homework 9 cleaning
Your Name Here
2026-07-25
Data Description
The nba_players data set has the overall advanced
metrics recorded for 566 players in the NBA for the 2023 - 2024 regular
season (no playoffs).
One of the advanced metrics is efficient, which is a
statistic that attempts to measure how efficient a player is while on
the basketball court. We’ll be using some of basketball-reference.com’s
other advanced statistics to predict how efficient a player is.
tibble(nba_players)## # A tibble: 396 × 17
## age team position games_played games_started efficient shooting three_pt
## <int> <chr> <chr> <int> <int> <dbl> <dbl> <dbl>
## 1 31 2TM SF 84 42 13.3 57.8 0.668
## 2 27 SAC C 82 82 23.2 63.7 0.081
## 3 27 BRK SF 82 82 14.9 56 0.457
## 4 25 LAL SG 82 57 15.5 61.3 0.447
## 5 21 HOU SG 82 82 14.7 54.1 0.454
## 6 21 OKC C 82 82 20.4 63.2 0.366
## 7 31 SAC PF 82 82 11.9 61.1 0.526
## 8 28 MIL PF 82 4 17.5 58.1 0.268
## 9 31 NOP C 82 82 19.8 61.9 0.167
## 10 25 MIN SG 82 20 10.9 57.8 0.623
## # ℹ 386 more rows
## # ℹ 9 more variables: free <dbl>, off_reb <dbl>, def_reb <dbl>, tot_reb <dbl>,
## # assist <dbl>, steal <dbl>, block <dbl>, turnover <dbl>, usage <dbl>The relevant columns are:
age: the age of the player at the start of the seasonshooting: A measure of shot accuracy that combines 1-, 2-, and 3-point attempts and accounts for the difficulty of said shotsthree_pt: The percentage of field goal attempts that are three point shotsfree: Number of free throw attempts per field goal attemptoff_reb: Percentage of offensive rebounds by the player when the player was eligible for the rebounddef_reb: Percentage of defensive rebounds by the player when the player was eligible for the reboundtot_reb: Percentage of total rebounds by the player when the player was eligible for the reboundassist: Percentage of teammate’s field goals the player assisted when playingsteal: Percentage of opponents’ possessions ended by the player stealing the ball when said player was playingblock: Percentage of two-point field goal attempts blocked by the player while they were playingturnover: Number of turnovers committed per 100 playsusage: Percentage of plays where the player was involved
Question 1) Exploratory data analysis
Question 1a) Scatter plots of efficiency by the relevant columns
Create a set of scatterplots with efficiency on
the y-axis and the other numeric columns on the respective
x-axes.
nba_players |>
# Placing the numeric predictors into the same column named value and predictors
pivot_longer(
cols = c(age, shooting:usage),
names_to = "stat",
values_to = "value"
) |>
mutate(stat = as_factor(stat)) |>
# Creating the set of scatterplots
ggplot(
mapping = aes(
x = value,
y = efficient
)
) +
geom_point(alpha = 0.5) +
geom_smooth(
method = "loess",
se = F,
formula = y ~ x
) +
# Separating the plots with different x-axes for each statistic
facet_wrap(
facets = vars(stat),
scales = "free_x"
) +
labs(
x = NULL,
y = 'Player Efficiency'
)
Which two variables appear to have the strongest association with efficiency?
Any response with shooting, free, usage, assist, def / tot_reb is correct
Which two variables appear to have the weakest association with efficiency? Any response with steal, off_reb, turnover, or age is correct
Question 1b) Why can’t we use position to predict
efficient using k-nearest neighbors?
Question 2) Finding a good model
Part 2a) Tuning the hyper-parameter and best choice to rescale
Determine the \(k\) and rescaling method that minimizes \(SSE\) and the choice of \(k\) and rescaling method that minimizes \(MAE\). Make sure you doing it properly! Search from k = 2 to k = 390. Use a single loop!
If you want to make two separate data sets for the normalized
results and standardized results, you can stack the rows together using
bind_rows(.id = 'rescale', 'norm' = ..., 'stan' = ...)
**Regardless of you answer from 1a), only use shooting,
three_pt, free, tot_reb,
assist, and usage to predict
efficient
# Normalizing and standardizing the data
nba_norm <-
nba_players |>
dplyr::select(shooting, three_pt, free, tot_reb, assist, usage) |>
mutate(
across(
.cols = everything(),
.fns = ~ (. - min(.)) / (max(.) - min(.))
)
)
nba_stan <-
nba_players |>
dplyr::select(shooting, three_pt, free, tot_reb, assist, usage) |>
mutate(
across(
.cols = everything(),
.fns = scale
)
)
# Data frames to save results for normalized and standardized data
k_norm_df <-
data.frame(
k = 2:390,
SSE = -1,
MAE = -1
)
k_stan_df <-
data.frame(
k = 2:390,
SSE = -1,
MAE = -1
)
# Performing the grid search
for (i in 1:nrow(k_stan_df)){
# Saving the residuals for normalized data
norm_error_loop <-
knn.reg(
train = nba_norm,
y = nba_players$efficient,
k = k_stan_df$k[i]
)$res
# Saving SSE and MAE for normalized data
k_norm_df[i, c('SSE', 'MAE')] <- c(
sum(norm_error_loop ^ 2), # SSE
sum(abs(norm_error_loop)) # MAE
)
### Standardized data
# Saving the predictions for normalized data
stan_error_loop <-
knn.reg(
train = nba_stan,
y = nba_players$efficient,
k = k_stan_df$k[i]
)$res
# Saving SSE and MAE for normalized data
k_stan_df[i, c('SSE', 'MAE')] <- c(
sum(stan_error_loop ^ 2), # SSE
sum(abs(stan_error_loop)) # MAE
)
}
k_search_results <-
bind_rows(
.id = 'rescale',
'norm' = k_norm_df,
'stan' = k_stan_df
)
k_search_results## rescale k SSE MAE
## 1 norm 2 1886.257 672.6500
## 2 norm 3 1715.423 633.9667
## 3 norm 4 1632.179 619.0000
## 4 norm 5 1635.808 613.7800
## 5 norm 6 1675.761 611.8000
## 6 norm 7 1780.424 622.8714
## 7 norm 8 1795.048 624.5625
## 8 norm 9 1780.503 620.0111
## 9 norm 10 1786.477 621.7500
## 10 norm 11 1781.269 617.4273
## 11 norm 12 1839.055 624.6167
## 12 norm 13 1880.292 634.1769
## 13 norm 14 1925.809 643.1143
## 14 norm 15 1942.598 647.2733
## 15 norm 16 1981.004 653.2688
## 16 norm 17 2004.650 655.1588
## 17 norm 18 2008.823 657.5500
## 18 norm 19 2049.346 661.0000
## 19 norm 20 2082.420 667.0550
## 20 norm 21 2093.330 668.9810
## 21 norm 22 2119.798 673.8182
## 22 norm 23 2139.974 675.7174
## 23 norm 24 2172.021 680.9708
## 24 norm 25 2189.682 680.2000
## 25 norm 26 2220.788 682.6692
## 26 norm 27 2253.365 689.1111
## 27 norm 28 2285.652 694.1607
## 28 norm 29 2311.324 698.1862
## 29 norm 30 2341.744 704.3133
## 30 norm 31 2372.333 711.1290
## 31 norm 32 2400.679 713.5281
## 32 norm 33 2417.596 714.2758
## 33 norm 34 2455.739 719.7706
## 34 norm 35 2481.598 725.4943
## 35 norm 36 2496.152 728.6139
## 36 norm 37 2511.940 729.2838
## 37 norm 38 2539.250 732.0132
## 38 norm 39 2556.372 733.7154
## 39 norm 40 2585.477 738.8850
## 40 norm 41 2613.479 743.0561
## 41 norm 42 2635.203 745.6976
## 42 norm 43 2647.386 747.3837
## 43 norm 44 2679.641 751.6432
## 44 norm 45 2692.627 752.7356
## 45 norm 46 2725.712 756.5935
## 46 norm 47 2731.261 756.6149
## 47 norm 48 2747.764 759.8104
## 48 norm 49 2755.926 759.4429
## 49 norm 50 2766.939 761.5960
## 50 norm 51 2782.391 762.2314
## 51 norm 52 2795.619 763.5135
## 52 norm 53 2807.968 765.2981
## 53 norm 54 2825.733 768.2852
## 54 norm 55 2848.867 771.9345
## 55 norm 56 2868.603 774.4018
## 56 norm 57 2880.405 776.2158
## 57 norm 58 2899.184 777.1379
## 58 norm 59 2917.146 779.0458
## 59 norm 60 2928.274 780.5550
## 60 norm 61 2944.588 782.2246
## 61 norm 62 2958.039 784.2726
## 62 norm 63 2970.575 786.8270
## 63 norm 64 2989.368 788.0312
## 64 norm 65 3006.377 789.9600
## 65 norm 66 3014.086 790.6591
## 66 norm 67 3030.480 791.2119
## 67 norm 68 3045.944 793.4941
## 68 norm 69 3066.037 795.8493
## 69 norm 70 3080.415 798.8514
## 70 norm 71 3088.848 799.1042
## 71 norm 72 3095.687 799.8486
## 72 norm 73 3114.279 802.1110
## 73 norm 74 3127.538 804.0608
## 74 norm 75 3136.818 805.4960
## 75 norm 76 3143.555 805.6513
## 76 norm 77 3158.056 808.1844
## 77 norm 78 3166.250 809.2205
## 78 norm 79 3179.158 810.8924
## 79 norm 80 3189.789 812.1000
## 80 norm 81 3204.670 814.3333
## 81 norm 82 3217.898 815.6927
## 82 norm 83 3230.370 817.1012
## 83 norm 84 3248.773 818.8369
## 84 norm 85 3262.921 819.7482
## 85 norm 86 3279.289 821.3407
## 86 norm 87 3291.377 822.8103
## 87 norm 88 3303.567 823.5830
## 88 norm 89 3317.421 825.1899
## 89 norm 90 3332.714 827.9422
## 90 norm 91 3344.386 829.2604
## 91 norm 92 3363.577 832.1272
## 92 norm 93 3378.583 834.5903
## 93 norm 94 3389.896 836.0872
## 94 norm 95 3409.201 838.6674
## 95 norm 96 3428.336 841.0500
## 96 norm 97 3442.216 843.8835
## 97 norm 98 3461.182 846.2939
## 98 norm 99 3477.100 848.8081
## 99 norm 100 3494.083 850.7510
## 100 norm 101 3506.706 851.5386
## 101 norm 102 3523.454 853.4804
## 102 norm 103 3533.049 854.5107
## 103 norm 104 3547.484 855.7202
## 104 norm 105 3563.483 857.4476
## 105 norm 106 3575.018 859.3245
## 106 norm 107 3587.025 860.8486
## 107 norm 108 3598.044 861.7287
## 108 norm 109 3610.458 862.8688
## 109 norm 110 3628.575 865.0245
## 110 norm 111 3639.129 866.3802
## 111 norm 112 3657.282 868.5777
## 112 norm 113 3677.168 870.3938
## 113 norm 114 3684.547 871.5447
## 114 norm 115 3685.835 871.8748
## 115 norm 116 3700.054 873.4836
## 116 norm 117 3711.200 875.6325
## 117 norm 118 3730.596 877.8551
## 118 norm 119 3746.630 879.6202
## 119 norm 120 3758.651 881.1667
## 120 norm 121 3771.813 882.2397
## 121 norm 122 3784.403 883.9139
## 122 norm 123 3793.172 884.7341
## 123 norm 124 3812.763 886.8621
## 124 norm 125 3834.438 888.7720
## 125 norm 126 3847.805 890.0833
## 126 norm 127 3859.876 891.4157
## 127 norm 128 3869.430 892.4438
## 128 norm 129 3879.514 894.0279
## 129 norm 130 3893.284 895.4885
## 130 norm 131 3914.096 898.1031
## 131 norm 132 3926.675 899.3424
## 132 norm 133 3940.934 901.1714
## 133 norm 134 3955.786 902.8530
## 134 norm 135 3968.917 904.5807
## 135 norm 136 3974.115 905.4529
## 136 norm 137 3987.796 907.9482
## 137 norm 138 4000.405 909.6428
## 138 norm 139 4012.832 911.0050
## 139 norm 140 4025.639 911.9179
## 140 norm 141 4039.087 913.2113
## 141 norm 142 4050.723 914.5268
## 142 norm 143 4069.958 916.4203
## 143 norm 144 4085.059 918.3618
## 144 norm 145 4100.754 919.9131
## 145 norm 146 4114.605 921.4507
## 146 norm 147 4130.871 923.4939
## 147 norm 148 4145.672 925.2115
## 148 norm 149 4157.602 926.2228
## 149 norm 150 4166.477 926.8880
## 150 norm 151 4174.787 927.7603
## 151 norm 152 4185.902 928.9000
## 152 norm 153 4205.368 931.5974
## 153 norm 154 4218.528 932.6643
## 154 norm 155 4233.334 934.2077
## 155 norm 156 4243.542 935.2686
## 156 norm 157 4256.011 936.7140
## 157 norm 158 4273.608 938.6323
## 158 norm 159 4287.185 940.1346
## 159 norm 160 4300.526 941.6706
## 160 norm 161 4319.538 943.8925
## 161 norm 162 4332.058 945.4519
## 162 norm 163 4344.526 946.7485
## 163 norm 164 4360.316 948.5427
## 164 norm 165 4376.635 950.4788
## 165 norm 166 4391.139 952.6801
## 166 norm 167 4404.110 954.4012
## 167 norm 168 4414.385 955.4887
## 168 norm 169 4423.127 956.7704
## 169 norm 170 4439.214 958.6612
## 170 norm 171 4455.395 960.3538
## 171 norm 172 4471.332 962.2808
## 172 norm 173 4488.187 964.1734
## 173 norm 174 4502.111 965.8638
## 174 norm 175 4516.913 967.3520
## 175 norm 176 4534.761 969.6631
## 176 norm 177 4544.981 971.1333
## 177 norm 178 4555.737 972.2618
## 178 norm 179 4568.295 973.7726
## 179 norm 180 4586.587 975.6717
## 180 norm 181 4605.444 977.3271
## 181 norm 182 4617.526 978.8593
## 182 norm 183 4634.352 980.5148
## 183 norm 184 4649.420 982.3614
## 184 norm 185 4662.370 983.9605
## 185 norm 186 4674.350 985.2280
## 186 norm 187 4687.805 987.1364
## 187 norm 188 4700.363 988.3793
## 188 norm 189 4712.668 989.8582
## 189 norm 190 4725.676 991.5953
## 190 norm 191 4741.107 992.8152
## 191 norm 192 4756.918 994.8620
## 192 norm 193 4770.746 996.6617
## 193 norm 194 4783.415 998.2825
## 194 norm 195 4797.454 1000.0374
## 195 norm 196 4814.343 1001.8699
## 196 norm 197 4824.872 1003.0345
## 197 norm 198 4839.781 1004.6611
## 198 norm 199 4854.603 1006.8899
## 199 norm 200 4866.035 1008.4740
## 200 norm 201 4876.468 1009.7234
## 201 norm 202 4890.851 1011.0530
## 202 norm 203 4903.791 1012.6749
## 203 norm 204 4917.540 1014.5064
## 204 norm 205 4930.333 1015.7741
## 205 norm 206 4942.516 1016.7845
## 206 norm 207 4954.343 1018.3647
## 207 norm 208 4967.224 1020.0462
## 208 norm 209 4979.048 1021.6789
## 209 norm 210 4992.962 1022.9852
## 210 norm 211 5003.704 1024.3005
## 211 norm 212 5019.056 1025.9392
## 212 norm 213 5030.265 1027.0620
## 213 norm 214 5044.072 1028.2636
## 214 norm 215 5055.062 1029.3591
## 215 norm 216 5067.880 1030.4639
## 216 norm 217 5081.076 1031.9641
## 217 norm 218 5095.210 1033.7697
## 218 norm 219 5114.428 1035.7219
## 219 norm 220 5130.184 1037.8295
## 220 norm 221 5145.034 1039.7543
## 221 norm 222 5159.764 1041.7081
## 222 norm 223 5175.637 1043.8780
## 223 norm 224 5189.768 1045.8879
## 224 norm 225 5207.131 1048.0871
## 225 norm 226 5222.123 1049.9155
## 226 norm 227 5237.394 1051.6269
## 227 norm 228 5249.164 1053.3882
## 228 norm 229 5261.940 1054.5380
## 229 norm 230 5274.464 1056.1900
## 230 norm 231 5288.193 1057.7996
## 231 norm 232 5305.995 1059.8556
## 232 norm 233 5316.599 1061.5103
## 233 norm 234 5332.744 1063.6662
## 234 norm 235 5344.943 1065.0536
## 235 norm 236 5361.207 1067.0686
## 236 norm 237 5374.908 1068.7207
## 237 norm 238 5388.894 1070.7550
## 238 norm 239 5403.271 1072.4494
## 239 norm 240 5419.394 1074.3563
## 240 norm 241 5431.081 1075.6896
## 241 norm 242 5444.773 1077.0116
## 242 norm 243 5459.770 1078.9160
## 243 norm 244 5471.326 1080.7369
## 244 norm 245 5485.411 1082.3759
## 245 norm 246 5502.285 1084.5122
## 246 norm 247 5519.112 1086.2215
## 247 norm 248 5533.393 1088.3077
## 248 norm 249 5545.756 1089.9827
## 249 norm 250 5559.999 1092.0796
## 250 norm 251 5576.557 1093.8207
## 251 norm 252 5591.030 1095.6968
## 252 norm 253 5605.798 1097.7775
## 253 norm 254 5621.825 1099.8756
## 254 norm 255 5627.613 1100.6475
## 255 norm 256 5642.274 1102.5160
## 256 norm 257 5657.329 1104.4440
## 257 norm 258 5672.687 1106.4333
## 258 norm 259 5690.288 1108.5405
## 259 norm 260 5707.237 1110.3919
## 260 norm 261 5723.013 1112.3762
## 261 norm 262 5735.431 1113.6378
## 262 norm 263 5749.728 1115.6951
## 263 norm 264 5765.037 1117.3523
## 264 norm 265 5783.521 1119.7057
## 265 norm 266 5800.904 1121.7169
## 266 norm 267 5817.609 1123.9569
## 267 norm 268 5831.938 1126.0601
## 268 norm 269 5848.342 1127.7948
## 269 norm 270 5861.377 1129.3859
## 270 norm 271 5877.873 1131.1845
## 271 norm 272 5892.277 1132.9452
## 272 norm 273 5907.885 1134.5941
## 273 norm 274 5922.386 1136.3748
## 274 norm 275 5939.323 1138.2680
## 275 norm 276 5954.614 1139.7641
## 276 norm 277 5964.879 1140.9747
## 277 norm 278 5976.429 1142.2849
## 278 norm 279 5995.861 1144.6871
## 279 norm 280 6010.792 1146.0425
## 280 norm 281 6024.109 1147.7039
## 281 norm 282 6041.633 1149.6333
## 282 norm 283 6058.749 1151.9399
## 283 norm 284 6073.200 1153.7197
## 284 norm 285 6086.632 1155.2986
## 285 norm 286 6102.421 1156.8430
## 286 norm 287 6114.921 1158.3049
## 287 norm 288 6128.069 1159.9583
## 288 norm 289 6140.849 1161.5633
## 289 norm 290 6159.390 1163.9697
## 290 norm 291 6172.104 1165.4007
## 291 norm 292 6188.728 1167.6589
## 292 norm 293 6204.557 1169.2966
## 293 norm 294 6223.037 1171.4109
## 294 norm 295 6239.273 1173.5000
## 295 norm 296 6252.689 1175.0892
## 296 norm 297 6271.512 1177.1882
## 297 norm 298 6289.460 1179.3527
## 298 norm 299 6306.995 1181.7281
## 299 norm 300 6323.116 1183.5437
## 300 norm 301 6335.956 1185.0432
## 301 norm 302 6355.192 1186.9490
## 302 norm 303 6373.187 1188.9010
## 303 norm 304 6387.579 1190.6691
## 304 norm 305 6401.547 1192.0193
## 305 norm 306 6414.974 1193.7944
## 306 norm 307 6432.658 1195.4121
## 307 norm 308 6448.715 1197.2269
## 308 norm 309 6463.253 1199.2650
## 309 norm 310 6476.647 1200.5652
## 310 norm 311 6492.615 1202.6994
## 311 norm 312 6506.956 1204.3465
## 312 norm 313 6523.570 1206.1112
## 313 norm 314 6539.955 1207.7672
## 314 norm 315 6555.054 1209.4632
## 315 norm 316 6570.572 1211.2690
## 316 norm 317 6584.581 1212.9527
## 317 norm 318 6600.495 1215.0585
## 318 norm 319 6615.204 1216.7138
## 319 norm 320 6632.708 1218.8106
## 320 norm 321 6646.859 1220.3290
## 321 norm 322 6660.927 1222.1171
## 322 norm 323 6673.771 1223.8251
## 323 norm 324 6692.025 1226.0148
## 324 norm 325 6710.285 1228.0748
## 325 norm 326 6726.592 1229.6301
## 326 norm 327 6741.132 1231.5235
## 327 norm 328 6755.694 1233.3262
## 328 norm 329 6774.793 1235.5842
## 329 norm 330 6790.252 1237.2876
## 330 norm 331 6807.039 1238.8961
## 331 norm 332 6822.784 1240.6961
## 332 norm 333 6836.589 1241.9991
## 333 norm 334 6850.892 1243.7898
## 334 norm 335 6866.791 1246.0746
## 335 norm 336 6885.031 1248.3223
## 336 norm 337 6901.553 1250.2175
## 337 norm 338 6916.988 1252.1648
## 338 norm 339 6932.908 1253.8354
## 339 norm 340 6946.797 1255.4971
## 340 norm 341 6960.656 1257.0613
## 341 norm 342 6972.196 1258.4974
## 342 norm 343 6984.292 1259.6601
## 343 norm 344 7000.148 1261.7247
## 344 norm 345 7017.374 1263.6928
## 345 norm 346 7033.991 1265.5546
## 346 norm 347 7047.290 1267.3458
## 347 norm 348 7059.978 1268.8480
## 348 norm 349 7074.052 1270.7367
## 349 norm 350 7086.494 1271.9840
## 350 norm 351 7099.083 1273.3359
## 351 norm 352 7115.067 1275.1767
## 352 norm 353 7131.155 1276.9079
## 353 norm 354 7147.889 1278.6960
## 354 norm 355 7165.346 1280.5915
## 355 norm 356 7180.942 1282.1927
## 356 norm 357 7198.894 1284.5104
## 357 norm 358 7216.953 1286.9042
## 358 norm 359 7236.802 1289.1404
## 359 norm 360 7253.666 1291.0603
## 360 norm 361 7271.616 1293.3837
## 361 norm 362 7288.565 1295.5818
## 362 norm 363 7307.030 1297.5259
## 363 norm 364 7328.611 1300.2190
## 364 norm 365 7347.018 1302.7658
## 365 norm 366 7366.240 1305.0787
## 366 norm 367 7386.538 1307.5673
## 367 norm 368 7410.914 1310.3073
## 368 norm 369 7431.119 1312.7339
## 369 norm 370 7452.818 1315.2384
## 370 norm 371 7472.506 1317.5798
## 371 norm 372 7491.020 1319.8565
## 372 norm 373 7514.668 1322.7327
## 373 norm 374 7537.090 1325.4406
## 374 norm 375 7558.979 1328.1011
## 375 norm 376 7581.434 1330.9191
## 376 norm 377 7597.760 1332.9011
## 377 norm 378 7620.422 1335.3275
## 378 norm 379 7645.055 1338.2040
## 379 norm 380 7668.995 1340.8032
## 380 norm 381 7694.806 1343.6948
## 381 norm 382 7717.012 1346.4610
## 382 norm 383 7737.483 1348.4992
## 383 norm 384 7759.339 1350.7091
## 384 norm 385 7780.039 1353.2462
## 385 norm 386 7805.719 1356.2676
## 386 norm 387 7831.277 1359.4191
## 387 norm 388 7859.368 1362.6041
## 388 norm 389 7888.052 1366.2853
## 389 norm 390 7920.716 1370.7067
## 390 stan 2 1570.690 612.9000
## 391 stan 3 1448.004 586.4000
## 392 stan 4 1444.944 572.4250
## 393 stan 5 1474.271 574.1600
## 394 stan 6 1511.977 573.3833
## 395 stan 7 1528.633 576.4857
## 396 stan 8 1528.193 578.5125
## 397 stan 9 1555.309 582.0111
## 398 stan 10 1600.132 586.5600
## 399 stan 11 1601.952 585.4091
## 400 stan 12 1621.782 585.2250
## 401 stan 13 1622.006 580.1615
## 402 stan 14 1641.044 582.4500
## 403 stan 15 1635.344 582.0933
## 404 stan 16 1644.692 580.7563
## 405 stan 17 1679.870 585.7471
## 406 stan 18 1690.889 584.9944
## 407 stan 19 1714.657 592.2263
## 408 stan 20 1741.004 595.0900
## 409 stan 21 1762.554 597.7333
## 410 stan 22 1781.231 602.1318
## 411 stan 23 1814.113 607.7000
## 412 stan 24 1843.433 613.7042
## 413 stan 25 1865.571 617.1160
## 414 stan 26 1884.506 620.3654
## 415 stan 27 1906.265 622.0111
## 416 stan 28 1926.388 626.2643
## 417 stan 29 1937.559 627.6414
## 418 stan 30 1975.741 634.2367
## 419 stan 31 1995.894 637.2677
## 420 stan 32 2015.013 640.2250
## 421 stan 33 2040.453 644.9030
## 422 stan 34 2049.486 645.6324
## 423 stan 35 2080.185 648.9314
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## 761 stan 373 7506.196 1326.1491
## 762 stan 374 7526.998 1328.9465
## 763 stan 375 7555.854 1332.3955
## 764 stan 376 7578.326 1335.0016
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## 766 stan 378 7626.756 1340.7238
## 767 stan 379 7645.823 1343.0332
## 768 stan 380 7666.590 1345.4445
## 769 stan 381 7687.926 1347.8900
## 770 stan 382 7710.993 1350.5126
## 771 stan 383 7734.239 1352.9796
## 772 stan 384 7752.434 1354.5125
## 773 stan 385 7776.858 1356.8745
## 774 stan 386 7800.360 1359.2782
## 775 stan 387 7825.925 1362.0566
## 776 stan 388 7853.794 1365.2649
## 777 stan 389 7879.102 1368.2951
## 778 stan 390 7909.302 1371.8174Use the chunk below after you’ve done the search to find the choice of k
# Best choice of SSE:
k_search_results |>
slice_min(SSE, n = 1)## rescale k SSE MAE
## 1 stan 4 1444.944 572.425# Best choice of MAE:
k_search_results |>
slice_min(MAE, n = 1)## rescale k SSE MAE
## 1 stan 4 1444.944 572.425Part 2B: Graph the results of the grid search
Graph both SSE and MAE for normalized and standardized data in the same graph (but not necessarily the same plot). Does it look like you found a true minimum?
k_search_results |>
pivot_longer(
cols = SSE:MAE,
names_to = 'metric',
values_to = 'value'
) |>
ggplot(
mapping = aes(
x = k,
y = value,
color = rescale
)
) +
geom_line() +
facet_wrap(
facets = vars(metric),
scales = 'free_y',
nrow = 2
)
Part 2C: Fit statistics for best k and rescale method
Using the choice of k and rescale method, calculate \(R^2\), \(\text{rmse}\), and \(\text{MAE}\) using cross-validation.
eff23_knn <-
knn.reg(
train = nba_stan,
y = nba_players$efficient,
k = 4,
)
## Rsquared
eff23_knn$R2Pred## [1] 0.8220365## rmse: sqrt(PRESS / (n - 1))
sqrt(eff23_knn$PRESS / (nrow(nba_players) - 1))## [1] 1.912613## MAE
mean(abs(nba_players$efficient - eff23_knn$pred))## [1] 1.445518Question 3) Players from the 2024 - 2025 NBA season
The code chunk below reads in the same data but from the 2024 - 2025 NBA regular season data set. For question 3, you’ll be predicting the 100 randomly selected players using kNN regression with k = 5 for the standardized data.
Part 3a) Making predictions for the 2024-2025 season
For the players from the 2024-2025 season, predict their efficiency. Make sure to standardize the data first!
When standardizing (or normalizing) the data for the data set
being predicted, you want to standardize using the statistics from the
training data. That is, when standardizing shooting for the
2024-2025 data set, you want to use the mean and standard deviation of
shooting from the 2023-2024 data set! Repeat for all six
predictors.
Display the predictions in a data frame that has two columns: efficient and predicted efficient
## Standardizing the nba24 data
nba24_stan <-
nba24 |>
dplyr::select(
shooting, three_pt, free, tot_reb, assist, usage
) |>
mutate(
shooting = (shooting - mean(nba_players$shooting)) / sd(nba_players$shooting),
three_pt = (three_pt - mean(nba_players$three_pt)) / sd(nba_players$three_pt),
free = (free - mean(nba_players$free) / sd(nba_players$free)),
tot_reb = (tot_reb - mean(nba_players$tot_reb)) / sd(nba_players$tot_reb),
assist = (assist - mean(nba_players$assist)) / sd(nba_players$assist),
usage = (usage - mean(nba_players$usage)) / sd(nba_players$usage)
)
nba24_stan## shooting three_pt free tot_reb assist usage
## 1 0.211338808 -0.061556838 -1.839362 -1.162642440 -0.030275114 0.17885610
## 2 -0.517948521 0.269150797 -1.705362 -0.604249186 0.160593664 1.55604806
## 3 -0.197773596 -0.195757037 -1.786362 -0.023520201 -0.674457241 -0.41136903
## 4 -1.051573395 0.671751396 -1.825362 -0.648920646 0.780917194 -0.50079708
## 5 2.683800726 -1.897223853 -1.506362 1.942024056 -0.614810748 -0.48291147
## 6 0.122401329 1.112694909 -1.781362 -0.715927837 2.403301810 -0.82273806
## 7 0.300276287 1.491331186 -1.808362 -1.095635250 -0.686386540 0.69753879
## 8 1.474251010 0.590272703 -1.648362 -0.604249186 -0.722174436 -0.51868269
## 9 0.104613833 0.944944659 -1.747362 -0.671256376 0.041300678 -0.46502586
## 10 0.069038841 1.524881236 -1.798362 -0.291548963 -0.805679526 -0.25039854
## 11 -0.233348588 1.409852494 -1.858362 -0.559577725 -0.471659164 0.33982659
## 12 0.211338808 0.877844560 -1.856362 -1.140306710 1.556321606 -0.42925464
## 13 -0.909273429 -0.320371508 -1.591362 -0.604249186 0.971785972 1.32353513
## 14 0.513726236 -1.652787776 -1.676362 2.656767422 0.351462443 0.75119562
## 15 -0.304498571 -0.195757037 -1.646362 -0.135198852 -0.686386540 -0.08942805
## 16 1.207438573 -1.935566768 -1.688362 2.612095962 -0.221143892 0.16097049
## 17 0.905051144 0.374593811 -1.761362 -0.336220423 -0.817608825 -0.50079708
## 18 1.065138607 1.529674100 -1.842362 -0.626584916 0.411108936 0.07154244
## 19 0.069038841 0.465658232 -1.784362 0.445530133 -0.245002490 0.51868269
## 20 0.709388690 1.189380737 -1.846362 -0.648920646 -0.626740046 -1.09102220
## 21 1.616550977 1.381095308 -1.754362 -0.894613678 -0.793750227 -1.05525098
## 22 -0.037686134 0.360215218 -1.744362 -0.112863121 -0.889184617 0.01788561
## 23 0.389213766 0.475243961 -1.631362 -0.313884693 0.745129298 2.28935807
## 24 0.157976320 0.537551196 -1.493362 -0.179870312 2.641887783 1.96741709
## 25 1.634338473 -0.627114822 -1.678362 -0.380891884 -0.543234956 -0.50079708
## 26 -0.357861058 0.355422354 -1.583362 -1.073299520 0.888280882 -0.12519927
## 27 -0.233348588 0.844294510 -1.739362 -0.715927837 -0.746033033 -0.48291147
## 28 -0.571311008 0.863465967 -1.673362 -0.581913455 -0.459729865 -0.35771220
## 29 -1.318385832 0.532758332 -1.761362 -0.291548963 -0.006416517 0.55445391
## 30 0.602663716 1.227723651 -1.845362 -0.313884693 -0.698315838 -0.12519927
## 31 0.157976320 -0.166999852 -1.651362 -0.447899074 1.484745814 0.12519927
## 32 1.225226069 0.475243961 -1.749362 0.311515752 -0.328507580 0.26828415
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## 230 -0.108836117 0.072643362 -1.602362 -0.648920646 0.172522963 0.53656830
## 231 -1.122723378 -0.440193115 -1.611362 -1.184978171 0.912139479 -0.33982659
## 232 -0.304498571 -0.214928494 -1.641362 0.668887435 -0.543234956 0.32194098
## 233 1.047351111 0.681337124 -1.638362 -0.514906265 0.458826131 0.76908123
## 234 -0.197773596 0.408143861 -1.716362 0.512537324 -1.187417083 -0.39348342
## 235 1.207438573 -1.911602446 -1.690362 1.629323833 -0.018345815 0.01788561
## 236 0.460363749 -1.743852197 -1.695362 2.344067199 0.434967533 -0.33982659
## 237 -0.108836117 -0.358714422 -1.753362 0.780566086 -0.734103734 0.14308488
## 238 1.082926102 -1.906809582 -1.478362 2.299395739 -1.044265499 -0.23251293
## 239 2.541500759 -1.935566768 -1.453362 1.584652373 -0.531305657 0.16097049
## 240 -0.766973462 -1.408351698 -1.728362 1.204944960 -1.008477603 -0.66176757
## 241 1.563188489 1.443402544 -1.785362 -0.604249186 0.220240158 -1.01947977
## 242 -0.429011042 0.345836625 -1.731362 -1.073299520 -0.173426698 1.19833586
## 243 -0.179986100 0.063057633 -1.707362 -0.693592106 0.434967533 -0.33982659
## 244 0.282488791 0.527965468 -1.767362 -1.207313901 0.983715271 0.14308488
## 245 0.015676354 -0.166999852 -1.627362 -0.447899074 -1.199346382 -1.14467903
## 246 -0.411223546 0.264357933 -1.766362 -0.872277948 0.709341402 1.53816245
## 247 -0.891485933 0.906601745 -1.797362 -1.050963789 1.508604412 0.21462732
## 248 -1.229448353 0.925773202 -1.763362 -0.805270757 -0.877255318 0.42925464
## 249 2.612650743 -1.873259532 -1.500362 0.847573277 -0.853396721 -1.10890781
## 250 0.478151245 0.187672105 -1.773362 -0.648920646 0.375321040 -0.03577122
## 251 0.033463849 0.820330188 -1.704362 0.445530133 -0.054133711 -0.96582294
## 252 0.851688657 -1.935566768 -1.482362 2.790781803 -0.614810748 -1.03736538
## 253 0.940626136 -1.101608384 -1.282362 -0.202206042 1.293877036 0.39348342
## 254 -0.162198605 -1.921188175 -1.690362 2.612095962 -0.865326019 -0.33982659
## 255 0.246913799 0.777194410 -1.767362 -0.760599297 -0.793750227 -1.09102220
## 256 -0.482373529 0.307493711 -1.639362 -0.805270757 -0.364295476 -0.75119562
## 257 2.488138272 -1.542551897 -1.234362 0.356187212 -0.256931788 -1.96741709
## 258 -0.535736017 0.480036825 -1.699362 -0.805270757 -0.686386540 0.42925464
## 259 0.282488791 -1.005751099 -1.672362 0.825237546 -0.113780205 0.07154244
## 260 -0.251136084 0.877844560 -1.805362 -0.782935027 0.065159275 0.01788561
## 261 -0.091048621 0.657372803 -1.777362 -0.425563344 0.232169456 -0.60811074
## 262 -1.940948186 0.336250897 -1.728362 0.378522943 -0.245002490 -0.94793733
## 263 0.442576253 0.566308382 -1.665362 -0.514906265 0.148664366 0.91216611
## 264 0.442576253 -0.114278345 -1.742362 -0.961620869 0.351462443 0.62599635
## 265 -1.140510874 0.293115118 -1.751362 0.043486990 -0.197285295 -0.69753879
## 266 1.171863582 -1.935566768 -1.756362 1.673995294 -0.984619006 -1.96741709
## 267 -0.197773596 0.163707783 -1.674362 -1.140306710 1.592109502 2.00318831
## 268 -0.891485933 0.331458033 -1.728362 -0.514906265 -0.531305657 -0.07154244
## 269 -1.229448353 1.644702843 -1.895362 -0.559577725 -0.662527942 -0.67965318
## 270 -1.923160690 0.911394609 -1.872362 -0.827606488 0.065159275 -0.14308488
## 271 -0.286711075 -0.444985979 -1.621362 0.110494180 -0.495517761 -0.94793733
## 272 -1.585198270 -0.531257536 -1.502362 0.378522943 -0.662527942 -0.41136903
## 273 -1.318385832 0.053471905 -1.728362 -0.425563344 -0.841467422 -0.32194098
## 274 -1.940948186 1.242102244 -1.794362 -0.179870312 -1.032336200 -1.26987830
## 275 0.264701295 -1.283737227 -1.534362 2.076038437 0.434967533 2.11050197
## 276 1.367526036 -0.277235730 -1.579362 -0.157534582 0.041300678 0.07154244
## 277 -0.606886000 -1.935566768 -1.791362 0.467865863 2.665746380 -0.96582294
## 278 -0.322286067 -0.507293215 -1.575362 2.321731469 0.256028054 0.35771220
## 279 -0.429011042 0.240393611 -1.760362 -0.090527391 -0.686386540 0.94793733
## 280 0.656026203 -0.291614323 -1.710362 -0.671256376 0.363391741 -0.48291147
## 281 -1.193873362 1.021630488 -1.706362 0.132829911 -1.020406902 -0.55445391
## 282 0.229126303 -0.248478544 -1.371362 -0.336220423 -1.068124096 -1.05525098
## 283 0.371426270 -0.114278345 -1.713362 -0.648920646 0.697412104 1.57393367
## 284 0.246913799 0.312286576 -1.554362 0.601880245 2.558382693 2.73649832
## 285 -0.179986100 -0.397057337 -1.580362 -0.671256376 2.546453394 2.43244295
## 286 0.602663716 1.831624550 -1.848362 -0.202206042 0.112876470 -0.69753879
## 287 -2.741385498 0.580686975 -1.783362 -0.983956599 -0.865326019 -1.09102220
## 288 -0.091048621 -1.254980041 -1.706362 2.366402930 0.256028054 0.23251293
## 289 0.744963682 0.566308382 -1.704362 0.847573277 -1.044265499 0.46502586
## 290 0.495938741 1.313995208 -1.861362 -1.229649631 -1.187417083 -0.67965318
## 291 -0.464586033 1.395473901 -1.822362 -0.715927837 0.279886651 -1.03736538
## 292 -1.193873362 0.666958532 -1.700362 0.065822720 -1.008477603 -1.00159416
## 293 -0.553523512 -0.502500351 -1.816362 1.763338214 -0.209214594 0.98370855
## 294 0.620451211 1.726181536 -1.758362 -0.492570535 -0.662527942 -0.37559781
## 295 -0.500161025 0.753230089 -1.895362 -0.939285139 0.578119117 -0.96582294
## 296 -1.247235849 -0.253271408 -1.868362 -1.050963789 1.639826697 0.73331001
## 297 -0.873698437 1.702217214 -1.849362 -1.095635250 -1.056194798 -1.62759050
## 298 -0.891485933 0.537551196 -1.650362 -0.961620869 -0.614810748 0.14308488
## 299 -0.660248487 0.585479839 -1.711362 -0.425563344 3.476938689 3.09421052
## 300 -0.037686134 0.796365867 -1.675362 -0.001184471 -0.853396721 0.96582294
## 301 -0.678035983 -0.660664871 -1.525362 0.021151260 -0.006416517 1.57393367
## 302 -0.980423412 0.767608681 -1.836362 -0.760599297 -0.889184617 -0.91216611
## 303 0.584876220 2.128782134 -1.635362 -0.983956599 -0.638669345 -0.48291147
## 304 0.371426270 1.381095308 -1.803362 1.741002484 0.518472624 -0.71542440
## 305 -0.891485933 -0.071142566 -1.778362 0.311515752 -0.268861087 -0.21462732
## 306 0.033463849 0.182879240 -1.765362 -0.827606488 -0.149568100 0.93005172
## 307 -0.393436050 -0.502500351 -1.516362 0.534873054 1.353523529 2.68284149
## 308 0.371426270 0.317079440 -1.718362 1.696331024 0.434967533 2.11050197
## 309 0.211338808 0.082229091 -1.763362 -0.894613678 0.661624208 -0.35771220
## 310 0.389213766 0.734058631 -1.708362 -0.336220423 0.232169456 -0.05365683
## 311 -1.015998404 1.429023951 -1.724362 -0.045855931 -1.044265499 0.07154244
## 312 0.780538674 -0.967408185 -1.657362 -0.738263567 1.663685294 -0.80485245
## 313 0.335851278 1.328373801 -1.851362 0.936916197 -0.698315838 -1.89587465
## 314 -0.375648554 1.127073502 -1.806362 0.110494180 -0.793750227 -0.28616976
## 315 -0.855910941 -1.250187177 -1.669362 0.869909007 -0.245002490 -1.48450562
## 316 0.478151245 1.127073502 -1.633362 -1.073299520 0.757058597 -0.94793733
## 317 0.567088724 0.355422354 -1.728362 -0.157534582 -0.614810748 -0.25039854
## 318 -1.069360891 -0.310785780 -1.617362 -0.425563344 -0.471659164 -0.75119562
## 319 1.420888523 0.532758332 -1.728362 -0.291548963 -0.960760409 -0.21462732
## 320 -0.482373529 0.178086376 -1.724362 -0.805270757 0.411108936 -0.08942805
## 321 -0.002111142 -0.991372506 -1.643362 1.227280690 -0.077992309 -0.10731366
## 322 1.314163548 -1.892430989 -1.574362 2.277060009 0.220240158 0.50079708
## 323 -0.251136084 0.475243961 -1.817362 -0.626584916 -0.686386540 -0.30405537
## 324 -0.286711075 -0.732557836 -1.590362 -0.045855931 0.757058597 0.84062367
## 325 0.638238707 -0.521671808 -1.536362 0.512537324 0.697412104 -0.01788561
## 326 -0.962635916 -0.981786778 -1.671362 1.182609230 -0.077992309 -0.01788561
## 327 0.104613833 0.556722653 -1.798362 -1.117970980 -0.698315838 0.03577122
## 328 0.798326169 -0.550428993 -1.705362 -0.559577725 -0.865326019 -1.26987830
## 329 -1.104935883 0.619029889 -1.517362 -0.336220423 -0.304648983 -0.76908123
## 330 0.798326169 0.154122055 -1.592362 0.601880245 -0.388154073 1.30564952
## 331 -0.678035983 -0.176585580 -1.716362 -0.626584916 -0.113780205 0.25039854
## 332 1.171863582 -0.588771907 -1.752362 0.914580467 -0.722174436 -0.48291147
## 333 0.389213766 1.194173601 -1.840362 0.333851482 -0.292719684 0.17885610
## 334 0.300276287 -1.115986977 -1.676362 1.003923388 -0.519376359 -0.51868269
## 335 0.780538674 2.200675098 -1.896362 -1.453006933 -1.414073757 -0.51868269
## 336 -0.535736017 0.317079440 -1.769362 -0.179870312 0.745129298 0.87639489
## 337 -1.229448353 -0.679836329 -1.729362 -0.112863121 -0.221143892 -0.25039854
## 338 -1.976523178 0.259565069 -1.789362 -0.916949408 1.150725452 0.23251293
## 339 -0.055473630 -0.478536029 -1.743362 -1.028628059 0.590048416 0.00000000
## 340 -0.108836117 0.259565069 -1.764362 -0.068191661 0.136735067 -0.53656830
## 341 -2.136610640 0.810744460 -1.732362 -1.095635250 1.771048982 -0.50079708
## 342 0.976201128 -0.598357636 -1.630362 0.959251928 -0.459729865 1.00159416
## 343 0.175763816 -1.609651997 -1.811362 1.808009675 -0.734103734 0.14308488
## 344 -0.678035983 -1.528173305 -1.554362 2.969467645 -0.936901811 0.08942805
## 345 -2.367848085 0.734058631 -1.748362 -0.983956599 0.041300678 -1.30564952
## 346 -0.108836117 0.144536326 -1.538362 -0.045855931 -0.805679526 0.16097049
## 347 0.424788757 -0.018421059 -1.843362 0.043486990 -0.662527942 -1.34142074
## 348 0.442576253 0.101400548 -1.631362 -1.006292329 -0.948831110 -1.18045025
## 349 4.106800391 -1.715095011 -1.645362 1.048594848 -0.805679526 -1.00159416
## 350 -2.901472960 -1.734266468 -1.516362 2.679103152 -0.698315838 -1.05525098
## 351 1.865575918 -1.475451798 -1.505362 0.088158450 -1.080053395 -0.41136903
## 352 -1.069360891 -0.205342766 -1.842362 0.758230356 -0.328507580 -0.82273806
## 353 0.318063782 1.285238023 -1.704362 -1.497678393 -0.316578282 -0.75119562
## 354 -0.517948521 -0.114278345 -1.668362 -0.246877503 -0.316578282 -0.87639489
## 355 -2.101035648 -0.890722356 -1.790362 -0.045855931 1.604038801 0.46502586
## 356 -0.002111142 -0.291614323 -1.606362 0.802901816 -0.769891630 1.35930635
## 357 -0.838123445 1.285238023 -1.823362 -0.827606488 0.005512782 0.30405537
## 358 -0.179986100 1.544052693 -1.791362 0.534873054 -1.056194798 -1.48450562
## 359 -0.268923579 -0.560014722 -1.652362 0.914580467 -0.197285295 -1.25199269
## 360 -0.642460991 -1.935566768 -1.493362 1.048594848 -1.091982694 -1.10890781
## 361 0.282488791 -0.473743165 -1.745362 0.088158450 0.208310859 1.62759050
## 362 -0.589098504 0.321872304 -1.649362 -0.782935027 0.983715271 1.64547611
## 363 0.264701295 -0.042385380 -1.690362 -0.313884693 1.448957918 0.60811074
## 364 -0.517948521 0.489622554 -1.623362 -0.224541772 -1.008477603 -0.28616976
## 365 -1.140510874 -0.574393315 -1.678362 -0.514906265 -0.412012671 -0.07154244
## 366 -1.033785899 -1.834916618 -1.728362 1.227280690 -0.853396721 -0.93005172
## 367 -0.624673496 0.786780138 -1.811362 0.132829911 -0.602881449 -0.51868269
## 368 0.905051144 -1.643202047 -1.727362 1.115602039 -0.984619006 -1.39507757
## 369 -4.235535146 1.659081436 -1.918362 -0.671256376 -0.877255318 0.44714025
## 370 -0.073261125 -0.689422057 -1.707362 1.160273499 0.697412104 0.69753879
## 371 -2.421210573 0.134950598 -1.773362 -0.715927837 0.613907013 0.08942805
## 372 2.328050809 -1.935566768 -1.557362 1.696331024 -0.042204413 -0.89428050
## 373 0.246913799 -0.373093015 -1.749362 -0.894613678 -0.101850906 -0.42925464
## 374 -0.642460991 -0.670250600 -1.641362 1.673995294 -0.626740046 -1.09102220
## 375 -0.357861058 -0.377885879 -1.764362 0.043486990 -0.364295476 -0.85850928
## 376 -3.079347918 -0.143035530 -1.743362 -1.207313901 0.530401922 -1.03736538
## 377 0.958413632 0.499208282 -1.797362 0.646551705 -0.829538123 0.44714025
## 378 -1.816435715 0.365008083 -1.593362 0.155165641 -0.137638802 -0.12519927
## 379 0.424788757 -1.935566768 -1.657362 2.589760231 -0.960760409 -0.19674171
## 380 -1.140510874 1.510502643 -1.871362 -0.827606488 0.303745248 0.42925464
## 381 -0.660248487 0.475243961 -1.710362 -0.447899074 0.828634389 1.59181928
## 382 -0.873698437 1.908310378 -1.828362 -0.470234805 0.506543325 -0.48291147
## 383 -0.855910941 1.668667164 -1.657362 -0.961620869 0.542331221 -1.52027684
## 384 0.620451211 0.082229091 -1.662362 0.691223165 -0.197285295 1.26987830
## 385 0.122401329 -0.790072207 -1.647362 0.512537324 -0.924972513 -0.73331001
## 386 -0.678035983 0.202050697 -1.631362 1.227280690 -0.531305657 1.12679342
## 387 -0.784760958 0.695715717 -1.663362 -1.006292329 0.840563687 0.35771220
## 388 -1.496260791 0.508794011 -1.720362 -0.447899074 -0.757962332 -1.77067538
## 389 -1.780860724 -0.152621259 -1.747362 -0.425563344 -0.960760409 -0.48291147
## 390 -0.055473630 0.527965468 -1.647362 -0.738263567 2.009634955 1.16256464
## 391 -1.336173328 0.460865368 -1.662362 -0.849942218 -1.175487784 -1.75278977
## 392 -0.944848420 0.336250897 -1.693362 0.936916197 -0.960760409 -0.51868269
## 393 1.082926102 -0.406643065 -1.588362 -0.805270757 1.019503167 0.71542440
## 394 0.086826337 0.796365867 -1.800362 -0.157534582 1.114937556 -0.16097049
## 395 -0.215561092 0.403350997 -1.731362 0.244508562 -0.376224775 -0.46502586
## 396 -4.680222541 0.959323252 -1.864362 -0.001184471 -1.294780771 -0.98370855
## 397 0.460363749 -0.305992915 -1.546362 1.249616420 -0.590952150 0.60811074
## 398 -0.286711075 0.374593811 -1.698362 2.143045628 -1.032336200 -0.60811074
## 399 1.349738540 1.194173601 -1.724362 -0.514906265 -0.913043214 -0.69753879
## 400 -0.233348588 -0.631907686 -1.755362 -0.537241995 -0.101850906 -0.16097049
## 401 0.140188824 1.323580937 -1.753362 0.378522943 -0.853396721 0.12519927
## 402 -1.407323312 -0.248478544 -1.688362 0.132829911 2.379443213 1.55604806
## 403 2.167963347 -1.830123754 -1.507362 1.584652373 -0.304648983 -0.69753879
## 404 -1.247235849 0.489622554 -1.871362 -1.028628059 0.757058597 -0.39348342
## 405 -1.549623278 0.575894110 -1.796362 -0.648920646 -0.161497399 -0.08942805
## 406 -1.371748320 0.729265767 -1.871362 -0.872277948 0.291815950 -0.19674171
## 407 -1.478473295 1.635117114 -1.830362 -0.202206042 -0.400083372 -0.73331001
## 408 -0.233348588 -1.077644063 -1.609362 1.450637992 -0.972689707 0.41136903
## 409 -0.073261125 -0.147828394 -1.658362 -0.559577725 0.601977714 1.32353513
## 410 0.478151245 -1.810952297 -1.465362 0.780566086 2.618029186 2.87958320
## 411 1.349738540 -0.492914622 -1.497362 1.093266309 -0.113780205 1.46662001## Predicting the 2024 season efficiency
eff24_knn <-
knn.reg(
train = nba_stan,
test = nba24_stan,
y = nba_players$efficient,
k = 5
)
data.frame(
efficient = nba24$efficient,
efficient_hat = eff24_knn$pred
)## efficient efficient_hat
## 1 14.0 11.60
## 2 15.1 13.38
## 3 13.3 11.26
## 4 9.0 11.44
## 5 22.1 18.70
## 6 14.7 14.18
## 7 14.4 12.96
## 8 14.9 13.04
## 9 11.6 13.00
## 10 12.2 11.70
## 11 12.3 12.66
## 12 14.5 13.50
## 13 13.7 13.42
## 14 20.8 17.78
## 15 11.1 11.26
## 16 22.3 18.00
## 17 14.8 11.26
## 18 17.6 13.84
## 19 15.8 14.18
## 20 9.8 10.66
## 21 13.5 12.34
## 22 12.5 12.38
## 23 20.1 18.36
## 24 20.0 17.96
## 25 16.0 14.60
## 26 13.0 11.68
## 27 10.5 10.28
## 28 9.5 10.70
## 29 10.4 9.98
## 30 11.2 11.80
## 31 15.8 13.84
## 32 17.4 14.70
## 33 18.4 17.98
## 34 10.2 10.04
## 35 18.9 16.70
## 36 12.5 10.58
## 37 19.2 16.06
## 38 10.4 9.90
## 39 21.4 18.90
## 40 11.6 10.60
## 41 12.7 11.78
## 42 10.3 10.28
## 43 16.5 13.94
## 44 17.7 13.62
## 45 19.7 18.94
## 46 16.2 13.60
## 47 9.9 10.34
## 48 9.8 10.14
## 49 13.5 11.60
## 50 15.6 14.78
## 51 18.3 20.10
## 52 12.0 11.48
## 53 30.7 20.44
## 54 16.6 13.98
## 55 15.6 12.02
## 56 21.4 17.02
## 57 16.1 12.88
## 58 17.0 16.72
## 59 19.3 18.94
## 60 11.0 9.76
## 61 19.9 17.52
## 62 12.7 12.72
## 63 14.3 14.70
## 64 15.9 15.44
## 65 12.2 10.44
## 66 12.6 11.70
## 67 15.4 15.48
## 68 9.9 12.20
## 69 9.7 11.10
## 70 11.9 11.92
## 71 15.4 11.06
## 72 17.3 17.14
## 73 15.5 15.16
## 74 19.6 14.24
## 75 19.0 17.38
## 76 10.2 13.04
## 77 11.7 10.36
## 78 9.9 10.34
## 79 11.8 13.26
## 80 11.3 11.38
## 81 12.4 10.56
## 82 9.9 10.34
## 83 14.0 12.74
## 84 10.7 10.62
## 85 14.8 17.82
## 86 18.1 16.50
## 87 21.8 16.92
## 88 13.9 11.74
## 89 20.3 17.40
## 90 15.4 16.32
## 91 9.2 10.52
## 92 19.6 18.10
## 93 11.6 9.18
## 94 9.6 9.62
## 95 21.7 17.78
## 96 23.4 17.78
## 97 18.3 18.70
## 98 14.5 10.82
## 99 16.1 13.60
## 100 17.7 15.60
## 101 13.6 14.72
## 102 12.9 12.08
## 103 11.2 10.64
## 104 7.4 9.76
## 105 14.9 13.90
## 106 14.6 14.34
## 107 13.8 12.06
## 108 20.9 18.34
## 109 22.3 17.18
## 110 11.3 10.32
## 111 9.7 13.42
## 112 13.3 12.14
## 113 12.8 12.50
## 114 13.4 13.10
## 115 11.1 10.94
## 116 16.5 16.32
## 117 16.6 10.86
## 118 32.0 24.06
## 119 20.6 18.98
## 120 22.7 18.68
## 121 22.9 18.62
## 122 14.9 13.00
## 123 21.5 18.72
## 124 18.1 16.10
## 125 14.7 13.78
## 126 16.5 16.32
## 127 19.2 16.32
## 128 21.0 17.82
## 129 20.3 17.78
## 130 17.5 16.52
## 131 18.7 15.58
## 132 17.9 16.26
## 133 15.1 13.16
## 134 11.3 11.12
## 135 12.3 11.58
## 136 13.7 11.46
## 137 9.1 7.84
## 138 16.6 16.80
## 139 12.4 13.10
## 140 7.8 9.18
## 141 12.3 10.50
## 142 8.8 9.04
## 143 13.7 13.24
## 144 11.4 11.04
## 145 10.7 9.80
## 146 12.2 11.66
## 147 17.8 14.68
## 148 30.5 23.28
## 149 12.9 13.58
## 150 12.9 11.88
## 151 12.0 11.42
## 152 17.4 16.26
## 153 14.2 13.54
## 154 12.9 10.10
## 155 8.6 10.28
## 156 12.5 12.62
## 157 18.2 16.64
## 158 14.3 13.86
## 159 12.6 11.98
## 160 12.9 11.62
## 161 17.2 13.50
## 162 21.6 18.66
## 163 17.8 16.38
## 164 15.0 13.58
## 165 10.6 12.16
## 166 11.7 12.16
## 167 16.8 13.28
## 168 13.6 13.90
## 169 9.5 10.30
## 170 17.7 16.22
## 171 14.2 11.04
## 172 15.9 13.48
## 173 12.0 11.40
## 174 14.4 13.38
## 175 10.5 9.06
## 176 15.2 13.64
## 177 12.6 10.04
## 178 13.7 12.90
## 179 17.4 16.64
## 180 11.8 11.70
## 181 17.6 16.10
## 182 16.0 14.62
## 183 18.7 16.50
## 184 18.2 12.82
## 185 17.8 17.28
## 186 10.1 10.18
## 187 16.6 18.90
## 188 9.0 9.26
## 189 11.9 12.14
## 190 11.9 12.20
## 191 9.2 9.64
## 192 21.2 19.00
## 193 18.3 18.66
## 194 13.5 13.44
## 195 14.1 13.74
## 196 15.7 13.50
## 197 18.5 16.98
## 198 16.2 14.46
## 199 16.3 16.88
## 200 12.2 11.96
## 201 11.0 11.90
## 202 11.1 14.34
## 203 15.1 12.32
## 204 15.6 16.32
## 205 19.7 14.52
## 206 12.8 10.88
## 207 13.5 10.86
## 208 20.1 18.34
## 209 17.5 13.46
## 210 16.4 14.02
## 211 12.9 11.44
## 212 8.3 8.86
## 213 10.9 11.86
## 214 7.7 8.14
## 215 15.6 14.36
## 216 15.0 14.22
## 217 7.1 8.18
## 218 10.8 10.52
## 219 13.6 11.52
## 220 17.2 16.34
## 221 10.1 9.86
## 222 10.7 11.66
## 223 21.3 19.00
## 224 16.5 17.28
## 225 20.0 17.60
## 226 14.0 13.86
## 227 16.5 18.08
## 228 16.6 16.72
## 229 9.4 10.52
## 230 13.8 11.52
## 231 9.9 12.00
## 232 14.0 15.24
## 233 18.2 15.38
## 234 12.6 13.16
## 235 20.0 17.22
## 236 18.9 16.98
## 237 18.5 14.22
## 238 16.6 17.36
## 239 24.7 18.52
## 240 13.6 14.30
## 241 12.7 14.18
## 242 10.4 11.36
## 243 11.9 12.54
## 244 14.0 13.12
## 245 12.0 10.50
## 246 15.8 13.54
## 247 13.4 12.36
## 248 9.6 9.14
## 249 15.8 17.90
## 250 14.0 13.36
## 251 11.7 10.94
## 252 15.4 17.64
## 253 22.4 16.50
## 254 17.7 16.68
## 255 10.7 10.38
## 256 10.2 10.36
## 257 12.9 16.52
## 258 10.9 10.16
## 259 15.9 16.66
## 260 11.1 11.12
## 261 15.9 13.46
## 262 8.1 8.34
## 263 17.3 15.16
## 264 15.2 14.54
## 265 11.3 10.68
## 266 10.0 15.16
## 267 19.5 17.46
## 268 10.8 9.90
## 269 8.8 8.24
## 270 9.7 8.10
## 271 12.3 10.32
## 272 12.6 10.16
## 273 8.1 8.84
## 274 6.9 6.52
## 275 26.3 18.76
## 276 17.0 14.76
## 277 12.4 15.66
## 278 15.2 16.98
## 279 15.5 12.60
## 280 13.1 13.66
## 281 9.0 8.66
## 282 10.2 10.32
## 283 19.9 17.50
## 284 24.1 17.94
## 285 19.3 18.26
## 286 12.6 12.84
## 287 3.7 6.82
## 288 19.7 17.30
## 289 18.7 13.96
## 290 9.7 9.74
## 291 10.9 11.56
## 292 9.8 8.96
## 293 17.7 16.90
## 294 12.8 12.74
## 295 10.9 12.22
## 296 10.2 11.94
## 297 6.9 8.44
## 298 10.9 9.52
## 299 19.1 19.46
## 300 15.6 13.14
## 301 15.7 14.20
## 302 7.9 8.76
## 303 11.2 10.94
## 304 16.4 12.70
## 305 11.1 12.12
## 306 12.0 12.68
## 307 20.0 17.28
## 308 24.2 16.58
## 309 12.8 12.74
## 310 13.8 13.32
## 311 9.2 10.10
## 312 16.3 13.94
## 313 12.1 11.00
## 314 13.7 11.10
## 315 10.6 12.02
## 316 12.3 12.64
## 317 15.5 12.54
## 318 9.6 9.40
## 319 14.6 13.90
## 320 13.1 9.96
## 321 18.6 16.66
## 322 23.9 18.00
## 323 11.3 10.88
## 324 13.0 15.14
## 325 14.9 15.18
## 326 12.9 14.28
## 327 11.7 10.94
## 328 10.2 11.16
## 329 10.7 9.50
## 330 22.3 15.62
## 331 12.7 10.72
## 332 15.6 15.80
## 333 14.2 12.88
## 334 16.0 15.06
## 335 9.5 10.90
## 336 14.5 13.48
## 337 10.9 11.50
## 338 6.5 11.90
## 339 16.1 11.90
## 340 12.1 12.70
## 341 10.3 12.24
## 342 19.0 16.08
## 343 17.7 17.30
## 344 16.0 17.30
## 345 9.2 6.98
## 346 16.3 12.38
## 347 11.3 11.48
## 348 12.0 10.24
## 349 20.2 19.26
## 350 9.1 12.66
## 351 15.2 15.94
## 352 10.8 11.52
## 353 10.8 10.72
## 354 11.4 11.56
## 355 12.6 12.22
## 356 18.8 16.42
## 357 9.8 10.48
## 358 8.5 10.12
## 359 12.1 11.06
## 360 8.9 14.48
## 361 20.5 17.32
## 362 14.5 14.84
## 363 16.7 15.48
## 364 11.4 11.14
## 365 10.5 9.62
## 366 10.8 15.20
## 367 11.5 11.48
## 368 13.0 14.34
## 369 3.7 6.68
## 370 17.3 16.70
## 371 8.3 9.98
## 372 20.1 18.70
## 373 12.0 11.56
## 374 13.2 13.78
## 375 11.0 11.22
## 376 7.5 8.14
## 377 18.4 13.60
## 378 10.8 8.68
## 379 19.0 16.68
## 380 12.2 10.10
## 381 14.4 13.54
## 382 12.2 12.04
## 383 9.8 10.32
## 384 17.8 15.62
## 385 14.6 12.42
## 386 12.3 15.96
## 387 12.4 11.04
## 388 5.6 7.86
## 389 10.2 7.84
## 390 17.5 16.14
## 391 7.4 7.84
## 392 14.4 10.86
## 393 18.3 18.44
## 394 16.8 13.42
## 395 11.9 12.54
## 396 2.4 3.92
## 397 19.2 16.08
## 398 13.9 13.26
## 399 13.6 12.80
## 400 11.9 11.12
## 401 17.6 12.82
## 402 15.4 15.72
## 403 19.8 18.70
## 404 10.1 10.06
## 405 11.9 8.86
## 406 9.8 9.14
## 407 10.3 8.58
## 408 18.4 17.30
## 409 14.7 15.18
## 410 27.3 19.80
## 411 22.3 17.98Part 3b) Fit statistics for NBA 24
Using the predictions from 3a), calculate \(R^2\), \(\text{rmse}\), and \(\text{MAE}\) for the 2024-2025 data.
## SSE for nba24
SSE24 <- sum((nba24$efficient - eff24_knn$pred)^2)
## R^2:
Rsquared24 <- 1 - SSE24 / sum((nba24$efficient - mean(nba24$efficient))^2)
## rmse
rmse24 <- sqrt(SSE24 /(nrow(nba24) - 1))
## MAE
mae24 <- mean(abs(nba24$efficient - eff24_knn$pred))
c(
'R-squared' = Rsquared24,
'rmse24' = rmse24,
'mae24' = mae24
)## R-squared rmse24 mae24
## 0.7046397 2.3126475 1.7056448How do the fit statistics compare to the ones calculated in part 2c (Better, worse)? Briefly explain why the results are not surprising
Part 3c: R-squared plot
Create a scatter plot to compare the efficiency for the 2024 - 2025 season to the predicted efficiency using an R-squared plot, which is a scatter plot with \(\hat{y}\) on the x-axis and \(y\) on the y-axis. Color each point by the player’s position. Make sure to make the graph look nice!
ggplot(
data = data.frame(y = nba24$efficient,
y_hat = eff24_knn$pred,
position = nba24$position),
mapping = aes(
x = y_hat,
y = y,
color = position
)
) +
geom_point() +
theme_bw()
Does it appear that kNN predicts efficiency well?