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

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 ...

Answer:
We have 835 observations in the training dataset.

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

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

Answer:
Yes, there’s a chance. The table shows some teams with 38 wins made the playoffs, though not all. It depends on the specific season and other teams’ performance.

C. What is the number of wins that can guarantee playoff presence?

Answer:
According to the table, teams with 50 or more wins always made the playoffs based on historical data.

D. Is there a relationship between the points difference and the number of wins?

NBA$PTSdiff = NBA$PTS - NBA$oppPTS
plot(NBA$PTSdiff, NBA$W)

Answer:
Yes, visually there’s a strong positive relationship. As points difference increases, so does the number of wins.

E. Is points difference (PTSdiff) significant in predicting wins?

WinsReg = lm(W ~ PTSdiff, data = NBA)
summary(WinsReg)
## 
## Call:
## lm(formula = W ~ PTSdiff, data = NBA)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.7393 -2.1018 -0.0672  2.0265 10.6026 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.100e+01  1.059e-01   387.0   <2e-16 ***
## PTSdiff     3.259e-02  2.793e-04   116.7   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.061 on 833 degrees of freedom
## Multiple R-squared:  0.9423, Adjusted R-squared:  0.9423 
## F-statistic: 1.361e+04 on 1 and 833 DF,  p-value: < 2.2e-16

Answer:
Yes, PTSdiff is significant with a p-value < 2e-16, which is well below 0.05.

F. Is number of blocks (BLK) significant at a 5% 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-16

Answer:
No, the p-value for BLK is around 0.63, which is greater than 0.05, so it’s not statistically significant.

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

max(NBA$PTS)
## [1] 10371

Answer:
The maximum number of points scored in a season is calculated directly above.

H. What is the meaning of the RMSE in the PointsReg model? Are you satisfied with it?

SSE = sum(PointsReg$residuals^2)
RMSE = sqrt(SSE / nrow(NBA))
RMSE
## [1] 184.4049

Answer:
The RMSE is about 184.4, meaning the model’s predictions are off by ±184 points on average. Since the average team scores about 8370 points, this is a small error, so yes, I’m satisfied with it.