Hello all,
Quite a few of you asked me to summarise the responses I got to this
query so here goes;
In multiple linear regression the predictors and outcome variable do not
need to be normally distributed, but the residuals do. One person
however stated that in many regression situations, you don't strictly
need the residuals to be normally distributed, just that the residuals
are idependently and identically distributed with equal variance
(properties that a normal distribution has). Other assumptions covered
in Tabachnick & Fidell were mentioned such as homoscedasticity of
residuals and independence of errors. Another noted that if the
predictor and outcome variables are normally distributed and if the
linear fit of the model follows the data reasonably well this may
improve the normality you observe in the residuals. Someone else drew my
attention to Tabachnick BG & Fidell LS (Using Multivariate Statistics,
4th Edn, 2001: Allyn & Bacon, MA) who stated that '... A higher
cases-to-IV ratio is needed when the DV is skewed...'
I was referred to the following;
Chatterjee, S. Price (1991). Regression Analysis by Example. 2nd ed.
Wiley.
Draper, S. Smith, H. (1998). Applied Regression Analysis. 3rd ed. John
Wiley.
Montgomery, D. C. Peck, E. A. (1992). Introduction to Linear Regression
Analysis. 2nd ed. Wiley.
Neter, J., Kunter, M. H., Nachtsheim, C. J. Wasserman, W. (1996)
Applied Linear Statistical Models, 4th ed. Irwin.
Weisberg, S. (1985). Applied Linear Regression. Wiley.
Dobson, A. J. (1990). An Introduction to Generalized Linear Models.
Chapman & Hall.
Tabachnick BG & Fidell LS (Using Multivariate Statistics, 4th Edn, 2001:
Allyn & Bacon, MA
Miles, J and Shevlin, M (2001). Applying regression and correlation.
London: Sage.
Field (2003) Discovering statistics usinfg spss for windows. Sage
Belsley, Kuk & Welsch (1980) Regression Diagnostics. Wiley
Berry & Feldman (1985) Multiple Regression in Practise. Sage.
Hope this helps. If I have done injustice to any of your comments let me
know!
Regards,
Rob
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