library(readr)
NBA <- read.csv("NBA_train.csv")
# 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)

The plot shows the difference (PTSdiff) and the number of wins (W) for the NBA teams in the dataset. The number of wins has a positive correlation, so we can see how it increases in the plot. This indicates that a significant number of wins can ensure the team makes it to the playoffs.

# 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

The linear regression shows the difference in points (PTSdiff) and the number of wins (W). It shows that a team that wins 41 games makes it to the playoffs. The results are statistically significant because the PV < 2e-16.