Statistics Set 4

This notbeook is for practice using baseball data to render univariate and multivariant linear models.

Univariate Linear Regression Model

Create a ULR model using some player stat to predict salary. Do the following:

With the baseball data linked above (some of it was explored in Statistics 4), create a univariate Linear Regression model predicting player salary using some player stat.
You will need to join a second table to the “Salaries.csv” table.
Cross-validate your model, and produce 68, 95, and 99.7% confidence intervals for your “slope”.
Report the R2R2 score for your univariate model.
Make a scatter plot of your data, with your model predictions overlaid in red.

Import and Clean data

We import the two files of salary and batting stats and remove the batter stats that have NaN in a column so we can process later.



In [1]:

    
import pandas as pd
import numpy as np
import os
import matplotlib.pyplot as plt
%matplotlib inline

baseball_dir = "lahman-csv_2015-01-24/"
salaries = pd.read_csv(baseball_dir + "Salaries.csv", sep=",")
batting = pd.read_csv(baseball_dir + "Batting.csv", sep=",")
batting.dropna(inplace=True)
batting.info()









    



<class 'pandas.core.frame.DataFrame'>
Int64Index: 58058 entries, 4560 to 99845
Data columns (total 22 columns):
playerID    58058 non-null object
yearID      58058 non-null int64
stint       58058 non-null int64
teamID      58058 non-null object
lgID        58058 non-null object
G           58058 non-null int64
AB          58058 non-null float64
R           58058 non-null float64
H           58058 non-null float64
2B          58058 non-null float64
3B          58058 non-null float64
HR          58058 non-null float64
RBI         58058 non-null float64
SB          58058 non-null float64
CS          58058 non-null float64
BB          58058 non-null float64
SO          58058 non-null float64
IBB         58058 non-null float64
HBP         58058 non-null float64
SH          58058 non-null float64
SF          58058 non-null float64
GIDP        58058 non-null float64
dtypes: float64(16), int64(3), object(3)
memory usage: 10.2+ MB

We are combining the two sheets by linking by player ID below and combines them into one giant table, then create a plot of all data points of batters who have hit at least one home run.



In [2]:

    
total_salaries = salaries.groupby(["playerID"])["salary"].sum()
total_batting = batting.groupby(["playerID"])[["HR", 'HBP', 'G','stint']].sum()

all_stats = pd.concat((total_batting, total_salaries), axis=1)
all_stats = all_stats[(all_stats.HR > 0) & (all_stats.salary > 0)]



In [3]:

    
plt.figure(figsize=(12, 4))
plt.scatter(all_stats.HR, all_stats.salary, edgecolor="None",
            s=5, c='k', alpha=0.2)
plt.yscale("log")
plt.xlabel("Home Runs", fontsize=12); plt.ylabel("Salary ($)", fontsize=12)
plt.minorticks_on()
plt.xlim(-50, 800)
plt.show()

We are creating a linear regression univariate model to best fit our data points that takes the home runs as our 'x' input and salary as our 'y'.



In [4]:

    
from sklearn import linear_model
import sklearn.cross_validation as cv

kfolds = cv.KFold(len(all_stats), n_folds=10)

regressor = linear_model.LinearRegression()
Xvals = np.array(all_stats.HR)[:, np.newaxis]
yvals = np.array(all_stats.salary)

slopes, intercepts = [], []

for train_index, test_index in kfolds:
    X_train, X_test = Xvals[train_index], Xvals[test_index]
    y_train, y_test = yvals[train_index], yvals[test_index]
    regressor.fit(X_train, y_train)
    slopes.append(regressor.coef_)
    intercepts.append(regressor.intercept_)

slope = np.mean(slopes)
intercept = np.mean(intercepts)

regressor.coef_ = slope
regressor.intercept_ = intercept

print("Our model is:\n\tSalary = %.2f x N_HomeRuns + %.2f" % (slope, intercept))









    



Our model is:
	Salary = 179557.56 x N_HomeRuns + 2702208.34



In [5]:

    
plt.figure(figsize=(12, 4))
plt.scatter(all_stats.HR, all_stats.salary, edgecolor="None",
            s=5, c='k', alpha=0.2)
plt.scatter(Xvals, regressor.predict(Xvals), edgecolor="None",
            s=2, c='r')
plt.yscale("log")
plt.xlabel("Home Runs", fontsize=12); plt.ylabel("Salary ($)", fontsize=12)
plt.minorticks_on()
plt.xlim(-50, 800)
plt.show()

Our r^2 value is .376 as seen below.



In [6]:

    
print("Score: {0}".format(regressor.score(Xvals, yvals)))









    



Score: 0.37611646407181426

Multivariate Linear Regression Model

Using no more than 4 characteristics, create a multivariate Linear Regression model predicting player salary.
Report the R2R2 score for your multivariate model. Aim for R2>0.5R2>0.5.
Make a scatter plot of your data side-by-side with a scatter plot of your model predictions.

We have included the categories games, home runs, hit by pitcher, and stint for our four mulitvariant categories.



In [7]:

    
N_folds = 10
kfolds = cv.KFold(len(all_stats), n_folds=N_folds)

regressor = linear_model.LinearRegression()
valid_data = ["HR", 'HBP', 'G', 'stint']
Xvals = np.array(all_stats[valid_data])
yvals = np.array(all_stats.salary)

coeffs, intercepts = [], []

for train_index, test_index in kfolds:
    X_train, X_test = Xvals[train_index], Xvals[test_index]
    y_train, y_test = yvals[train_index], yvals[test_index]
    regressor.fit(X_train, y_train)
    coeffs.append(regressor.coef_)
    intercepts.append(regressor.intercept_)

coeffs = np.array(coeffs).mean(axis=0) #averages each column
intercept = np.array(intercepts).mean(axis=0)

regressor.coef_ = coeffs
regressor.intercept_ = intercept

Using these four categories we were able to get an r^2 value of .414 as seen below.



In [8]:

    
print("Score: {0}".format(regressor.score(Xvals, yvals)))









    



Score: 0.41481368292482745

Below gives us our model versus the actual data.



In [9]:

    
fig = plt.figure(figsize=(12, 4))
fig.subplots_adjust(wspace=0)
ax = plt.subplot(121)
ax.scatter(all_stats.HR, all_stats.salary, edgecolor="None",
            s=5, c='k', alpha=0.2)
ax.set_yscale("log")
ax.set_xlabel("Home Runs", fontsize=12); ax.set_ylabel("Salary ($)", fontsize=12)
ax.set_xlim(-50, 800); ax.minorticks_on()

ax = plt.subplot(122)
ax.scatter(Xvals[:, 1], regressor.predict(Xvals), edgecolor="None",
            s=2, c='r')
ax.set_xlabel("Home Runs", fontsize=12)
ax.set_ylim(1E4, 1E9)
ax.set_yscale("log"); ax.set_yticklabels([])
ax.set_xlim(-50, 800); ax.minorticks_on()

plt.show()