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 ?