As in the least-squares analysis, nonsignificant [[beta].

In addition, the least-squares analysis assumes the regression relationship (2) in the conditional mean holds same across the distribution of y.

A linear least-squares analysis yields a very modest negative slope and [r.

Again, a linear least-squares analysis yields a very modest negative slope and an [r.

In this case, the least-squares analysis gave a positive rather than negative slope, and the [r.

The underlying principles of probability theory indicate that least-squares analysis is appropriate only if (i) the data points have an associated Gaussian error distribution and (ii) the proposed model is a complete representation of the observed data.

In this paper, several applications of maximum likelihood that go beyond least-squares analysis are discussed.

At the same time, however, our precision decreases because we have allowed the possibility of more sources of uncertainty than in a standard least-squares analysis.

Although it is customary to use the standard error or variance of observations as weighting factors for

least-squares analysis, it is often difficult to measure or estimate appropriate weighting factors to be used in real applications.