Regression Analysis Microsoft Excel

Description

This is today’s most complete guide to regression analysis with Microsoft® Excel for any business analytics or research task. Drawing on 25 years of advanced statistical experience, Microsoft MVP Conrad Carlberg shows how to use Excel’s regression-related worksheet functions to perform a wide spectrum of practical analyses.

Carlberg clearly explains all the theory you’ll need to avoid mistakes, understand what your regressions are really doing, and evaluate analyses performed by others. From simple correlations and t-tests through multiple analysis of covariance, Carlberg offers hands-on, step-by-step walkthroughs using meaningful examples.

He discusses the consequences of using each option and argument, points out idiosyncrasies and controversies associated with Excel’s regression functions, and shows how to use them reliably in fields ranging from medical research to financial analysis to operations.

You don’t need expensive software or a doctorate in statistics to work with regression analyses. Microsoft Excel has all the tools you need—and this book has all the knowledge!

• Understand what regression analysis can and can’t do, and why
• Master regression-based functions built into all recent versions of Excel
• Work with correlation and simple regression
• Make the most of Excel’s improved LINEST() function
• Plan and perform multiple regression
• Distinguish the assumptions that matter from the ones that don’t
• Extend your analysis options by using regression instead of traditional analysis of variance
• Add covariates to your analysis to reduce bias and increase statistical power

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Table of Contents

Introduction................................... 1

1 Measuring Variation: How Values Differ.......................... 5

How Variation Is Measured...........................................5

        Sum of Deviations..........................................................6

        Summing Squared Deviations...............................................7

        From the Sum of Squares to the Variance................................10

        Using the VAR.P( ) and VAR.S( ) Functions....................................11

The Standard Deviation................................................14

The Standard Error of the Mean............................................15

        About z-Scores and z-Values.................................................18

        About t-Values.....................................................................23

2 Correlation.........................................29

Measuring Correlation...........................................................................29

        Expressing the Strength of a Correlation.....................30

        Determining a Correlation’s Direction...................................32

Calculating Correlation.......................................................34

        Step One: The Covariance..................................34

        Watching for Signs........................................................36

    From the Covariance to the Correlation Coefficient..........................38

        Using the CORREL( ) Function...................................................41

        Understanding Bias in the Correlation............................41

        Checking for Linearity and Outliers in the Correlation ........................44

        Avoiding a Trap in Charting.............................48

Correlation and Causation..............................................53

        Direction of Cause........................................54

        A Third Variable................................................55

Restriction of Range..........................................................................55

3 Simple Regression.....................................59

Predicting with Correlation and Standard Scores.........................60

        Calculating the Predictions............................61

        Returning to the Original Metric............................63

        Generalizing the Predictions........................................64

Predicting with Regression Coefficient and Intercept.................................65

        The SLOPE( ) Function........................................................65

        The INTERCEPT( ) Function.....................69

        Charting the Predictions....................................70

Shared Variance...........................................71

        The Standard Deviation, Reviewed.............................71

        More About Sums of Squares..................................73

        Sums of Squares Are Additive..............................................74

        R2 in Simple Linear Regression.........................................77

        Sum of Squares Residual versus Sum of Squares Within.......................81

The TREND( ) Function............................................82

        Array-entering TREND( )..........................................84

        TREND( )’s new x’s Argument..................................85

        TREND( )’s const Argument...................................................86

        Calculating the Zero-constant Regression.............................88

Partial and Semipartial Correlations..........................90

        Partial Correlation............................................91

        Understanding Semipartial Correlations........................................................95

4 Using the LINEST( ) Function...........................103

Array-Entering LINEST( ).............................. 103

        Understanding the Mechanics of Array Formulas.....................104

        Inventorying the Mistakes............................................105

Comparing LINEST( ) to SLOPE( ) and INTERCEPT( )..........................107

        The Standard Error of a Regression Coefficient..................................109

        The Meaning of the Standard Error of a Regression Coefficient........................109

        A Regression Coefficient of Zero......................................................110

        Measuring the Probability That the Coefficient is Zero in the Population...............112

        Statistical Inference as a Subjective Decision............................113

        The t-ratio and the F-ratio..............................116

        Interval Scales and Nominal Scales.............................116

The Squared Correlation, R2.....................................117

The Standard Error of Estimate...........................120

        The t Distribution and Standard Errors.......................121

        Standard Error as a Standard Deviation of Residuals..............125

        Homoscedasticity: Equal Spread................................128

Understanding LINEST( )’s F-ratio....................129

        he Analysis of Variance and the F-ratio in Traditional Usage......................129

        The Analysis of Variance and the F-ratio in Regression.........................131

        Partitioning the Sums of Squares in Regression.....................133

        The F-ratio in the Analysis of Variance........................................136

        The F-ratio in Regression Analysis..................................................140

        The F-ratio Compared to R2............................................................................146

The General Linear Model, ANOVA, and Regression Analysis........................146

Other Ancillary Statistics from LINEST( ).....................................149

5 Multiple Regression...................................151

A Composite Predictor Variable.........................152

        Generalizing from the Single to the Multiple Predictor........................153

        Minimizing the Sum of the Squared Errors.......................................156

Understanding the Trendline...........................................................160

Mapping LINEST( )’s Results to the Worksheet......................................163

Building a Multiple Regression Analysis from the Ground Up......................166

        Holding Variables Constant............................................166

        Semipartial Correlation in a Two-Predictor Regression................167

        Finding the Sums of Squares....................................169

        R2 and Standard Error of Estimate......................................170

        F-Ratio and Residual Degrees of Freedom.................................172

        Calculating the Standard Errors of the Regression Coefficients...........................173

        Some Further Examples................................................176

Using the Standard Error of the Regression Coefficient..........................181

        Arranging a Two-Tailed Test....................................186

        Arranging a One-Tailed Test.....................................189

Using the Models Comparison Approach to Evaluating Predictors...................192

        Obtaining the Models’ Statistics.......................................192

        Using Sums of Squares Instead of R2............................196

Estimating Shrinkage in R2..................................................197

6 Assumptions and Cautions Regarding Regression Analysis................199

About Assumptions.................................................199

        Robustness: It Might Not Matter...................................202

        Assumptions and Statistical Inference.................................204

The Straw Man............................................................................204

Coping with Nonlinear and Other Problem Distributions.........................211

The Assumption of Equal Spread...........................................213

        Using Dummy Coding..........................................215

        Comparing the Regression Approach to the t-test Approach..................217

        Two Routes to the Same Destination.....................................218

Unequal Variances and Sample Sizes..................................220

        Unequal Spread: Conservative Tests..........................................220

        Unequal Spread: Liberal Tests.............................................................225

        Unequal Spreads and Equal Sample Sizes.........................226

        Using LINEST()Instead of the Data Analysis Tool......................................230

        Understanding the Differences Between the T.DIST()Functions........................231

        Using Welch’s Correction................................237

        The TTEST()Function................................................243

7 Using Regression to Test Differences Between Group Means.........................245

Dummy Coding.............................................................246

        An Example with Dummy Coding....................................246

        Populating the Vectors Automatically.....................................250

        The Dunnett Multiple Comparison Procedure..........................253

Effect Coding...................................................................259

        Coding with -1 Instead of 0.........................................260

        Relationship to the General Linear Model..............................261

        Multiple Comparisons with Effect Coding...............................264

Orthogonal Coding................................................267

        Establishing the Contrasts................................267

        Planned Orthogonal Contrasts Via ANOVA..........................268

        Planned Orthogonal Contrasts Using LINEST( )...........................269

Factorial Analysis.......................................................272

        Factorial Analysis with Orthogonal Coding....................274

        Factorial Analysis with Effect Coding..............................279

Statistical Power, Type I and Type II Errors.....................283

        Calculating Statistical Power..............................285

        Increasing Statistical Power...........................................286

Coping with Unequal Cell Sizes.......................................288

        Using the Regression Approach...............................289

        Sequential Variance Assignment...............................................291

8 The Analysis of Covariance..............................295

Contrasting the Results.............................................297

        ANCOVA Charted................................305

Structuring a Conventional ANCOVA......................308

        Analysis Without the Covariate....................308

        Analysis with the Covariate..............................310

Structuring an ANCOVA Using Regression.......................315

Checking for a Common Regression Line..........................316

        Summarizing the Analysis...............................320

Testing the Adjusted Means: Planned Orthogonal Coding in ANCOVA...............321

ANCOVA and Multiple Comparisons Using the Regression Approach.......................328

Multiple Comparisons via Planned Nonorthogonal Contrasts..................................330

Multiple Comparisons with Post Hoc Nonorthogonal Contrasts...............................332

TOC, 9780789756558, 4/13/2016

Updates

Updates & Corrections

Please visit the author's site at conradcarlberg.com.

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