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Regression Analysis Microsoft Excel
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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

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.

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