Predictive analytics Assignment PDF

Introduction
Predictive analytics is often viewed as a segment of data analytics whose role is majorly
to determine a set of unknown future values given historical data. In an article on the role of
predictive analytics, Batterham, Christensen, and Mackinnon (2009) note that, “...the science of
predictive analytics can generate future insights with a significant degree of precision.”
Therefore, well defined and logical models are crucial in offering significant forecast on future
performance on virtually any endeavor as long as there is reliable data.
Elsewhere, Hastie, Tibshirani and Friedman (2001) define predictive analytics as a
stepwise method of examining meaningful information from data using specified tools and
methodologies.
However, in the world of data, it is not always true that complete historical data will
always available. In such scenarios, predictive analytics is essentially the best option to enable
precise re-imaging of how the original outcome would be given ideal conditions.
Purpose of project
The purpose of this paper is therefore to employ the use of logical and well defined
predictive analytics tools to predict the performance of the teams in the 2016-2017 and 2017-
2018 seasons of the NBA using historical data given the loss of win and loss data. As such, the
project outcomes will include prediction of wins and determining which teams will be in the
playoffs in the 2016-2017 and 2017-2018 seasons.

Predictive modeling
Given the above argument, it is clear that in predictive modeling, the main objective is to
predict the outcome of a single response variable, say Y, given either multiple or a single
predictor variable X.
Multiple regression predictive tool
One of the methods used in analysis of relationships between different factors is linear
regression. In simple linear regression, a single response variable is assumed to be linearly
related to a single predictor variable. In contrast, multiple linear regression is used to examine
the relationship between a single response variable with multiple predictor variables hence the
model of the form:
Yi = α + β1Xi,1 + · · · + βpXi,p + £i Where ; α= Y intercept, βi, i=1,2,..., p are the
regressors coefficients and Xi are the predictor
variables.
Given the purpose of the project, multiple linear regression will be the effective tool for
predicting future wins given historical data.
Process of multiple regression modeling
Initially, the win/loss proxy stats from the historical data are dropped due to their effect
on the prediction outcome. Now, in prediction of the NBA wins for the seasons 2010-2011 to
2015-2016, the following multiple regression model is adopted:
Win= α + β1Age+ β2 Offensive Rating+ β3 Defensive Rating+ β4 Offensive Rebound+...+ β16
Turnover %

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.95382
R Square 0.909773
Adjusted R0.900917
Standard E4.079699
Observatio 180
ANOVA
df SS MS F Significance F
Regression 16 27355.37 1709.71 102.7227 2.49E-76
Residual 163 2712.963 16.64394
Total 179 30068.33
CoefficientsStandard Error t Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0%
Intercept -161.164 150.8347 -1.06848 0.286883 -459.006 136.6778 -459.006 136.6778
Age 0.681496 0.221691 3.074084 0.002476 0.24374 1.119252 0.24374 1.119252
Offensive R2.113902 1.811313 1.167055 0.244893 -1.46276 5.690565 -1.46276 5.690565
Defensive -0.80814 1.509823 -0.53526 0.593203 -3.78947 2.173193 -3.78947 2.173193
Offensive 0.04298 0.967672 0.044416 0.964627 -1.86781 1.953768 -1.86781 1.953768
Free throw -47.8179 50.44918 -0.94784 0.344613 -147.436 51.8003 -147.436 51.8003
1.697983 2.039191 0.832675 0.406247 -2.32865 5.724619 -2.32865 5.724619
Opp Effecti -173.196 236.1274 -0.73349 0.464316 -639.459 293.067 -639.459 293.067
Free Throw-78.9851 284.5738 -0.27756 0.781705 -640.911 482.9412 -640.911 482.9412
3-Point At 3.994306 12.45832 0.320614 0.748914 -20.6062 28.59481 -20.6062 28.59481
Free Throw33.38872 138.7253 0.240682 0.810104 -240.542 307.3192 -240.542 307.3192
Effective F -171.814 562.0798 -0.30568 0.760241 -1281.71 938.0821 -1281.71 938.0821
Defensive 0.930437 0.785285 1.18484 0.237805 -0.62021 2.48108 -0.62021 2.48108
Net Rating 0.015544 0.009414 1.651138 0.100636 -0.00305 0.034132 -0.00305 0.034132
247.3421 684.8978 0.361137 0.718464 -1105.07 1599.758 -1105.07 1599.758
Pace Facto 0.119268 0.151237 0.788617 0.431481 -0.17937 0.417905 -0.17937 0.417905
Opponent Turnover
True Shooting%
Figure 1:Original model
That is, all the predictor variables are included in the model. The R-squared of the model
is 0.9538 indicating that the model accounts for up to 95% of the variability. However, from the
output, not all variables are significant in predicting the wins. Using a confidence interval of
95%, the only significant variable is age with a p-value of 0.0024 which is less than 0.05. In

order to determine the significance of each variable, every predictor variable is examined
individually.
Upon individual examination of the variables significance, only the following variables were
significant with p-values of below 0.05:
i. Age
ii. Offensive Rating
iii. Defensive Rating
iv. Turnover %
v. True Shooting%
vi. Effective Field Goal %
vii. Offensive rebound %
Given that the original predictive model was multiple regression all the significant variables
which were then standardized to increase the models precision, however, the new model
accounts for only 95% of the variability. The variables were then included in the new model that
is:
Win= α + β1Age+ β2 Offensive Rating+ β3 Defensive Rating+ β4 Turnover % + β4 True
Shooting%+ β4 Effective Field Goal % + β16 Offensive rebound%