Solved – About interpretation of the results of quantile regression

quantile regressionregression

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 ?

Best Answer

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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