What type of regression to use with 1 to 10 scale dependent variable? I am a bit new to analytics. I have this survey dataset with the attributes below.
Independent variable:


*

*a. Are we trustworthy? (Value: 1 to 10) 

*b. Do we offer solutions that you need (Value: 1 to 10) 

*c. Are we proactive (Value: 1 to 10) 

*d. Do we provides consistent quality of service (Value: 1 to 10) 

*e. Do we provide exceptional service (Value: 1 to 10)


Dependent variable:


*

*How likely you will recommend us to others? (Value: 1 to 10)


Here I want to do a regression between the DV and IV. Previously I have done logistic regression in R language for binomial outcomes and continuous IVs. But this scenario consists of entirely ordinal data. 
How can I regress this data and find some relationship? Please share your ideas on useful  techniques to solve this. Apart from regression, is there any another method?
 A: Here is R example using package MASS with polr function (ordered factorial response) which can use logistic link or be probit.  
library(MASS);
recmodel=polr(recom~trust+solutions+proact+qs+es,data=surveydata,method=c("logistic"));  
summary(recmodel);  

I think it is important to give R notice that all variables are ordinal which means that it must not use them as interval variables.  
Inference can be done as a comparison to some baseline. For example value 1 can be such.
A: 1) Judging by the questions in the survey, the likelihood of multi-collinearity is high. You should definitely check for correlation and VIF between your predictor variables before thinking of running the regression. 
2) Apart from regression and at the cost of sounding simplistic, I suggest you do some summary statistics and exploratory analysis. a) What is the distribution of responses for each question? b) Depending on the response on an individual question, how the response variable moves. For e.g.: What % of people who rated beetween 5 & 7 on question 2, also said they were likely (rating above 7) to recommend to others? 
The descriptive analysis will visualize and give good direction of where you need to head with the regression analysis.
A: As pointed out in the comments, the dependent variable can be handled with ordinal logit. For the independent variables, the most flexible approach is to convert each variable to 10 dummy variables (assuming you drop the constant from the model). Interpretation will get a little bit messy, but you are not imposing any functional form assumptions on the independent variables.
A: You can also try the stereotype logistic regression model (a type of reduced-rank generalized linear regression model) that relaxes the constraint of ordering (without reverting to a multinomial logistic regression model, which with ten outcome levels will present a great deal of parameters that might hinder your ability to interpret the relationships in tee data). The constraint of ordering relies on the proportional odds assumption, which may be violated in some instances when using the ordinal regression model. See ?rrvglm in the VGAM package for examples on fitting the stereotype logistic model.
