Fitting Models to Biological Data Using Linear and Nonlinear Regression A Practical Guide to Curve Fitting

About this book

Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book, by the author of the very successful Intuitive Biostatistics, addresses this relavtively focused need of an extraordinarily broad range of scientists.

Contents

FITTING DATA WITH NONLINEAR REGRESSION; 1. An example of nonlinear regression; 2. Preparing data for nonlinear regression; 3. Nonlinear regression choices; 4. The first five questions to ask about nonlinear regression results; 5. The results of nonlinear regression; 6. Troubleshooting "bad fits"; FITTING DATA WITH LINEAR REGRESSION; 7. Choosing linear regression; 8. Interpreting the results of linear regression; MODELS; 9. Introducing models; 10. Tips on choosing a model; 11. Global models; 12. Compartmental models and defining a model with a differential equation; HOW NONLINEAR REGRESSION WORKS; 13. Modeling experimental error; 14. Unequal weighting of data points; 15. How nonlinear regression minimized the sum-of-squares; CONFIDENCE INTERVALS OF THE PARAMETERS; 16. Asymptotic standard errors and confidence intervals; 17. Generating confidence intervals by Monte Carlo simulations; 18. Generating confidence intervals via model comparison; 19. comparing the three methods for creating confidence intervals; 20. Using simulations to understand confidence intervals and plan experiments; COMPARING MODELS; 21. Approach to comparing models; 22. Comparing models using the extra sum-of-squares F test; 23. Comparing models using Akaike's Information Criterion; 24. How should you compare modes-AICe or F test?; 25. Examples of comparing the fit of two models to one data set; 26. Testing whether a parameter differs from a hypothetical value; HOW DOES A TREATMENT CHANGE THE CURVE?; 27. Using global fitting to test a treatment effect in one experiment; 28. Using two-way ANOVA to compare curves; 29. Using a paired t test to test for a treatment effect in a series of matched experiments; 30. Using global fitting to test for a treatment effect in a series of matched experiments; 31. Using an unpaired t test to test for a treatment effect in a series of unmatched experiments; 32. Using global fitting to test for a treatment effect in a series of unmatched experiments; FITTING RADIOLIGAND AND ENZYME KINETICS DATA; 33. The law of mass action; 34. Analyzing radioligand binding data; 35. Calculations with radioactivity; 36. Analyzing saturation radioligand binding data; 37. Analyzing competitive binding data; 38. Homologous competitive binding curves; 39. Analyzing kinetic binding data; 40. Analyzing enzyme kinetic data; FITTING DOES-RESPONSE CURVES; 41. Introduction to dose-response curves; 42. The operational model of agonist action; 43. Dose-response curves in the presence of antagonists; 44. Complex dose-response curves; FITTING CURVES WITH GRAPHPAD PRISM; 45. Nonlinear regression with Prism; 46. Constraining and sharing parameters; 47. Prsim's nonlinear regression dialog; 48. Classic nonlinear models built-in to Prism; 49. Importing equations and equation libraries; 50. Writing user-defined models in Prism; 51. Linear regression with Prism; 52. Reading unknowns from standard curves; 53. Graphing a family of theoretical curves; 54. Fitting curves without regression

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