Playing Moneyball in the NBA

Module 4 Activities

In-Class Activity 12

Bosco M Morales

Special Topics in Data Analytics

Spring 2025

# Get working directory
getwd()

[1] "/cloud/project"

# 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 ...

View(nba)

A. How many observations do we have in the training dataset?

There are 835 observations in the training data set.

# From Video #2
# How many wins to make it to the playoffs?
View(table(nba$W,nba$Playoffs))

# From Video #2
# How many wins to make it to 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

B. Is there any chance that a team winning 38 games can make it to the playoffs? Why?

Yes. There is a chance for a team winning 38 games to make to the playoffs According to our data a team who has won 38 games made it to the playoffs 7 out of 15 times. Just a bit less than half the time.

C. What is the number of wins that can guarantee for any team a presence in the playoffs based on historical data?

Given historical data, winning at least 40 games could guarantee for any team making it to the playoffs

D. Can you determine (visually) if there is any relationship between the points difference (PTSdiff) and the number of wins (W)?Explain.

Yes, there is a linear relationship. Please see scatter plot below

# Compute Points Difference 
nba$PTSdiff = nba$PTS - nba$oppPTS

# Check for linear relationship
plot(nba$PTSdiff, nba$W)

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

41 + 0.03259 (diffPTS)

E. 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?

Yes, because the p-value for PTSdiff is reported as < 2e-16, which is much smaller than 0.05. The predictor variable points difference (PTSdiff) is statistically significant at the 5% significance level. Also, the triple asterisks next to the p-value also indicate high statistical significance.

# 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

F. 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?

According to the model ran for this activity (PointsReg) the number of blocks (BLK) is not significant given that p > 0.05. See model results above.

summary(nba$PTS)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   6901    7934    8312    8370    8784   10371 

G. What has been the maximum number of points in a season?

The maximum number of points in a season is 10371

# Residuals
PointsReg$residuals 

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

RMSE

[1] 184.4049

H. What is the meaning of the RMSE(Root mean squared error) in the PointsReg model? Are you satisfied with this value?

Meaning of RMSE (184.4): The model’s prediction of team wins is, on average, based on a season-long point differential error of 184 points, or about 2.2 points per game.

Are we satisfied Yes — this level of error is quite reasonable and suggests your model is doing a good job.

# Average Number of Points in a Season
mean(nba$PTS)

# Remove Insignificant Variables
summary(PointsReg)

# Linear Regression model two for wins
PointsRegTwo = lm (PTS ~ X2PA + X3PA + FTA +AST + ORB + DRB + STL + BLK, data=nba)

summary(PointsRegTwo)

# Linear Regression model three for wins
PointsRegThree = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + STL+ BLK, data=nba)

summary(PointsRegThree)

# Linear Regression model four for wins
PointsRegFour = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + STL, data=nba)

summary(PointsRegFour)

# Compute SSE and RMSE for Model Four
SSE_4 = sum(PointsRegFour$residuals^2)

RMSE_4 = sqrt(SSE_4/nrow(nba))

# Sum of Squared Error for Model 4
SSE_4

[1] 28421465

# RMSE for Model 4
RMSE_4

[1] 184.493

Video 4

# Read in Test data
nba_test = read.csv("NBA_test.csv")

# Make predictions on test set
PointsPredictions = predict(PointsRegFour, newdata = nba_test)

# Compute out-of-sample R^2
SSE_test = sum ((PointsPredictions - nba_test$PTS)^2)

SST = sum((mean(nba$PTS) - nba_test$PTS)^2)

R2 = 1 - (SSE_test / SST)

R2

[1] 0.8127142

# Compute the RMSE

RMSE_test = sqrt( SSE_test /nrow(nba_test))

RMSE_test

[1] 196.3723

I. How well did your predictions work on the testing dataset? Report the new R2 and RMSE.

The predictions on the testing dataset worked reasonably well but were less accurate than on the training data. The Root Mean Squared Error (RMSE) was approximately 196.37, meaning that the predicted number of wins based on the season-long point differential was off by about 196 points across the season. When broken down across 82 games, this equates to an average error of approximately 2.4 points per game (196.37 ÷ 82), which is still within an acceptable range in sports analytics.

The R-squared (R²) value of 0.8127 indicates that the model explains about 81.27% of the variability in season wins. While this is lower than the training R² of 94.23%, it still shows a strong predictive relationship and suggests that the model generalizes fairly well to new data — though with slightly less precision than it had on the training set.

In-Class 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.

# Given the linear equation.. we need to solve for 

# 49 = 41 + 0.03259 (diffPTS)

# diffPTS = (-41 + 49) / 0.03259

diffPTS_49 = (-41 + 49) / 0.0326

diffPTS_49

[1] 245.3988

The expected points difference for a team to make it to the postseason given 49 wins is 245.

In-Class Activity 14

Consider the following vectors representing the number of three-pointers made and attempted by a basketball player in five games: Three-Pointers Made: c(4, 5, 3, 6, 7) Three-Pointers Attempted: c(9, 10, 8, 11, 12) Calculate the three-point shooting percentage for each game and select the correct average three-point shooting percentage for the five games.

three_pointers_made <- c(4,5,3,6,7)

three_pointers_attempted <- c(9,10,8,11,12)

# Calculate the shooting percentage for each game
shooting_percentage <- (three_pointers_made / three_pointers_attempted) * 100

# Print individual game percentages
print(round(shooting_percentage),2)

[1] 44 50 38 55 58

mean(round(shooting_percentage, 2))

[1] 48.964

The correct average three-point shooting percentage for the five games is 48.964%