Let us suppose we have following data
x y 1 5 2 4 3 5 4 4 5 7
I would like to do Quantile regression in excel, I have found following information about given method
based on this information let choose $q=75$ or 75% quantile, in excel I have done following structure, first create dummy variable based on indicator function and also choose arbitrary values of alpha and beta
$$\beta=0.2 $$ dummy variable has been filled using following method
initially all values are zero, now I have calculated one column for sum
and finally I have calculated sum of all those values, and then using solver I have estimated coefficients which minimizes sum, I have got following values and result
please tell me if I am wrong, and also statistically could you explain me please what does this mean? What does those coefficient describe in terms of quantile?