NBA dataset analysis and linear regression prediction.

nba.R

NBA <- read.csv('nba_train.csv')

# Seems around 42 wins, the team has a good chance of making it to the playoffs.
table(NBA$W, NBA$Playoffs)

NBA$PTSdiff <- NBA$PTS - NBA$oppPTS
WinsReg <- lm(W ~ PTSdiff, data = NBA)

PointsReg <- lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + TOV + STL + BLK, data=NBA)
SSE <- sum(PointsReg$residuals^2)
# Average error is 184 points.
RMSE <- sqrt(SSE / nrow(NBA))
# Average points for a year is 8370, so an error of 184 points isn't so bad.
mean(NBA$PTS)

# Remove TOV because p-value is largest value, so the least statistically significant.
PointsReg2 <- lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + DRB + STL + BLK, data=NBA)

# Remove DRB because highest p-value. Notice R-squared stays the same, so we're justified in removing the feature.
PointsReg3 <- lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + STL + BLK, data=NBA)

# Remove BLK. R-squared stays the same, looking good.
PointsReg4 <- lm(PTS ~ X2PA + X3PA + FTA + AST + ORB + STL, data=NBA)

SSE4 <- sum(PointsReg4$residuals^2)
# Average error is 184.5, about the same as first model, but simpler (less features).
RMSE4 <- sqrt(SSE4 / nrow(NBA))

NBA_test <- read.csv('NBA_test.csv')

# Predict how many points in 2012-2013 season.
PointsPredictions <- predict(PointsReg4, newdata=NBA_test)

SSE_test <- sum((PointsPredictions - NBA_test$PTS)^2)
SST <- sum((mean(NBA$PTS) - NBA_test$PTS)^2)
# R-squared is 0.81
R2 <- 1 - SSE_test/SST
# Root mean squared error on the test set is 196, close to the training set.
RMSE_test <- sqrt(SSE_test / nrow(NBA_test))