Finding the line of regression

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SUMMARY

The discussion centers on deriving the regression line of y on x using two normal equations: 5a + 10b = 40 and 10a + 25b = 95. The regression equation is defined as y = Ax + B, where A represents the regression coefficient and B is the y-intercept. Participants clarify that the normal equations are used to find the regression line, and the challenge lies in determining the regression coefficient A from the provided equations.

PREREQUISITES
  • Understanding of regression analysis concepts
  • Familiarity with normal equations in statistics
  • Knowledge of solving linear equations
  • Basic grasp of regression coefficients and intercepts
NEXT STEPS
  • Study how to derive regression coefficients from normal equations
  • Learn about the method of least squares in regression analysis
  • Explore the interpretation of regression lines in statistical modeling
  • Investigate software tools for performing regression analysis, such as R or Python's scikit-learn
USEFUL FOR

Statisticians, data analysts, students studying regression analysis, and anyone interested in understanding the derivation of regression lines from normal equations.

Doffy
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Two normal equations are given :
5a + 10b = 40
10a + 25b = 95
What is the regression line of y on x?

I can easily find the common points from both the equations but how do I find the regression coefficeint?
 
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Doffy said:
Two normal equations are given :
5a + 10b = 40
10a + 25b = 95
What is the regression line of y on x?

I can easily find the common points from both the equations but how do I find the regression coefficeint?

Hi Doffy! Welcome to MHB! (Smile)

A regression equation is usually given as $y=Ax+B$.
The regression coefficient in this equation is $A$ and the y-intercept is $B$.

However, I'm not clear on what you have there.
What are those "normal equations"?
And what do your $a$ and $b$ represent?
 
Thanks for the welcome!:)

And the above two equations were obtained for deriving the regression line of y on x(it said so in the question).

In my opinion, by solving the above equations, the point I would get could become (x bar, y bar). But I cannot find the regression coefficient. What do you think?
 

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