Version 5.0 Regression Guide Harvey Motulsky President, GraphPad Software Inc. GraphPad Prism All rights reserved. This Regression Guide is a companion to GraphPad Prism 5. Available for both Mac and Windows, Prism makes it very easy to graph and analyze scientific data. Download a free demo from www.graphpad.com The focus of this Guide is on helping you understand the big ideas behind regression so you can choose an analysis and interpret the results. Only about 10% of this Guide is specific to Prism, so you may find it very useful even if you use another regression program. The companion Statistics Guide explains how to do statistical analyses with Prism, Both of these Guides contain exactly the same information as the Help system that comes with Prism 5, including the free demo versrion. You may also view the Prism Help on the web at: http://graphpad.com/help/prism5/prism5help.html Copyright 2007, GraphPad Software, Inc. All rights reserved. GraphPad Prism and Prism are registered trademarks of GraphPad Software, Inc. GraphPad is a trademark of GraphPad Software, Inc. Citation: H.J. Motulsky, Prism 5 Statistics Guide, 2007, GraphPad Software Inc., San Diego CA, www.graphpad.com. To contact GraphPad Software, email [email protected] or [email protected]. Contents I. Correlation Key concepts: Correlation............................................................................................................................................10 How to: Correlation............................................................................................................................................11 Interpreting results:............................................................................................................................................13 Correlation Analysis checklist.............................................................................................................................................15 Correlation II. Fitting a curve without a model Spline and Lowess............................................................................................................................................17 curves Using nonlinear............................................................................................................................................19 regression with an empirical model III. Generating curves and simulating data Plotting a function............................................................................................................................................21 Simulating data............................................................................................................................................23 with random error Using a script to............................................................................................................................................28 simulate many data sets Simulations and............................................................................................................................................29 script to assess confidence intervals IV. Linear regression Key concepts: Linear............................................................................................................................................32 regression The goal of linear regression How linear regression works Advice: Avoid Scatchard, Lineweaver-Burke and similar transforms Advice: When to fit a line with nonlinear regression How to: Linear ............................................................................................................................................36regression Finding the best-fit slope and intercept Interpolating from a linear standard curve Results of linear............................................................................................................................................39 regression Slope and intercept r2, a measure of goodness-of-fit of linear regression Is the slope significantly different than zero? Comparing slopes and intercepts Runs test following linear regression Analysis checklist: Linear regression Graphing tips: Linear regression Deming regression............................................................................................................................................47 Key concepts: Deming regression How to: Deming regression Analysis checklist: Deming regression V. Nonlinear regression Key concepts in............................................................................................................................................51 nonlinear regression Introducing nonlinear regression The goal of nonlinear regression The differences between linear and nonlinear regression Distinguishing nonlinear regression from other kinds of regression Preparing data for nonlinear regression Understanding models What is a model? Three example models Why can't GraphPad Prism choose a model? Advice: How to understand a model Comparing models Questions that can be answered by comparing models Approaches to comparing models How the F test works to compare models How the AICc computations work Global nonlinear regression What is global nonlinear regression? Using global regression to fit incomplete datasets Fitting models where the parameters are defined by multiple data sets Column constants Advice: Don't use global regression if datasets use different units Outlier elimination and robust nonlinear regression When to use automatic outlier removal When to avoid automatic outlier removal Outliers aren't always 'bad' points The ROUT method of identifying outliers Robust nonlinear regression How nonlinear regression works Why minimize the sum-of-squares? How nonlinear regression works Unequal weighting in nonlinear regression How standard errors and confidence intervals are computed How confidence and prediction bands are computed Replicates How dependency is calculated Nonlinear regression............................................................................................................................................82 tutorials Example: Fitting an enzyme kinetics curve Example: Comparing two enzyme kinetics models Example: Interpolating from a sigmoidal standard curve Example: Automatic outlier elimination (exponential decay) Example: Global nonlinear regression (dose-response curves) Example: Ambiguous fit (dose-response) Nonlinear regression............................................................................................................................................112 with Prism Choosing a built-in model Dose-response - Key concepts What are dose-response......................................................................................................................................... curves? 112 The EC50 ......................................................................................................................................... 113 Confidence intervals......................................................................................................................................... of the EC50 114 Hill slope ......................................................................................................................................... 115 Choosing a dose-response......................................................................................................................................... equation 116 Converting concentration......................................................................................................................................... to log(concentration) 118 Dose-response - Stimulation Equation: log(agonist)......................................................................................................................................... vs. response 119 Equation: log(agonist)......................................................................................................................................... vs. response -- Variable slope 120 Equation: log(agonist)......................................................................................................................................... vs. normalized response 121 Equation: log(agonist)......................................................................................................................................... vs. normalized response -- Variable slope 122 Dose-response - Inhibition Equation: log(inhibitor)......................................................................................................................................... vs. response 123 Equation: log(inhibitor)......................................................................................................................................... vs. response -- Variable slope 125 Equation: log(inhibitor)......................................................................................................................................... vs. normalized response 126 Equation: log(inhibitor)......................................................................................................................................... vs. normalized response -- Variable slope 127 Dose-response -- Special Asymmetrical (five......................................................................................................................................... parameter) 128 Equation: Biphasic........................................................................................................................................