R Notebook
In class activity 12 Question 1 How many observations do we have in the training dataset?
We have 835 observations in the training dataset(NBA_train)
# 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 ...Question 2 Is there any chance that a team winning 38 games can make it to the playoffs? Why? Based on historical data, there is about a 50% that a team with 38 wins can make the playoffs. Now with the new format implemented in recent years, a team with 38 wins would have an even higher chance to make it.
# 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 1Question 3 What is the number of wins that can guarantee for any team a presence in the playoffs based on historical data?
Based on our results, a team with 49 wins has never failed to make the playoffs.
# 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-16Question 4 Can you determine (visually) if there is any relationship between the points difference (PTSdiff) and the number of wins (W)?Explain.
By looking into the scatter plot displayed above, we can notice that there exists a correlation between our dependent variable: number of wins and our independent variable: points difference.
Question 5 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?
Based on the output, yes, the predictor Points Difference, is significant at a 5% significance level. (p-value <<<0.05 or |t|>>>2)
Question 6 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?
Based on the model output, BLK (number of blocks) is not significant at a 5% significance level. (p-value=0.5256 > 0.05)
# 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-16Question 7 What has been the maximum number of points in a season? The maximum number of points scored in a season is 10,371.
max(NBA$PTS)[1] 10371Question 8 What is the meaning of the RMSE(Root mean squared error) in the PointsReg model? Are you satisfied with this value?
It is the average distance between the actual values and the theoretical values on the regression line.
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.
#Based on WinsReg Model, Wins = Intercept + coefficient * points difference
#49=41+0.03259*PtsDiff
IdealPtsDiff =(49-41)/0.03259
IdealPtsDiff[1] 245.4741The expected point difference for a team to make it to the postseason is 245 points.