obtained from least squares vs obtained with least squares

Both phrases are correct, but they are used in different contexts. 'Obtained from least squares' is used when referring to the source or origin of the result, while 'obtained with least squares' is used when describing the method or tool used to obtain the result.

Last updated: March 19, 2024 • 737 views

obtained from least squares

This phrase is correct and commonly used when referring to the source or origin of the result obtained through the least squares method.

This phrase is used to indicate that the result was derived or calculated using the least squares method.

Examples:

The coefficients were obtained from least squares estimation.
The data points were obtained from least squares fitting.

Show examples from the web [+]

How reliable are the slope, intercept and other polynomial coefficients obtained from least-squares calculations on experimental data? The single most ...
The constants obtained from least-squares ﬁts to the individual bands, runs (2-5), are are given in the next four rows of Table I, together with their standard errors ...
In this paper we investigate the consistency of parameter estimates obtained from least squares iden- tification with a quadratic parameter constraint.
We investigate the consistency of parameter estimates obtained from least squares identification with a quadratic parameter constraint. For generality, we ...

Alternatives:

derived from least squares
calculated using least squares

obtained with least squares

This phrase is correct and commonly used when describing the method or tool used to obtain the result through the least squares method.

This phrase is used to indicate that the result was achieved using the least squares method as a tool or technique.

Examples:

The solution was obtained with least squares regression.
The model parameters were obtained with least squares analysis.

Show examples from the web [+]

... with all six of the alternative regression methods were significantly (P < .01) lower than the LLQ values obtained with least squares linear regression analysis.
decision boundary obtained with Least squares, why it has this precise direction. Q3: Explain what w0 encodes. Exercise 2. Q1: What are kernels, and what are ...
Q2: Explain this result. In particular, explain what happens with the decision boundary obtained with Least squares, why it has this precise direction.
present results obtained with least·squares fitting of the wrong model. The residuals (here given by observed values minus calculated values) show the following.

Alternatives:

achieved using least squares
determined through least squares

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obtained from least squares vs obtained with least squares