Model: y = a + b*Ln(x)+ c*x

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You can then use standard least squares methods to solve for the unknowns and get your initial guesses.In summary, the problem discussed in the conversation is finding initial guesses for the parameters a, b, and c in a linear equation. The equation is already linear in these parameters, so standard least squares methods can be used to determine their values.
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scantor145
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I have calibration data and I'm want to use the following model:

y = a + b*Ln(x)+ c*x

I'm looking for a way to make initial guesses for the three paramaters a, b and c.

Is there any way to linearize this expression so that I can use least squares analysis to determine values for a, b and c.
 
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Your problem is already linear in a, b and c (which are the variables you're trying to fit).

edit: to be a bit more explicit, given a pair of data values (x_i, y_i) you get a the following equation

a*1 + b*Ln(x_i) + c*x_i = y_i

which is a linear combination of the unknowns (a, b, c).
 
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1. What is the meaning of the variables in the model y = a + b*Ln(x) + c*x?

The variable y represents the dependent variable, while x is the independent variable. The constants a, b, and c are coefficients that determine the relationship between the variables.

2. How do you interpret the Ln(x) term in this model?

The Ln(x) term in this model represents the natural logarithm of the independent variable x. It is used in the model to account for non-linear relationships between the variables.

3. Can this model be used for any type of data?

This model can be used for data that follows a logarithmic relationship between the independent and dependent variables. However, it is important to note that the data should be continuous and the independent variable should be positive.

4. How do you determine the values of the coefficients a, b, and c?

The values of the coefficients can be determined through statistical methods such as linear regression. These methods involve finding the best-fitting line that minimizes the distance between the actual data points and the predicted values from the model.

5. What is the significance of the constant term a in the model?

The constant term a represents the y-intercept of the line of best fit. It indicates the predicted value of the dependent variable when the independent variable is equal to 0. This can be helpful in understanding the relationship between the variables and making predictions.

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