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
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
About the Author :
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.
