Activity 12 and 13

# VIDEO 1

# Read in the data
NBA = read.csv("NBA_train.csv")
str(NBA)

'data.frame':   835 obs. of  20 variables:
 $ SeasonEnd: int  1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 ...
 $ Team     : chr  "Atlanta Hawks" "Boston Celtics" "Chicago Bulls" "Cleveland Cavaliers" ...
 $ Playoffs : int  1 1 0 0 0 0 0 1 0 1 ...
 $ W        : int  50 61 30 37 30 16 24 41 37 47 ...
 $ PTS      : int  8573 9303 8813 9360 8878 8933 8493 9084 9119 8860 ...
 $ oppPTS   : int  8334 8664 9035 9332 9240 9609 8853 9070 9176 8603 ...
 $ FG       : int  3261 3617 3362 3811 3462 3643 3527 3599 3639 3582 ...
 $ FGA      : int  7027 7387 6943 8041 7470 7596 7318 7496 7689 7489 ...
 $ X2P      : int  3248 3455 3292 3775 3379 3586 3500 3495 3551 3557 ...
 $ X2PA     : int  6952 6965 6668 7854 7215 7377 7197 7117 7375 7375 ...
 $ X3P      : int  13 162 70 36 83 57 27 104 88 25 ...
 $ X3PA     : int  75 422 275 187 255 219 121 379 314 114 ...
 $ FT       : int  2038 1907 2019 1702 1871 1590 1412 1782 1753 1671 ...
 $ FTA      : int  2645 2449 2592 2205 2539 2149 1914 2326 2333 2250 ...
 $ ORB      : int  1369 1227 1115 1307 1311 1226 1155 1394 1398 1187 ...
 $ DRB      : int  2406 2457 2465 2381 2524 2415 2437 2217 2326 2429 ...
 $ AST      : int  1913 2198 2152 2108 2079 1950 2028 2149 2148 2123 ...
 $ STL      : int  782 809 704 764 746 783 779 782 900 863 ...
 $ BLK      : int  539 308 392 342 404 562 339 373 530 356 ...
 $ TOV      : int  1495 1539 1684 1370 1533 1742 1492 1565 1517 1439 ...

# VIDEO 2

# How many wins to make the playoffs?
table(NBA$W, NBA$Playoffs)

    
      0  1
  11  2  0
  12  2  0
  13  2  0
  14  2  0
  15 10  0
  16  2  0
  17 11  0
  18  5  0
  19 10  0
  20 10  0
  21 12  0
  22 11  0
  23 11  0
  24 18  0
  25 11  0
  26 17  0
  27 10  0
  28 18  0
  29 12  0
  30 19  1
  31 15  1
  32 12  0
  33 17  0
  34 16  0
  35 13  3
  36 17  4
  37 15  4
  38  8  7
  39 10 10
  40  9 13
  41 11 26
  42  8 29
  43  2 18
  44  2 27
  45  3 22
  46  1 15
  47  0 28
  48  1 14
  49  0 17
  50  0 32
  51  0 12
  52  0 20
  53  0 17
  54  0 18
  55  0 24
  56  0 16
  57  0 23
  58  0 13
  59  0 14
  60  0  8
  61  0 10
  62  0 13
  63  0  7
  64  0  3
  65  0  3
  66  0  2
  67  0  4
  69  0  1
  72  0  1

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

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

# Linear regression model for wins
WinsReg = lm(W ~ PTSdiff, data=NBA)
summary(WinsReg)

Call:
lm(formula = W ~ PTSdiff, data = NBA)

Residuals:
    Min      1Q  Median      3Q     Max 
-9.7393 -2.1018 -0.0672  2.0265 10.6026 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 4.100e+01  1.059e-01   387.0   <2e-16 ***
PTSdiff     3.259e-02  2.793e-04   116.7   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.061 on 833 degrees of freedom
Multiple R-squared:  0.9423,    Adjusted R-squared:  0.9423 
F-statistic: 1.361e+04 on 1 and 833 DF,  p-value: < 2.2e-16

# VIDEO 3

# Linear regression model for points scored
PointsReg = lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + TOV + STL + BLK, data=NBA)
summary(PointsReg)

Call:
lm(formula = PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + TOV + 
    STL + BLK, data = NBA)

Residuals:
    Min      1Q  Median      3Q     Max 
-527.40 -119.83    7.83  120.67  564.71 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -2.051e+03  2.035e+02 -10.078   <2e-16 ***
X2PA         1.043e+00  2.957e-02  35.274   <2e-16 ***
X3PA         1.259e+00  3.843e-02  32.747   <2e-16 ***
FTA          1.128e+00  3.373e-02  33.440   <2e-16 ***
AST          8.858e-01  4.396e-02  20.150   <2e-16 ***
ORB         -9.554e-01  7.792e-02 -12.261   <2e-16 ***
DRB          3.883e-02  6.157e-02   0.631   0.5285    
TOV         -2.475e-02  6.118e-02  -0.405   0.6859    
STL         -1.992e-01  9.181e-02  -2.169   0.0303 *  
BLK         -5.576e-02  8.782e-02  -0.635   0.5256    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 185.5 on 825 degrees of freedom
Multiple R-squared:  0.8992,    Adjusted R-squared:  0.8981 
F-statistic: 817.3 on 9 and 825 DF,  p-value: < 2.2e-16

SSE = sum(PointsReg$residuals^2)
SSE

[1] 28394314

# Root mean squared error
RMSE = sqrt(SSE/nrow(NBA))
RMSE

[1] 184.4049

# Average number of points in a season
mean(NBA$PTS)

[1] 8370.24

# Remove insignifcant variables
summary(PointsReg)

Call:
lm(formula = PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + TOV + 
    STL + BLK, data = NBA)

Residuals:
    Min      1Q  Median      3Q     Max 
-527.40 -119.83    7.83  120.67  564.71 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -2.051e+03  2.035e+02 -10.078   <2e-16 ***
X2PA         1.043e+00  2.957e-02  35.274   <2e-16 ***
X3PA         1.259e+00  3.843e-02  32.747   <2e-16 ***
FTA          1.128e+00  3.373e-02  33.440   <2e-16 ***
AST          8.858e-01  4.396e-02  20.150   <2e-16 ***
ORB         -9.554e-01  7.792e-02 -12.261   <2e-16 ***
DRB          3.883e-02  6.157e-02   0.631   0.5285    
TOV         -2.475e-02  6.118e-02  -0.405   0.6859    
STL         -1.992e-01  9.181e-02  -2.169   0.0303 *  
BLK         -5.576e-02  8.782e-02  -0.635   0.5256    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 185.5 on 825 degrees of freedom
Multiple R-squared:  0.8992,    Adjusted R-squared:  0.8981 
F-statistic: 817.3 on 9 and 825 DF,  p-value: < 2.2e-16

PointsReg4 = 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] 28421465

RMSE_4

[1] 184.493

# Read in test set
NBA_test = read.csv("NBA_test.csv")

# Make predictions on test set
PointsPredictions = predict(PointsReg4, newdata=NBA_test)

# Compute out-of-sample R^2
SSE = sum((PointsPredictions - NBA_test$PTS)^2)
SST = sum((mean(NBA$PTS) - NBA_test$PTS)^2)
R2 = 1 - SSE/SST
R2

[1] 0.8127142

# Compute the RMSE
RMSE = sqrt(SSE/nrow(NBA_test))
RMSE 

[1] 196.3723

Questions: Activity 12 How many observations do we have in the training dataset? 835 entries

Is there any chance that a team winning 38 games can make it to the playoffs? Why? Yes, there is a chance. We have seen that 7 out of 15 times teams with 38 wins have managed to quality to the play-offs

What is the number of wins that can guarantee for any team a presence in the playoffs based on historical data? Our data shows that the number of wins that guarantee any wins is 49

Can you determine (visually) if there is any relationship between the points difference (PTSdiff) and the number of wins (W)?Explain. Yes, let us look at the scatter-plot displayed below. We can see that here is a strong positive linear relationship between number of wins and points difference in the NBA. The trend is upward sloping

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? The model we built above used points difference as the only predictor to estimate the number of wins. Yes, the predictor PTSdiff is significant at a 5% significance level

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? Model PointReg indicates that BLK (blocks) is not signifficant at the 5% significance level

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

max(NBA$PTS)

[1] 10371

The maximum number of points in a season has been 10371

What is the meaning of the RMSE(Root mean squared error) in the PointsReg model? Are you satisfied with this value? This is the average distance between observed and predicted values (number of points scored). A low RMSE score ensures that the prediction model is capable of archiving great accuracy. Therefore, I am satisfied with this value

How well did your predictions work on the testing dataset? Report the new R2 and RMSE. R2 is 0.81 and RMSE is 196.87

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.

#Wins = Intercept + Estimate * RDiff
# We are told that the desired number of wins is 49, and we are able to obtain
# intercept and estimate from the model summary
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

Win = 49, Intercept = 41, Estimate = .03259 Now, we need to solve for RD

Expected_RD =  ((49-41)/.03259)
Expected_RD

[1] 245.4741

we can see that the expected points difference is 245.5 which is above the RMSE value.