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Unformatted text preview: iology Undergraduate Society (B.U.G.S.) Presents… Lecture 18: Regression Analysis I Sources of Information Dytham: Chapter 8 p. 162170. otulsky: Chapter 18, 19 Triola et al.: Chapter 9 Sokal & Rohlf: Chapter 14 Regression Æ What is the relationship between two (or more) variables? How well do the data fit a mathematical relationship? ( Î modeling & prediction) Outline : • Introduction to regression & SLR • H o testing in SLR & Assumptions • Using SPSS to perform SLR Lecture 2 • Confidence & Prediction intervals • Assessing assumptions of SLR Introduction to Regression Analysis • In essence, regression involves fitting lines (or models) to datasets. • it is a common activity of life scientists. Regression analysis is undertaken for a wide variety of reasons: 1. Description: • Fitted models may provide succinct and readily grasped summaries of processes and relationships. Body weight [blood insulin] Linear [norepinephrine] Pulse rate Sigmoidal Time # open channels Exponential Introduction to Regression Analysis 2. Prediction: Often need to use a model to estimate a value of a dependent variable (Y) for values of an independent variable (X). • Interpolation • Calibration Body length weight • Standard curves (common use of prediction): Regression is used to analyze many assays. The assay is run with known concentrations of the substance being measured. Regression is used to fit a line or curve to the graph of concentration versus assay response (which might be optical density, radioactivity, fluorescence, absorbance, etc.). That line or curve can then be used to determine the concentration from the response obtained with unknown samples. 25 3. To test a theoretical relationship: • Does the functional relationship between a dependent variable (Y) and one or more predictor variables have a form you expected? Does the system work as you think it does? 4. To compare several datasets (e.g., rates) • Rates are common measurements in life sciences and frequently one needs to know if it is reasonable to treat 2 or more rates as though they were the same. • Because rates are simply the slopes of regression lines, comparison of rates is a a function of regression analysis. 5. Model building • The construction of mathematical models of systems, whether of predatorprey systems or lab cultures, often require models of the subprocesses that comprise the system. Commonly, subprocesses in models are regression equations. 6. Adjusting for a confounding variable • Regression techniques can answer questions like this: Did the new treatment alter the incidence of ulcers after adjusting for effects of age and aspirin consumption? Different Kinds of Regression Regression includes a large family of techniques: Simple Linear Regression (SLR) • The most common form of regression....
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This note was uploaded on 07/10/2010 for the course BIOL 361 taught by Professor Hall during the Winter '08 term at Waterloo.
 Winter '08
 Hall
 Biology

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