## Leastsquares Analysis

The process used to obtain model parameter estimates from a set of observed data is called least-squares analysis (Meyer, 1975). In the story, Isaac Newton reasoned that if he formed a function that was the square of differences between model-derived and observed data, he could take the derivatives of this function with respect to each model parameter, set them to zero, and then solve for the model parameters. In his case, the model parameters were the original artifact message. Although least-squares analysis was not invented until the middle 1800s by Gauss (Gauss, 1855), Newton could potentially have done this analysis in the middle 1600s because he knew how to differentiate functions.

### Linear Least-Squares Analysis

Figure 10.7.5 demonstrates how the least-squares process works for a simple example, the best fit of a straight line through a set of observed data. If the intercept parameter of the line is fixed and the slope is allowed to vary, the least-squares function forms a parabola with its nadir at a clearly defined slope value

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