.6927947 40.9701699 -88.3066869 126.5679875 -128.7529512 -166.6757304
## 595 596 597 598 599 600
## -208.2444446 -105.4053449 -69.9961388 -104.0297252 -475.1678378 -290.6421238
## 601 602 603 604 605 606
## 195.4801727 -116.0865727 -136.0505114 -118.3811054 125.8235124 -145.2484421
## 607 608 609 610 611 612
## -144.5655628 -435.6270621 -230.6201428 -112.7403208 -243.8883351 13.9124625
## 613 614 615 616 617 618
## -392.1393056 -233.5727670 88.6125994 -203.7574893 -207.3393547 36.7326516
## 619 620 621 622 623 624
## 71.7237279 -110.6124268 -151.5524839 95.2365977 -227.3589026 -98.5962165
## 625 626 627 628 629 630
## -210.8715081 -53.6787512 33.2644764 -380.2334407 -217.0512157 -135.7283167
## 631 632 633 634 635 636
## 208.5947156 -198.2473902 -147.6362401 -282.5390059 -55.4726214 3.0618526
## 637 638 639 640 641 642
## -118.7764165 -15.9756605 1.5396468 2.2068206 -78.5559489 20.5194552
## 643 644 645 646 647 648
## -376.9064555 -367.5790965 78.4730898 88.0528050 -178.9859105 283.6342652
## 649 650 651 652 653 654
## 18.0639226 1.4275017 -22.1910648 334.1581029 -44.6704981 -166.2133428
## 655 656 657 658 659 660
## -112.8182784 175.7515262 60.9355144 -331.2815975 -175.1322112 34.9727118
## 661 662 663 664 665 666
## 430.8913232 -260.7815266 -99.5985786 -306.5331420 -144.2463445 -71.9561309
## 667 668 669 670 671 672
## 40.4095734 -9.9170555 9.7141807 72.8730721 -61.2840291 -51.9936086
## 673 674 675 676 677 678
## -452.8596863 -81.9437393 69.2906290 254.7395766 -22.9459505 215.8931262
## 679 680 681 682 683 684
## -16.9537293 -107.9068394 202.3017464 287.5765859 180.7757394 -305.5932029
## 685 686 687 688 689 690
## 56.2240459 4.5320328 -44.0648823 -278.0391307 -13.3280981 -112.7276708
## 691 692 693 694 695 696
## 422.1750569 -131.0023955 51.4971549 -86.9745423 28.8396258 -107.9302127
## 697 698 699 700 701 702
## -55.3683153 -16.7225380 60.3453436 3.3520616 140.9429255 -17.9219329
## 703 704 705 706 707 708
## -296.8381962 136.2394242 106.7244264 168.2861008 26.7860625 339.8954937
## 709 710 711 712 713 714
## 187.8922770 -202.6392008 148.7995083 268.8921528 0.6597544 -119.2916116
## 715 716 717 718 719 720
## -23.0549542 -28.1758366 206.7679556 -138.5838793 -210.7824121 -29.6626073
## 721 722 723 724 725 726
## 210.3268820 -212.8798945 88.1962039 129.1032851 11.9530477 -166.3796048
## 727 728 729 730 731 732
## -372.3297260 67.5130804 1.7122210 -179.0745146 -28.4404659 151.2765881
## 733 734 735 736 737 738
## -425.3360446 344.3671825 -47.2592021 136.9801455 63.4427397 203.2044716
## 739 740 741 742 743 744
## 27.7908779 251.4279736 84.5817590 -155.6577645 150.3787715 138.7921016
## 745 746 747 748 749 750
## 198.4699948 101.8590582 345.8144412 35.1336113 169.1641149 354.9998851
## 751 752 753 754 755 756
## 251.7571721 47.8412497 77.9677328 66.2799291 216.7990909 155.1577399
## 757 758 759 760 761 762
## -131.2437994 230.2449071 218.7156645 116.0349148 -78.5937100 -23.1321308
## 763 764 765 766 767 768
## 99.7713990 280.2227149 40.8527845 19.4188914 72.9388151 120.7266716
## 769 770 771 772 773 774
## 439.1035137 456.0100354 47.3239201 186.1096824 31.7505381 -54.0912550
## 775 776 777 778 779 780
## 73.0035369 234.4761589 27.9146721 -21.6493313 -75.0167664 148.4251726
## 781 782 783 784 785 786
## 106.3308316 76.0196340 37.3592068 56.5562663 -41.8917486 -200.7598142
## 787 788 789 790 791 792
## -55.5159544 109.1518868 321.3239680 219.8866600 -73.6034103 3.1961900
## 793 794 795 796 797 798
## -171.1408177 190.8979178 101.1845265 253.1734885 263.7840087 199.5924560
## 799 800 801 802 803 804
## 463.8379676 219.1540922 52.3032317 140.7498122 195.8267787 -55.3103142
## 805 806 807 808 809 810
## 153.8564182 61.1275837 92.8158603 -108.8302808 73.3423661 -360.6001538
## 811 812 813 814 815 816
## 134.1518035 73.3435884 141.0017271 272.8259956 -33.1611977 19.7818711
## 817 818 819 820 821 822
## -149.9998706 190.0065593 261.3992751 308.7602526 -135.4172110 108.2677094
## 823 824 825 826 827 828
## -171.3410196 102.4439076 156.0829202 210.0521687 109.4908936 -20.5354175
## 829 830 831 832 833 834
## 59.2845716 175.9235274 30.6531825 262.6728011 70.0671862 -17.5789419
## 835
## -8.3393046PointsReg2 = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + STL + BLK, data=NBA)
summary(PointsReg2)##
## Call:
## lm(formula = PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + STL +
## BLK, data = NBA)
##
## 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=NBA)
summary(PointsReg3)##
## Call:
## lm(formula = PTS ~ X2PA + X3PA + FTA + AST + ORB + STL + BLK,
## data = NBA)
##
## 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=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# Read in test set
NBA_test = read.csv("NBA_test.csv")# Make predicitions on test set
PointsPredictions = predict(PointsReg4, newdata=NBA_test)# Compute out-of-sample R^2
SSE = sum((PointsPredictions - NBA_test$PTS)^2)
SSE## [1] 1079739SST = sum((mean(NBA$PTS) - NBA_test$PTS)^2)
SST## [1] 5765192R2 = 1 - SSE/SST
R2## [1] 0.8127142Activity 12 A) 835 observations of 20 variables B) Yes, because a team winning 38 game made it to the playoffs 8 times and did not make it 7 times. C) 49 to 72 wins can guarantee for any team a presence in the playoffs based on historical data. D) There is a positive relationship between the points difference and the number of wins. As the points difference increases, the number of wins increases. (See Scatterplot below). E) The predictor variable points difference is significant at a 5% significance level because p-value according to the regression model below is at p-value: < 2.2e-16, which is significantly lower than 5%. F) According to to model run below where Block is one of the features. It appears Block is not significant at 5% significance level. G) The maximum number of points in a season is 10371. H) RMSE(Root mean squared error) in the PointsReg model tells us how spread the data is. It measures the average difference between the predicted and actual values. The value is not that large, which means it is satisfying. I) Our predicitions work well on the dataset. The new R2 and RSME are respectively 0.8127142 and 1079739.
# Compute the RMSE
RMSE = sqrt(SSE/nrow(NBA_test))
RMSE## [1] 196.3723# ***Activity 12***
# H) RMSE(Root mean squared error) in the PointsReg model tells us how spread the data is. It measures the #average difference between the predicted and actual values. The value is not that large, which means it is #satisfying.# ***Activity 13***
# WinsReg = lm(W ~ PTSdiff, data=NBA)
# 49=41+0.0326*(x)
# The expected points difference is 245.3988 for a team to make it to the postseason.
x_1=(49-41)/0.0326
x_1## [1] 245.3988Activity 14
Threepts_made<-c(4, 5, 3, 6, 7)
Threepts_attmpt<-c(9, 10, 8, 11, 12)
Three_pts_pct = Threepts_made/Threepts_attmpt
Three_pts_pct## [1] 0.4444444 0.5000000 0.3750000 0.5454545 0.5833333# average for each game
mean(Three_pts_pct)## [1] 0.4896465The average three-point shooting percentage for the five games is 0.4896465.