Answers.Body: <p>Mm, I understand what you want to say, but I think you're slightly wrong with terminology. If you consider a d-dimensional vector space, people usually a hyper-plane (d - 1)-dimensional, because it's a subspace of lower dimensionality. So for your example d = 2 the logistic regression would fit a 1-dimentional line (which would separate 2 classes) and the linear regression would fit a 2-dimentional plane (for every combination of 2 features the prediction would lay on some plane in 3-D space). So the general rule would be logreg -&gt; (d-1)-dimensional hyperplane in d-dimensional vector space, linear regression -&gt; d-dimensional hyperplane in (d+1)-dimensional vector space.</p>
  
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Answers.CreationDate: 2020-09-10T21:57:57.417Z
Answers.LastActivityDate: 2020-09-10T21:57:57.417Z
Answers.UserDisplayName: Michał Słodki
Body: <p>Geometric interpretation of Logistic Regression and Linear regression is considered here.</p>
  <p>I was going through Logistic regression and Linear regression. In the optimization equation of both following term is used. <span class="math-container">$$W^{T}.X$$</span></p>
  <p>W is a vector which holds weights of the hyper-plane.</p>
  <p>I realized following about the dimensions of the fitted hyper-plane. Want to confirm it.</p>
  <p>Let,
  d = Number of features for both Logistic Regression and Linear Regression.</p>
  <p>Logistic Regression case:
  Fitted hyper-plane is d-dimensional.</p>
  <p>Linear Regression case:
  Fitted hyper-plane is (d + 1) dimensions.</p>
  <p>Example</p>
  <p>d = 2</p>
  <p>feature 1 : weight,
  feature 2 : height</p>
  <p>Logistic Regression:
  Its a 2 class classification.
  y : {obsess, normal)</p>
  <p>Linear Regression:
  y: blood pressure (real value)</p>
  <p>Here,</p>
  <ul>
  <li>Logistic Regression will fit a 2-D line.</li>
  <li>Linear Regression will fit a 3-D plane.</li>
  </ul>
  <p>Please confirm if this understanding is correct and same happens even in higher dimensions.</p>
  
Tags: <linear-regression><logistic-regression>
Title: Hyper-plane in logistic regression vs linear regression for same number of features
UserDisplayName: Ajey
ThreadText: # Hyper-plane in logistic regression vs linear regression for same number of features
  
  (Asked by: username_0 on 2020-09-09)
  
  Geometric interpretation of Logistic Regression and Linear regression is considered here.
  
  I was going through Logistic regression and Linear regression. In the optimization equation of both following term is used. $$W^{T}.X$$
  
  W is a vector which holds weights of the hyper-plane.
  
  I realized following about the dimensions of the fitted hyper-plane. Want to confirm it.
  
  Let,
  d = Number of features for both Logistic Regression and Linear Regression.
  
  Logistic Regression case:
  Fitted hyper-plane is d-dimensional.
  
  Linear Regression case:
  Fitted hyper-plane is (d + 1) dimensions.
  
  Example
  
  d = 2
  
  feature 1 : weight,
  feature 2 : height
  
  Logistic Regression:
  Its a 2 class classification.
  y : {obsess, normal)
  
  Linear Regression:
  y: blood pressure (real value)
  
  Here,
  
  * Logistic Regression will fit a 2-D line.
  * Linear Regression will fit a 3-D plane.
  
  Please confirm if this understanding is correct and same happens even in higher dimensions.
  
  **Tags:** linear-regression, logistic-regression
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2020-09-10. Score: 0
  
  Mm, I understand what you want to say, but I think you're slightly wrong with terminology. If you consider a d-dimensional vector space, people usually a hyper-plane (d - 1)-dimensional, because it's a subspace of lower dimensionality. So for your example d = 2 the logistic regression would fit a 1-dimentional line (which would separate 2 classes) and the linear regression would fit a 2-dimentional plane (for every combination of 2 features the prediction would lay on some plane in 3-D space). So the general rule would be logreg -> (d-1)-dimensional hyperplane in d-dimensional vector space, linear regression -> d-dimensional hyperplane in (d+1)-dimensional vector space.
  
  
  ---
  
  