Applied Regression Analysis for Business (eBook)

Jacek Welc obtained his Ph.D. in Economics for his thesis on “Autoregressive Distributed Lags in Forecasting Regional Business Cycles” in 2008 from the Wroclaw University of Economics, after having graduated there with a Master of Economics in 2003. Besides having published more than forty research papers, Welc has been active in professional corporate finance services, including financial statement auditing and company valuations, which mainly involve companies listed on the Warsaw Stock Exchange. Pedro J. Rodriguez Esquerdo obtained his Ph.D. in Mathematics in 1983 from the University of California, Santa Barbara, after he graduated with a Master in Statistics in 1980 and a Master in Economics in 1981. He published several academic textbooks on mathematics and statistics including “Estadistica Descriptiva. Una Introduccion Conceptual Al Analisis”.

Preface ........................................................................................................................... 1Chapter 1 – Basics of regression models .................................................................. 21.1. Types and applications of regression models. .............................................................................. 21.2. Basic elements of a single-equation linear regression model. ..................................................... 4Chapter 2 – Relevance of outlying and influential observations for regression analysis ..................................................................................................... 72.1. Nature and dangers of univariate and multivariate outlying observations. ................................ 72.2. Tools for detection of outlying observations. ............................................................................. 192.3. Recommended procedure for detection of outlying and influential observations. .................... 322.4. Dealing with detected outlying and influential observations. .................................................... 33Chapter 3 – Basic procedure for multiple regression model building ............. 353.1. Introduction. ............................................................................................................................... 353.2. Preliminary specification of the model. ...................................................................................... 353.3. Detection of potential outliers in the dataset. ........................................................................... 403.4. Selection of explanatory variables (from the set of candidates). ............................................... 483.5. Interpretation of the obtained regression’ structural parameters. ............................................ 57Chapter 4 – Verification of multiple regression model ...................................... 604.1. Introduction. ............................................................................................................................... 604.2. Testing general statistical significance of the whole model: F test. ........................................... 614.3. Testing the normality of regression residuals’ distribution. ....................................................... 634.4. Testing the autocorrelation of regression residuals. .................................................................. 724.5. Testing the heteroscedasticity of regression residuals. .............................................................. 874.6. Testing the symmetry of regression residuals. ........................................................................... 974.7. Testing the randomness of regression residuals. ..................................................................... 1064.8. Testing the specification of the model: Ramsey’s RESET test. ................................................. 1154.9. Testing the multicollinearity of explanatory variables. ............................................................ 1214.10. What to do if the model is not correct? .................................................................................. 1254.11. Summary of verification of our model .................................................................................... 130Chapter 5 – Common adjustments to multiple regressions .............................. 1325.1. Dealing with qualitative factors by means of dummy variables. ............................................. 1325.2. Modeling seasonality by means of dummy variables. ............................................................. 1365.3. Using dummy variables for outlying observations. .................................................................. 1482815.4. Dealing with structural changes in modeled relationships. ..................................................... 1555.5. Dealing with in-sample non-linearities. .................................................................................... 164Chapter 6 – Common pitfalls in regression analysis .......................................... 1716.1. Introduction. ............................................................................................................................. 1716.2. Distorting impact of multicollinearity on regression parameters. ........................................... 1716.3. Analyzing incomplete regressions. ........................................................................................... 1766.4. Spurious regressions and long-term trends. ............................................................................. 1806.5. Extrapolating in-sample relationships too far into out-of-sample ranges. .............................. 1866.6. Estimating regressions on too narrow ranges of data. ............................................................ 1936.7. Ignoring structural changes within modeled relationships and within individual variables. ... 197Chapter 7 – Regression analysis of discrete dependent variable .................... 2097.1. The nature and examples of discrete dependent variables. ..................................................... 2097.2. The discriminant analysis. ........................................................................................................ 2097.3. The logit function. ..................................................................................................................... 218Chapter 8 – Real-life case-study: The quarterly sales revenues of Nokia Corporation............................................................................................................... 2238.1. Introduction. ............................................................................................................................. 2238.2. Preliminary specification of the model. .................................................................................... 2238.3. Detection of potential outliers in the dataset .......................................................................... 2258.4. Selection of explanatory variables (from the set of candidates). ............................................. 2318.5. Verification of the obtained model. .......................................................................................... 2348.6. Evaluation of the predictive power of the estimated model. ................................................... 246Chapter 9 – Real-life case-study: Identifying overvalued and undervalued airlines ........................................................................................................................ 2529.1. Introduction. ............................................................................................................................. 2529.2. Preliminary specification of the model. .................................................................................... 2529.3. Detection of potential outliers in the dataset .......................................................................... 2549.4. Selection of explanatory variables (from the set of candidates). ............................................. 2589.5. Verification of the obtained model. .......................................................................................... 2599.6. Evaluation of model usefulness in identifying overvalued and undervalued stocks. ............... 268Appendix – Statistical Tables ................................................................................... 271A1. Critical values for F-statistic for k = 0,05................................................................................. 271A2. Critical values for t-statistic. ...................................................................................................... 273A3. Critical values for Chi-squared statistic. .................................................................................... 274282A4. Critical values for Hellwig test. .................................................................................................. 275A5. Critical values for symmetry test for k = 0,10. ........................................................................ 276A6. Critical values for maximum series length test for k = 0,05. ................................................... 276A7. Critical values for number of series test for k = 0,05. ............................................................. 277