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2018 | OriginalPaper | Chapter

7. Regression Analysis

Authors : Erik Mooi, Marko Sarstedt, Irma Mooi-Reci

Published in: Market Research

Publisher: Springer Singapore

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Abstract

We first provide comprehensive, but simple, access to essential regression knowledge by discussing how regression analysis works, the requirements and assumptions on which it relies, and how you can specify a regression analysis model that allows you to make critical decisions for your business, clients, or project. Each step involved in regression analysis is linked to its execution in Stata (using menus and code). We show how to use a range of Stata’s easy-to-learn statistical procedures that underlie regression analysis, which will allow you to analyze, chart, and validate regression analysis results and to assess your analysis’s robustness. Interpretation of Stata output can be difficult, but we make this easier by means of an annotated case study. We conclude with suggestions for further readings on the use, application, and interpretation of regression analysis.

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previous chapter Hypothesis Testing & ANOVA

next chapter Principal Component and Factor Analysis

Strictly speaking, the difference between the predicted and the observed y-values is \( \widehat{e} \).

This only applies to the standardized βs.

This is only a requirement if you are interested in the regression coefficients, which is the dominant use of regression. If you are only interested in prediction, collinearity is not important.

The VIF is calculated using a completely separate regression analysis. In this regression analysis, the variable for which the VIF is calculated is regarded as a dependent variable and all other independent variables are regarded as independents. The R² that this model provides is deducted from 1 and the reciprocal value of this sum (i.e., 1/(1 − R²)) is the VIF. The VIF is therefore an indication of how much the regression model explains one independent variable. If the other variables explain much of the variance (the VIF is larger than 10), collinearity is likely a problem.

This term can be calculated manually, but also by using the function mmult in Microsoft Excel where x ^T x is calculated. Once this matrix has been calculated, you can use the minverse function to arrive at (x ^T x)⁻¹ .

In Stata this can be done by using the, robust option.

The test also includes the predicted values squared and to the power of three.

Specifically, in the mentioned regression model y = α + β ₁ x ₁ + β ₂ x ₂ + β ₃ x ₃ + e, the Breusch-Pagan test determines whether \( \widehat{e^2}=\alpha +{\beta}_{BP1}{x}_1+{\beta}_{BP2}{x}_2+{\beta}_{BP3}{x}_3+{e}_{BP} \).

This hypothesis can also be read as that a model with only an intercept is sufficient.

The AIC is specifically calculated as AIC = n·ln(SS _E/n) + 2·k, where n is the number of observations and k the number of independent variables, while the BIC is calculated as BIC = n·ln(SS _E/n) + k·ln(n).

Cohen’s (1994) classical article “The Earth is Round (p < 0.05)” offers an interesting perspective on significance and effect sizes.

Using the Stata command egen commitment=rowmean(com1 com2 com3)

Note that a p-value is never exactly zero, but has values different from zero in later decimal places.

Note that it is possible to show all categories for regression tables by typing set showbaselevels on. This can be made permanent by typing set showbaselevels on, permanent.

Note that while the constant has the highest value (1.19), this is not a coefficient and should not be interpreted as an effect size.

Please note that only Stata 13 or above feature built-in routines to calculate η ².

The seed specifies the initial value of the random-number generating process such that it can be replicated later.

We would like to thank Dr. D.I. Gilliland and AgriPro for making the data and case study available.

Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Thousand Oaks: Sage.

Baum, C. F. (2006). An introduction to modern econometrics using Stata. College Station: Stata Press.

Breusch, T. S., & Pagan, A. R. (1980). The Lagrange multiplier test and its applications to model specification in econometrics. Review of Economic Studies, 47(1), 239–253.CrossRef

Cameron, A.C. & Trivedi, P.K. (1990). The information matrix test and its implied alternative hypotheses. (Working Papers from California Davis – Institute of Governmental Affairs, pp. 1–33).

Cameron, A. C., & Trivedi, P. K. (2010). Microeconometrics using stata (Revised ed.). College Station: Stata Press.

Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155–159.CrossRef

Cohen, J. (1994). The earth is round (p < .05). The American Psychologist, 49(912), 997–1003.CrossRef

Cook, R. D., & Weisberg, S. (1983). Diagnostics for heteroscedasticity in regression. Biometrika, 70(1), 1–10.CrossRef

Durbin, J., & Watson, G. S. (1951). Testing for serial correlation in least squares regression, II. Biometrika, 38(1–2), 159–179.CrossRef

Fabozzi, F. J., Focardi, S. M., Rachev, S. T., & Arshanapalli, B. G. (2014). The basics of financial econometrics: Tools, concepts, and asset management applications. Hoboken: Wiley.CrossRef

Green, S. B. (1991). How many subjects does it take to do a regression analysis? Multivariate Behavioral Research, 26(3), 499–510.CrossRef

Greene, W. H. (2011). Econometric analysis (7^th ed.). Upper Saddle River: Prentice Hall.

Hair, J. F., Jr., Black, W. C., Babin, B. J., & Anderson, R. E. (2013). Multivariate data analysis. Upper Saddle River: Pearson.

Hill, C., Griffiths, W., & Lim, G. C. (2008). Principles of econometrics (3^rd ed.). Hoboken: Wiley.

Kelley, K., & Maxwell, S. E. (2003). Sample size for multiple regression: Obtaining regression coefficients that are accurate, not simply significant. Psychological Methods, 8(3), 305–321.

Mason, C. H., & Perreault, W. D., Jr. (1991). Collinearity, power, and interpretation of multiple regression analysis. Journal of Marketing Research, 28, 268–280.CrossRef

Mooi, E. A., & Frambach, R. T. (2009). A stakeholder perspective on buyer–supplier conflict. Journal of Marketing Channels, 16(4), 291–307.CrossRef

O’brien, R. M. (2007). A caution regarding rules of thumb for variance inflation factors. Quality and Quantity, 41(5), 673–690.CrossRef

Ramsey, J. B. (1969). Test for specification errors in classical linear least-squares regression analysis. Journal of the Royal Statistical Society, Series B, 31(2), 350–371.

Sin, C., & White, H. (1996). Information criteria for selecting possibly misspecified parametric models. Journal of Econometrics, 71(1–2), 207–225.

StataCorp. (2015). Stata 14 base reference manual. College Station: Stata Press.

Treiman, D. J. (2014). Quantitative data analysis: Doing social research to test ideas. Hoboken: Wiley.

VanVoorhis, C. R. W., & Morgan, B. L. (2007). Understanding power and rules of thumb for determining sample sizes. Tutorial in Quantitative Methods for Psychology, 3(2), 43–50.CrossRef

White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica: Journal of the Econometric Society, 48(4), 817–838.CrossRef

Title: Regression Analysis
Authors: Erik Mooi
Marko Sarstedt
Irma Mooi-Reci
Publisher: Springer Singapore
Book: Market Research
Print ISBN: 978-981-10-5217-0

Electronic ISBN: 978-981-10-5218-7

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-981-10-5218-7_7