python sklearn multiple linear regression display

Question

I calculated my multiple linear regression equation and I want to see the adjusted R-squared. I know that the score function allows me to see r-squared, but it is not adjusted.

import pandas as pd #import the pandas module
import numpy as np
df = pd.read_csv ('/Users/jeangelj/Documents/training/linexdata.csv', sep=',')
df
       AverageNumberofTickets   NumberofEmployees   ValueofContract Industry
   0              1                    51                  25750    Retail
   1              9                    68                  25000    Services
   2             20                    67                  40000    Services
   3              1                   124                  35000    Retail
   4              8                   124                  25000    Manufacturing
   5             30                   134                  50000    Services
   6             20                   157                  48000    Retail
   7              8                   190                  32000    Retail
   8             20                   205                  70000    Retail
   9             50                   230                  75000    Manufacturing
  10             35                   265                  50000    Manufacturing
  11             65                   296                  75000    Services
  12             35                   336                  50000    Manufacturing
  13             60                   359                  75000    Manufacturing
  14             85                   403                  81000    Services
  15             40                   418                  60000    Retail
  16             75                   437                  53000    Services
  17             85                   451                  90000    Services
  18             65                   465                  70000    Retail
  19             95                   491                  100000   Services

from sklearn.linear_model import LinearRegression
model = LinearRegression()
X, y = df[['NumberofEmployees','ValueofContract']], df.AverageNumberofTickets
model.fit(X, y)
model.score(X, y)
>>0.87764337132340009

I checked it manually and 0.87764 is R-squared; whereas 0.863248 is the adjusted R-squared.

Answer 1

There are many different ways to compute R^2 and the adjusted R^2, the following are few of them (computed with the data you provided):

from sklearn.linear_model import LinearRegression
model = LinearRegression()
X, y = df[['NumberofEmployees','ValueofContract']], df.AverageNumberofTickets
model.fit(X, y)

SST = SSR + SSE (ref definitions)

# compute with formulas from the theory
yhat = model.predict(X)
SS_Residual = sum((y-yhat)**2)       
SS_Total = sum((y-np.mean(y))**2)     
r_squared = 1 - (float(SS_Residual))/SS_Total
adjusted_r_squared = 1 - (1-r_squared)*(len(y)-1)/(len(y)-X.shape[1]-1)
print r_squared, adjusted_r_squared
# 0.877643371323 0.863248473832

# compute with sklearn linear_model, although could not find any function to compute adjusted-r-square directly from documentation
print model.score(X, y), 1 - (1-model.score(X, y))*(len(y)-1)/(len(y)-X.shape[1]-1)
# 0.877643371323 0.863248473832 

Another way:

# compute with statsmodels, by adding intercept manually
import statsmodels.api as sm
X1 = sm.add_constant(X)
result = sm.OLS(y, X1).fit()
#print dir(result)
print result.rsquared, result.rsquared_adj
# 0.877643371323 0.863248473832

Yet another way:

# compute with statsmodels, another way, using formula
import statsmodels.formula.api as sm
result = sm.ols(formula="AverageNumberofTickets ~ NumberofEmployees + ValueofContract", data=df).fit()
#print result.summary()
print result.rsquared, result.rsquared_adj
# 0.877643371323 0.863248473832