Body: <p>good evening, I wanted to know how the system of equations is solved step by step to arrive at the formulas for β0 and β1 in simple linear regression. In the following picture, there is the system of equations and the solutions. <a href="https://i.sstatic.net/LhYuEigd.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/LhYuEigd.jpg" alt="formulae" /></a>:</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-04-14T08:39:46.537Z
Comments.Text: multiply the second one by $x_i$, split the terms in the summation, separate $\beta_1$ from the rest?
Comments.UserDisplayName: Alberto
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-04-15T12:24:24.083Z
Comments.Text: Can you please provide the equations in mathjax instead of giving screenshots? You can use tools that automatically do this, for example, in the past, I used Mathpix: Snipping Tool.
Comments.UserDisplayName: nbro
Tags: <linear-regression>
Title: How is the system of equations that generates β0 ​and β1 in simple linear regression solved, resulting in the formulas?
UserDisplayName: Martín Badino
ThreadText: # How is the system of equations that generates β0 ​and β1 in simple linear regression solved, resulting in the formulas?
  
  (Asked by: username_0 on 2024-04-14)
  
  good evening, I wanted to know how the system of equations is solved step by step to arrive at the formulas for β0 and β1 in simple linear regression. In the following picture, there is the system of equations and the solutions. [![formulae](https://i.sstatic.net/LhYuEigd.jpg)](https://i.sstatic.net/LhYuEigd.jpg):
  
  **Tags:** linear-regression
  > **Comments:**
  > **username_1**: multiply the second one by $x_i$, split the terms in the summation, separate $\beta_1$ from the rest?  
  > **username_2**: Can you please provide the equations in mathjax instead of giving screenshots? You can use tools that automatically do this, for example, in the past, I used Mathpix: Snipping Tool.  
  
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  ## 0 answers
  
  