<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>

CC BY-SA 4.0
2020-09-10T21:57:57.417Z
2020-09-10T21:57:57.417Z
Michał Słodki
<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>

<linear-regression><logistic-regression>
Hyper-plane in logistic regression vs linear regression for same number of features
Ajey
# 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


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## 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.


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