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# Regression Analysis Microsoft Excel

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## Description

This is today's most complete guide to regression analysis with Microsoft (R) 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
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
Add covariates to your analysis to reduce bias and increase statistical power

## Product details

• Paperback | 368 pages
• 183 x 229 x 21mm | 580g
• Que Corporation,U.S.
• United States
• English
• 0789756552
• 9780789756558
• 630,500

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

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

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

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

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

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

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

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

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 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

Conrad Carlberg (www.conradcarlberg.com) is a nationally recognized expert on Quantitative analysis and on data analysis and management applications such as Microsoft Excel, SAS, and Oracle. He holds a Ph.D. in statistics from the University of Colorado and is a many-time recipient of Microsoft's Excel MVP designation.

Carlberg is a Southern California native. After college he moved to Colorado, where he worked for a succession of startups and attended graduate school. He spent two years in the Middle East, teaching computer science and dodging surly camels. After finishing graduate school, Carlberg worked at US West (a Baby Bell) in product management and at Motorola.

In 1995 he started a small consulting business that provides design and analysis services to companies that want to guide their business decisions by means of quantitative analysis-approaches that today we group under the term "analytics." He enjoys writing about those techniques and, in particular, how to carry them out using the world's most popular numeric analysis application, Microsoft Excel.