MHB Jordan's Question from Facebook (About Regression)

  • Thread starter Thread starter Sudharaka
  • Start date Start date
  • Tags Tags
    Regression
AI Thread Summary
To analyze the model y = A + B e^x, it is suggested to transform the data by setting X = e^x, which simplifies the equation to a linear form y = A + B X. This transformation allows for the application of linear least squares regression on the new dataset X against y. Evaluating e^x at each point x generates the necessary data for this regression analysis. The discussion emphasizes the effectiveness of this method for fitting the model. Overall, this approach provides a straightforward way to handle non-linear relationships in regression analysis.
Sudharaka
Gold Member
MHB
Messages
1,558
Reaction score
1
Jordan from Facebook writes:

Help please,

2yod9uh.jpg
 
Mathematics news on Phys.org
Sudharaka said:
Jordan from Facebook writes:

Help please,

2yod9uh.jpg

If we assume that a model of the form [math]\displaystyle \begin{align*} y = A + B\,e^{x} \end{align*}[/math] is appropriate, then we note that if we have [math]\displaystyle \begin{align*} X = e^{x} \end{align*}[/math], then we have a nice linear equation [math]\displaystyle \begin{align*} y = A + B\,X \end{align*}[/math].

So it would help to start by evaluating [math]\displaystyle e^x [/math] at each point x, giving a new set of data which we can call X. Then perform a linear least squares regression for data set y against data set X.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top