title: Seaborn Regplot and Scikit-Learn Logistic Models Calculated Differently?
body: <p>I'm using both the Scikit-Learn and Seaborn logistic regression functions -- the former for extracting model info (i.e. log-odds, parameters, etc.) and the later for plotting the resulting sigmoidal curve fit to the probability estimations.</p>
  
  <p>Maybe my intuition is incorrect for how to interpret this plot, but I don't seem to be getting results as I'd expect:</p>
  
  <pre><code>#Build and visualize a simple logistic regression
  ap_X = ap[['TOEFL Score']].values 
  ap_y = ap['Chance of Admit'].values
  
  ap_lr = LogisticRegression()
  ap_lr.fit(ap_X, ap_y)
  
  def ap_log_regplot(ap_X, ap_y):
      plt.figure(figsize=(15,10))
      sns.regplot(ap_X, ap_y, logistic=True, color='green')
      return None
  
  ap_log_regplot(ap_X, ap_y)
  plt.xlabel('TOEFL Score')
  plt.ylabel('Probability')
  plt.title('Logistic Regression: Probability of High Chance by TOEFL Score')
  plt.show
  </code></pre>
  
  <p><a href="https://i.stack.imgur.com/7jaL3.png" rel="noreferrer"><img src="https://i.stack.imgur.com/7jaL3.png" alt="enter image description here"></a></p>
  
  <p>Seems alright, but then I attempt to use the <code>predict_proba</code> function in Scikit-Learn to find the probabilities of <code>Chance to Admit</code> given some arbitrary value for <code>TOEFL Score</code> (in this case 108, 104, and 112):</p>
  
  <pre><code>eight = ap_lr.predict_proba(108)[:, 1]
  four = ap_lr.predict_proba(104)[:, 1]
  twelve = ap_lr.predict_proba(112)[:, 1]
  print(eight, four, twelve)
  </code></pre>
  
  <p>Where I get:</p>
  
  <pre><code>[0.49939019] [0.44665597] [0.55213799]
  </code></pre>
  
  <p>To me, this seems to indicate that a TOEFL Score of 112 gives an individual a 55% chance of being admitted based on this data set. If I were to extend a vertical line from 112 on the x-axis to the sigmoid curve, I'd expect the intersection at around .90.</p>
  
  <p>Am I interpreting/modeling this correctly? I realize that I'm using two different packages to calculate the model coefficients but with another model using a different data set, I seem to get correct predictions that fit the logistic curve.</p>
  
  <p>Any ideas or am I completely modeling/interpreting this inaccurately?</p>