tag:blogger.com,1999:blog-21831384.post7516459931197767019..comments2019-10-03T14:11:35.530+05:30Comments on BzST | Business Analytics, Statistics, Teaching: Interpreting log-transformed variables in linear regressionGalit Shmuelihttp://www.blogger.com/profile/06119270323184007583noreply@blogger.comBlogger17125tag:blogger.com,1999:blog-21831384.post-34591488289078636262013-05-21T22:43:46.116+05:302013-05-21T22:43:46.116+05:30Thanks*100 !! :DThanks*100 !! :DAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-21831384.post-32949673862185610572013-05-21T21:44:48.316+05:302013-05-21T21:44:48.316+05:30Yes, that is correct. See the Wikipedia entry on D...Yes, that is correct. See the Wikipedia entry on <a href="http://en.wikipedia.org/wiki/Data_transformation_(statistics)#Data_transformation_in_regression" rel="nofollow">Data transformation</a>. It reads:<br /><br />"If desired, the confidence interval can then be transformed back to the original scale using the inverse of the transformation that was applied to the data."Galit Shmuelihttps://www.blogger.com/profile/06119270323184007583noreply@blogger.comtag:blogger.com,1999:blog-21831384.post-62625725833181704692013-05-13T13:37:08.361+05:302013-05-13T13:37:08.361+05:30Sorry to belabor this but if possible, it would be...Sorry to belabor this but if possible, it would be great to know how to calculate the confidence interval for this percent change. Using the 'clparm' option in SAS gives me the 95% CI around the CO-EFFICIENT. I am guessing to obtain the 95% CI around "percent change", I'd have to treat these 2 values like I treated the co-efficient itself, i.e. (ExpLimit1-1)*100, (Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-21831384.post-10217133303051955532013-05-09T19:47:21.537+05:302013-05-09T19:47:21.537+05:30Ok. I think I get it. Exponentiating and then conv...Ok. I think I get it. Exponentiating and then converting to percent change is simply average percent change in the outcome variable and there's no need to say 'mean' of the outcome variable- just the outcome variable.<br /><br />THANK you once again for creating this blog and for your help.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-21831384.post-76894147296433438182013-05-09T10:49:42.386+05:302013-05-09T10:49:42.386+05:30If you are using the geometric mean interpretation...If you are using the geometric mean interpretation, then it is the exact interpretation (you are not doing any approximation to percentages). Galit Shmuelihttps://www.blogger.com/profile/06119270323184007583noreply@blogger.comtag:blogger.com,1999:blog-21831384.post-90428704814587897222013-05-09T10:30:55.125+05:302013-05-09T10:30:55.125+05:30Thanks. I understood that the exponentiated co-eff...Thanks. I understood that the exponentiated co-efficient gives the ratio of the geometric means. I was concerned about interpreting this when one substracts 1 from this and multiplies by 100. Is this ((expB-1)*100) then, the average percent change in "geometric means"? Many thanks for your help.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-21831384.post-25602187051246010252013-05-09T09:18:34.830+05:302013-05-09T09:18:34.830+05:30Think of it this way: Suppose GENDER=1 for men, an...Think of it this way: Suppose GENDER=1 for men, and 0 for women.<br />If you plug in GENDER=0 with some set of X values into the equation, you get the fitted ln(Y) for women. Then plug in GENDER=1 with the same X values, you get the fitted ln(Y)for men. Note that ln(y) is not the geometric mean (you have to take an exponent to get the geometric mean). The difference between these fitted ln(y) Galit Shmuelihttps://www.blogger.com/profile/06119270323184007583noreply@blogger.comtag:blogger.com,1999:blog-21831384.post-11892679993988877542013-05-09T00:32:23.220+05:302013-05-09T00:32:23.220+05:30Ok, a little confused. The 'average percent di...Ok, a little confused. The 'average percent difference' in the geometric means of the two groups ?<br /><br />Or the 'average percent difference' in the average, i.e. means of the two groups?<br /><br />Thanks!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-21831384.post-71757720137530333452013-05-07T15:48:31.971+05:302013-05-07T15:48:31.971+05:30Yes, it means the "average percentage differe...Yes, it means the "average percentage difference". The percentage difference between women and men can take different values, so we're talking about the average across these values.<br /><br />If you compute a confidence interval for a beta parameter, then the CI will also need to be interpreted in the same manner. For a 90% CI, you'll say that you are 90% confident that the Galit Shmuelihttps://www.blogger.com/profile/06119270323184007583noreply@blogger.comtag:blogger.com,1999:blog-21831384.post-82427189051155551522013-05-07T13:58:34.111+05:302013-05-07T13:58:34.111+05:30Thanks. By "average difference", do you ...Thanks. By "average difference", do you mean percent change in mean, and more specifically, geometric mean? Since the absolute value of my co-efficients is large (upto 0.6), I'd like to use the more precise formula: 100(expB-1) percent. How does one calculate the confidence interval for this PERCENT CHANGE? Again, by applying the same formula to the logged CI values? Thanks a bunch!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-21831384.post-86254909638503122482013-05-02T12:27:18.274+05:302013-05-02T12:27:18.274+05:30Hi Grace,
It sounds like you're in the case of...Hi Grace,<br />It sounds like you're in the case of "a unit increase in X in associated with an average of 100b percent increase in Y."<br /><br />If you X = Gender (Male/Female), then the coefficient of Gender, multiplied by 100, would be interpreted as the average difference between Y for males and females.<br /><br />The best way to make sure your interpretations are correct, is Galit Shmuelihttps://www.blogger.com/profile/06119270323184007583noreply@blogger.comtag:blogger.com,1999:blog-21831384.post-39140082299652466632013-05-02T11:42:49.260+05:302013-05-02T11:42:49.260+05:30Thanks for the article. Only my right-skewed outco...Thanks for the article. Only my right-skewed outcome is log-transformed, the predictor variables are as they are. So, I am interpreting the exponentiated co-efficient of logoutcome as ratio of geometric means of the two predictor groups (eg. female vs. male). I'm multiplying this by 100 to get the outcome for females as percent of outcome for males, on the original scale. Does this sound Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-21831384.post-80473239973557688642013-02-18T15:19:38.438+05:302013-02-18T15:19:38.438+05:30Sorry, had no idea how I missed that. =)Sorry, had no idea how I missed that. =)eric hoohttps://www.blogger.com/profile/15021924129768595856noreply@blogger.comtag:blogger.com,1999:blog-21831384.post-84624543047764045682013-02-15T21:56:21.524+05:302013-02-15T21:56:21.524+05:30Hi Eric,
As the post says:
"The interpretatio...Hi Eric,<br />As the post says:<br />"The interpretation of b is: a unit increase in X in associated with an average of 100b percent increase in Y. This approximate interpretation works well for |b|<0.1. <b>Otherwise, the exact relationship is: a unit increase in X is associated with an average increase of 100(exp(b)-1) percent.</b>"Galit Shmuelihttps://www.blogger.com/profile/06119270323184007583noreply@blogger.comtag:blogger.com,1999:blog-21831384.post-39574069477013080542013-02-15T15:53:01.895+05:302013-02-15T15:53:01.895+05:30Thank you for the excellent post!
I was wondering...Thank you for the excellent post!<br /><br />I was wondering how you would interpret the coefficient when it is more than 0.1? I browsed through the book by Vittinghoff too but he did not mention how to deal with this scenario.<br /><br />Your expert advise on the matter is greatly appreciated.eric hoohttps://www.blogger.com/profile/15021924129768595856noreply@blogger.comtag:blogger.com,1999:blog-21831384.post-64358617366315779752012-11-02T09:42:53.016+05:302012-11-02T09:42:53.016+05:30Thanks for catching this Mahin! I corrected the po...Thanks for catching this Mahin! I corrected the post.Galit Shmuelihttps://www.blogger.com/profile/06119270323184007583noreply@blogger.comtag:blogger.com,1999:blog-21831384.post-10665994924442673852012-11-02T08:46:22.065+05:302012-11-02T08:46:22.065+05:30Kindly pay attention to the last part of the write...Kindly pay attention to the last part of the write up on LOG-Log multiplicative model. <br />I suppose there is a mixed up of information here specially "b" and "d" usage in the equation and the model specification of the multiplicative model. Should the model be written as X1 to the power "b" and X2 to the power C and so on? Mahinhttps://www.blogger.com/profile/03306366083967347690noreply@blogger.com