Least squares linear regression is a common tool in ecological research. One of the central assumptions of least squares linear regression is that the independent variable is measured without error. But this variable is measured with error whenever it is a sample mean. The significance of such contraventions is not regularly assessed in ecological studies. A simulation program was made to provide such an assessment. The program requires a hypothetical data set, and using estimates of S$ sp2$ it scatters the hypothetical data to simulate the effect of sampling error. A regression line is drawn through the scattered data, and SSE and r$ sp2$ are measured. This is repeated numerous times (e.g. 1000) to generate probability distributions for r$ sp2$ and SSE. From these distributions it is possible to assess the likelihood of the hypothetical data resulting in a given SSE or r$ sp2$. The method was applied to survey data used in a published TP-CHLa regression (Pace 1984). Beginning with a hypothetical, linear data set (r$ sp2$ = 1), simulated scatter due to sampling exceeded the SSE from the regression through the survey data about 30% of the time. Thus chances are 3 out of 10 that the level of uncertainty found in the surveyed TP-CHLa relationship would be observed if the true relationship were perfectly linear. If this is so, more precise and more comprehensive models will only be possible when better estimates of the means are available. This simulation approach should apply to all least squares regression studies that use sampled means, and should be especially relevant to studies that use log-transformed values.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.22720 |
| Date | January 1995 |
| Creators | Beedell, David C. (David Charles) |
| Contributors | Peters, R. H. (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Biology.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001464783, proquestno: MM05533, Theses scanned by UMI/ProQuest. |
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