Regression Analysis Microsoft Excel

         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