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After applying quantile regression with t=0.5,0.6 on the data set WBC( Wisconsin Breast Cancer)with 678 observations and 9 independent variables($inp_1,inp_2,...inp_9$) and 1 dependent variable(op) I have got the following results for beta values.

| t         |  0.5          |  0.6      |
| b1        |  0.002641     |  0        | 
| b2        |  0.045746     |  0.01     | 
| b3        |  0.005282     |  0        | 
| b4        |  0.004397     | -0.002    | 
| b5        |  0.002641     |  0.004    | 
| b6        |  0.065807     |  0.1111   | 
| b7        |  0.005282     |  0.002    | 
| b8        |  0.031394     |  0        | 
| b9        |  0.004993     |  0        | 
| intercept | -0.181388     | -0.009    | 

How to interpret the above beta coefficients and what do they mean exactly?.

  • t=0.5 means are we considering first 50% of the total data?
  • t=0.6 means are we considering the first 60% of the total data?

can we write a equation like

$y=intercept+\sum_{i=1}^{9}b_i*inp_i$ as in Linear Regression to calculate the predicted output of y or not?

If we are taking into consideration 5 quantiles of data ,Does it mean that we are dividing data it into 5 parts??which variables i have to consider if the data is to be divided into 5 parts?

and

I have got 5 equations for 5 quantiles, what exactly do each equation represent? Can I write single equation for the data set as in mean regression by combining the 5 equations of each quantile ?

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  • $\begingroup$ I have edited the question to make it more readable. Please check if I have accidentically changed the meaning (or numbers). Sidenote: You do not have to to sign your posts. Nevertheless, welcome on this site :) $\endgroup$ – steffen Dec 2 '11 at 9:52
  • $\begingroup$ @Narendar reddy kalam: Why have you chosen the quantile regression model? What are the property of the estimated slopes that you want and which lead you to choose this estimation technique? $\endgroup$ – user603 Dec 2 '11 at 12:02
  • $\begingroup$ @user603 i am trying to use the quantile regression technique to regression and classification problems as linear regression is used for the same purpose but it will give the estimates of dependent variables with respect to changes in the meanvalue of them according to unit variations in the independent(x) variables but it will not give good estimation for a new observation which have characteristics similar to lower and higher quantiles of the data. $\endgroup$ – Narendar reddy kalam Dec 2 '11 at 18:55
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You can interpret the results of quantile regression in a very similar way to OLS regression, except that, rather than predicting the mean of the dependent variable, quantile regression looks at the quantiles of the dependent variable. By choosing .5 and .6, you are using the 50th and 60th percentiles.

I wrote about quantile regression on my blog here. I also did a presentation about it, quantile regression using PROC QUANTREG in SAS.

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  • $\begingroup$ thank u sir,your document is very informative.but my doubt is can i use the results of quantile regression for future prediction.Lets take your birth weight example only,quantile regression will give very good view of the all the categories of the babies.but if i have all the independent variables values(like moters age,paretal care,mothers weightetc..),so can i use these values for predicting birth weight of baby??because quantile regression will give the relation between the childs birth weight and mother's charecteristics. $\endgroup$ – Narendar reddy kalam Dec 3 '11 at 6:40
  • $\begingroup$ my basic question is can i use quantile regression for future prediction what i mean is if i have the model which is given by quantile rgression like y=intercept+b1*x1+....+bn*xn where b1,b2..bn are coffiecients given by the model.so can i use this equation for future new observation to predict birth weight value of the child.if we can use it for future prediction?? $\endgroup$ – Narendar reddy kalam Dec 3 '11 at 6:59
  • $\begingroup$ The question of whether you can use quantile regression for prediction will have the same answer as whether you can use OLS regression. The answer doesn't depend on the statistical technique but on the sample and such $\endgroup$ – Peter Flom Dec 3 '11 at 12:31
  • $\begingroup$ ,yes sir,i agree with you.But the problem is after building model using OLS we have only one equation of y=betaX+intercept. But with quantile regression,(if i take 5 quantiles into consideration) we have 5 such equantions y=betax+intercept corresponding to 5 different quantile values.So which equation i have to consider for future predictions.. $\endgroup$ – Narendar reddy kalam Dec 5 '11 at 5:43
  • $\begingroup$ @Narendarreddykalam What do you WANT to predict ? If you want to use it as a robust alternative to OLS, then you predict the 50-percentile and you are done. $\endgroup$ – steffen Dec 5 '11 at 10:19
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With OLS you predict a mean value for given xs, with the median regression you predict a median value given the same xs, so if you estimate a regression for the 1st QUARTILE, you get the predicted 1st quartile given the same xs.

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