```Date: Wed, 28 Sep 2005 08:31:07 -0400 Reply-To: Art@DrKendall.org Sender: "SPSSX(r) Discussion" From: Art Kendall Organization: Social Research Consultants Subject: Re: Logarithmic transformation of not normal data Comments: To: razan_mikwar@YAHOO.COM In-Reply-To: Content-Type: text/plain; charset=us-ascii; format=flowed Depending on the number of cases you have and the subject matter area, a multiple correlation of .55 (r**2= .3) could be suspiciously high. What are your variables? how are they measured? How many cases do you have? How were they selected? Art Art@DrKendall.org Social Research Consultants University Park, MD USA Inside the Washington, DC beltway. (301) 864-5570 Hector Maletta wrote: >Razan, >see my comments below. >Hector > > > _____ > >From: Razan Mikwar [mailto:razan_mikwar@yahoo.com] >Sent: Thursday, September 15, 2005 2:30 AM >To: Hector Maletta >Subject: RE: Logarithmic transformation of not normal data > > >Hi Mr.Hector, > >First of all thank you very much for your quick response. >Secondly: >1-I don't want high correlation coefficient what I need to make it higher is >the coefficient of determination(R squre), and about residuals I've already >tested there normality and they are normal. > >R2 is the squared correlation coefficient, so both are essentially the same. >If residuals are normal, nothing is necessary to get more normal residuals >such as a log transformtion. > >2-I don't know what do you mean by the 2nd point but I've tested that there >is no correlation between independent variables i.e there is no >multicollinearity, and the scatter between the DV and each IV is not u >shaped. > >What I mean in my second point is that a low R or R2 may be due to either: >the absence of any relationship between your DV and the set of IV, or the >presence of a relationship that is not linear. This can be ascertained by >plotting predicted and observed values. A formless cloud is the first case, >a regular but not linear shape, e.g. a cloud in the shape of an U, is the >second case. In the latter situation you may transform some of the variables >to get a linear, instead of non-linear relationship, or you may try >non-linear regression or curve fitting. > >3 & 4- I'm trying hardly not to another model other than linear in order not >to test another assumptions that's why I'm trying to find a way to solve the >problem,Moreover Idon't know how to detect which model that would fit. > >Models are based on theory. Trying blindly anything that fits is not good >advice. > >5-As I mentioned before I've tested collinearity but there is only one >assumption that I wasn't able to test is that residuals and independent >variables are independent from each other because I don't have the residuals >as separated variable. > >Collinearity might have been one problem, but you evidently do not have it. >Perhaps it is simply that your IV do not predict the DV well. That happens. > > >Razan > > >Razan, > >1. Your variables do not need to be normally distributed in order to use >regression, and even less so in order to get high correlation coefficient. >You are confused by the fact that linear regression requires that residuals, >i.e. random errors of prediction (difference between predicted and observed >values) have a normal distribution both sides of the regression line. > >2. A low or near zero linear [multiple] correlation coefficient may be due >to (a) the absence of any systematic relationship between your IV and DV, or >(b) the existence of a relationship which is non linear. As an example of >(b), if your scatterplot shows a cloud of points with the shape of a U, >there would be possibly a quadratic relationship but the linear coefficient >may be zero. > >3. The method of least squares to estimate regression functions is based on >the assumption of a linear relationship between the variables involved. When >the relationship is not linear there are two ways to go: (i) identify the >non-linear function linking the variables, and transform it in some way that >yields a linear function, then apply least squares linear regression; or (b) >approximate a non linear function by means of non-linear regression or >curve-fitting, which do not use the least squares algorithm. Some non linear >functions are amenable to linearization, some are not. For instance, a >quadratic equation like y=a+bX+cX^2 can be linearized if you define a new >variable Z=X^2, and use the linear equation y=a+bX+cZ; likewise the equation >y=aX^b can be linearized by taking logarithms as log y=log a + b(log X). > >4. The fact that a certain mathematical function fits your data is no great >deal. You can always find some function that does that. The trick is finding >a function for which you have a theoretical explanation. So it is not >advisable to go around blindly trying different mathematical functions until >any of them "fits". In fact, you may find several, perhaps an infinite >number of functions that reasonably fit the data, and that is arguably worse >than not having any. > >5. If no reasonable function fits the shape of the data, perhaps your data >just show little relationship at all between the variables... > >Hector > > > > > >>-----Original Message----- >> >> > > > >>From: SPSSX(r) Discussion [ >> >> >mailto:SPSSX-L@LISTSERV.UGA.EDU] On Behalf > > > >>Of Razan >> >> > > > >>Sent: Monday, September 12, 2005 11:04 PM >> >> > > > >>To: SPSSX-L@LISTSERV.UGA.EDU >> >> > > > >>Subject: Logarithmic transformation of not normal data >> >> > > > > > > >>Hi, >> >> > > > > > > >>I've made a multiple linear regression using SPSS by one dependent >> >> > > > >>variable and two indepent variables and all assumptions were satisfied >> >> > > > >>but R squre is very low about 0.3,so I think that is because my >> >> > > > >>variable are not normally distributed that's why I was thinking about >> >> > > > >>transforming my data uasing logarithmic transformation to normal >> >> > > > >>distributio and repeat the regression,but I don't know how to >> >> > > > >>transform them? >> >> > > > >>and do I have to test any other assumptions after applying the >> >> > > > >>transformation?] >> >> > > > > > > >>Thanks >> >> > > > > ```

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