Quanlitative variables are not numeric, but regression models operate on numeric variables. Categorical predictors with k categories are represented as k or k-1 numeric variables coding the different categories. The dependent variable must be numeric. If the response is binary (categorical with two levels), it is convenient to code the categories as 0 and 1, so the model will be about the proprotion of the response categories. This is used by logistic regression models. If the response have more than two levels, multinominal logistic models are used, and if the categories are ordered, the best tool is an ordered logistic regression.

Some hits of a Google search (logistic multinominal ordered regression):

https://havardhegre.files.wordpress.com/2014/03/logisticregression2011.pdf

http://www.kenbenoit.net/courses/ME104/ME104_Day8_CatOrd.pdf

http://www.karlin.mff.cuni.cz/~antoch/robust10/PREDNASKY/CTVRTEK_DOPOLEDNE/zezula.pdf

Hello Ameur Haouari ,I trust you are well. to me there is no problem,but you need to understand the different type of model to fit. fore instance i have a project on malaria prevalence in Kenya so i have malaria status as my response where i have 1. with malaria and 0.without malaria.

so am going to fit  a logistic regression model.

the model looks like this

log(P/1−P)=β0+β1x1+β2x2 ,…,+βkxk

where P= Pr(y=1)

In the model, the Odds for the kth independent variable is 𝑒𝛽𝑘 where β0, β1, β2 ,…,βK are the regression coefficients, x1, x2,…,xk are the predictor variables and k is the number of predictors.

i wish you all the best

I think there is no problem to use of qualitative variables as dependent variables in the regression equation.

Using a qualitative variable as dependent variable in linear regression leads to answers that are utter rubbish. Can you say that if one person is married and another person is single, then on average they are widows? Linear regression models are based on means, variances and correlation coefficients, none of which make any sense if your dependent variable is qualitative. An appropriate model is logistic regression. You have binary logistic regression if your dependent variable has two categories, or multinomial logistic regression (ordinal or nominal according to the nature of your dependent variable) if there are more than two categories. The independent variables my be qualitative (then they are called factors) or quantitative (called covariates).

As suggested by both Jochen Wilhelm and Francois Steffens, you may proceed with regression if dependent variable has two levels or multinomial logistic regression if you have to hundle with more levels. 

It's not at all a problem to have qualitative variable as dependent variable in regression analysis. you may use binary, ordinal or multi nominal logistic regression as per the level of DV.

But this is not the case with linear regression where DV is metric.