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.