Linearity Assumption in OLS with Dummy Variables Let's say that I have a continuous response variable and have constructed a regression model with multiple predictors. Most of my predictors are continuous but I have one which is a dummy variable. How do I determine whether the ols assumption of linearity is met or violated? And if the linearity assumption is violated, how would I go about transforming the dummy variable?
 A: It's time this question had an answer.

I have a continuous response variable and a regression model with multiple predictors.
  Most of my predictors are continuous 

The continuity or otherwise of a predictor makes no no difference; a relationship only need be linear over the domain where it's defined, for it to be linear.

How do I determine whether the ols assumption of linearity is met or violated? 

With a 0/1 predictor ($d$ say) there are only two possibilities:
$E(Y|d=0,\underline{x})=E(Y|d=1,\underline{x})$ or
$E(Y|d=0,\underline{x})\neq E(Y|d=1,\underline{x})$ 
(where $\underline{x}$ is all the other predictors)
In either case, linearity is satisfied, since the population coefficient is the difference in expected values in either case. 
It is, however, possible that the size of the coefficient depends on the values of the other parameters (i.e. interactions between other predictors and $d$ may exist).

And if the linearity assumption is violated, how would I go about transforming the dummy variable?

The (conditional) linearity of $y$ in terms of $d$ is automatically satisfied - 
fortunately, because we can't gain anything substantive here by attempting to transform a dummy.
A: Adding to the excellent answer by Glen_b, it is worth noting that adding a categorical variable into a regression cannot cause problems with the linearity assumption in and of itself.  If there is an issue of non-linearity in the model it will be due to some underlying relationship that is not captured by the specified model form, but the inclusion of a categorical variable cannot cause this problem.
To see this more clearly, consider a regression with an arbitrary categorical variable $h = 1,...,k$ with $k \geqslant 2$ possible outcomes, and one or more other terms encapsulated by $\mathbf{x}.$  The categorical variable is represented in a regression by $k-1$ indicator variables for the categories (with one base category).  So the relevant terms in the model will look like this:
$$\mathbb{E}(Y_i|\mathbf{x},\mathbf{h}) = \beta_0 + \sum_{\ell=1}^{k-1} \beta_\ell \cdot \mathbb{I}(h_i = \ell) + \text{Other terms for } x_i.$$
The linearity assumption in regression requires that the regression equation be linear with respect to the coefficient parameters.  The presence of the categorical variable $h$ in the regression adds the parameters $\beta_1,...\beta_{k-1}$ which apply across categories.  Each individual indicator term simply adds a term for the difference in conditional expectation based on whether the categorical variable is in that category or not.  The addition of such terms cannot constitute non-linearity.
