Dependent variables in regression I have two variables in a regression problem, where I predict the end interest rate for a loan application.


*

*x1: risk band (A+,A,B,C)

*x2: initial rate (6%, 7%, 8%, 9%)


Based on these two variables, I'm trying to predict what the actual end rate, y, will be (i.e 6.3%).
Risk band is dependent on initial rate and vice versa. i.e A+ -> 6%. I would need to convert the risk band to 0s and 1s for each degrees of freedom in the category.
I have read the linear regression requires that the input features be independent. In my case, they are not. Would it make sense to include both in the model?
So a possible input feature vector might look like this:
[0,0,1,9] -> C risk band, 9% initial rate
[0,0,0,6] -> A+ risk band, 6% initial rate
I can z-score the initial rate to make the ranges smaller.

Given the answer below, If I choose to represent initial rate as a categorical feature as well, then I would have a problem because they would be scalar multiples of the risk band. For example
[0,0,1,0,0,1] -> C risk band, 9% initial rate
[0,0,0,0,0,0] -> A risk band, 6% initial rate
However, If I use an ordinal feature for the intial rate, then there shouldn't be a problem, because they are not scalar multiples of risk band. For example,
[0,0,1,9] -> C risk band, 9% initial rate
[0,0,0,6] -> A+ risk band, 6% initial rate
Is that correct?
 A: EDIT: If the mapping is constant, i.e. A+ always => 6%, then you should remove x1 or x2. They are the same variable. My answer below is relevant for subtle dependences, but in this case the answer is much simpler. 

It's ok but not ideal. The more dependent the features are the less useful they will be to your final model, but they won't hurt you. See here for an explanation of methods for when variables are dependent:
http://www.psych.yorku.ca/lab/psy6140/lectures/MultivariateRegression2x2.pdf
If they are dependent, i.e. one of your features is a scalar multiple of the other. Because then you will end up with a symmetric matrix (A^T * A) which is not invertible - and then you have problems. So it's fine if they are correlated, just not to a scalar multiple. 
Essentially what linear regression does is transform all of your training examples x as linear equations
0 * x1 + 0 * x2 + 1 * x3 + 9 * x4 + 1 * x5 = 0.09

into a matrix A with each row as an equation and each column as a feature or variable. Generally, if our dimensions are m x n, where m is the number of features (plus the x5 which is for our origin offset) and n is the number of examples. 
Solving the equation
x = (A^T * A)^(-1) * A^T * b

where b is the target rates, will give you the coefficients of your line which minimizes the squared error of the training set. (Note the inversion of A^T * A!)
Your next step is to include higher-order features like the squares or cubes of your data - you might very well find that the relationship in the true underlying model is not linear. 
