Answers.Body: <p>As said above, they are weights to your hypothesis function that are changed during training to minimize your Error function. You can think of them like slope and y intercept in basic algebra. However, a linear regression hypothesis function can be parameterized by many more weight terms than just theta_0, and theta_1.</p>
  
  <p>I detail this process more in this post: <a href="https://ai.stackexchange.com/questions/4629/how-does-an-activation-functions-derivative-measure-error-rate-in-a-neural-netw/4639#4639">How does an activation function&#39;s derivative measure error rate in a neural network?</a></p>
  
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Answers.CreationDate: 2018-02-20T04:22:05.090Z
Answers.LastActivityDate: 2018-02-20T05:47:03.980Z
Answers.LastEditDate: 2018-02-20T05:47:03.980Z
Answers.UserDisplayName: sma
Answers.Body: <p>The prediction made by linear regression can simply be thought of as a vector dot product.</p>
  
  <p><span class="math-container">$$\overrightarrow{x}^T \cdot \overrightarrow{y}$$</span></p>
  
  <p>One of those two vectors is the "data" for one case (like a row in your data matrix), the other is a vector of the model's parameters, which is usually called <span class="math-container">$\overrightarrow{\theta}$</span> or <span class="math-container">$\overrightarrow{\beta}$</span>.</p>
  
  <p>So in the case shown by yourself, we have:</p>
  
  <p><span class="math-container">$$h(x) = \theta_0 + \theta_1 \cdot x$$</span></p>
  
  <p>Often we add a row of ones to the beginning of the data matrix, that way we are consistent in the sense that the <span class="math-container">$\theta_0 = 1 \cdot \theta_0$</span></p>
  
  <p>This way we arrive at:</p>
  
  <p><span class="math-container">$$h(x) = \overrightarrow{\theta}^T \cdot  \overrightarrow{x}$$</span></p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-03-02T14:31:39.037Z
Answers.LastActivityDate: 2019-03-02T14:31:39.037Z
Answers.UserDisplayName: BioHazZzZard
Body: <p>I have completed week 1 of Andrew Ng's course. I understand that the cost function for linear regression is defined as <span class="math-container">$J (\theta_0, \theta_1) = 1/2m*\sum (h(x)-y)^2$</span> and the <span class="math-container">$h$</span> is defined as <span class="math-container">$h(x) = \theta_0 + \theta_1(x)$</span>. But I don't understand what <span class="math-container">$\theta_0$</span> and <span class="math-container">$\theta_1$</span> represent in the equation. Is someone able to explain this?</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-02-15T18:20:19.817Z
Comments.Text: Specifically, theta0 is the bias and theta1 is 'slope' of the regression line.
Comments.UserDisplayName: Daniel
Tags: <linear-regression><math>
Title: Understanding a few terms in Andrew Ng's definition of the cost function for linear regression
UserDisplayName: Nicholas Pysklywec
ThreadText: # Understanding a few terms in Andrew Ng's definition of the cost function for linear regression
  
  (Asked by: username_0 on 2018-02-15)
  
  I have completed week 1 of Andrew Ng's course. I understand that the cost function for linear regression is defined as $J (\theta\_0, \theta\_1) = 1/2m\*\sum (h(x)-y)^2$ and the $h$ is defined as $h(x) = \theta\_0 + \theta\_1(x)$. But I don't understand what $\theta\_0$ and $\theta\_1$ represent in the equation. Is someone able to explain this?
  
  **Tags:** linear-regression, math
  > **Comments:**
  > **username_1**: Specifically, theta0 is the bias and theta1 is 'slope' of the regression line.  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_2 on 2018-02-20. Score: 1
  
  As said above, they are weights to your hypothesis function that are changed during training to minimize your Error function. You can think of them like slope and y intercept in basic algebra. However, a linear regression hypothesis function can be parameterized by many more weight terms than just theta\_0, and theta\_1.
  
  I detail this process more in this post: [How does an activation function's derivative measure error rate in a neural network?](https://ai.stackexchange.com/questions/4629/how-does-an-activation-functions-derivative-measure-error-rate-in-a-neural-netw/4639#4639)
  
  
  ---
  
  ### Answer by username_3 on 2019-03-02. Score: 1
  
  The prediction made by linear regression can simply be thought of as a vector dot product.
  
  $$\overrightarrow{x}^T \cdot \overrightarrow{y}$$
  
  One of those two vectors is the "data" for one case (like a row in your data matrix), the other is a vector of the model's parameters, which is usually called $\overrightarrow{\theta}$ or $\overrightarrow{\beta}$.
  
  So in the case shown by yourself, we have:
  
  $$h(x) = \theta\_0 + \theta\_1 \cdot x$$
  
  Often we add a row of ones to the beginning of the data matrix, that way we are consistent in the sense that the $\theta\_0 = 1 \cdot \theta\_0$
  
  This way we arrive at:
  
  $$h(x) = \overrightarrow{\theta}^T \cdot \overrightarrow{x}$$
  
  
  ---
  
  