Linearity means that there is a straight line relationship between the IVs and the DV. This assumption is important because regression analysis only tests for a linear relationship between the IVs and the DV. Any nonlinear relationship between the IV and DV is ignored. You can test for linearity between an IV and the DV by looking at a bivariate scatterplot (i.e., a graph with the IV on one axis and the DV on the other). If the two variables are linearly related, the scatterplot will be oval. You can also test for linearity by using the residual plots described previously. This is because if the IVs and DV are linearly related, then the relationship between the residuals and the predicted DV scores will be linear. Nonlinearity is demonstrated when most of the residuals are above the zero line on the plot at some predicted values, and below the zero line at other predicted values. In other words, the overall shape of the plot will be curved, instead of rectangular.
If your data are not linear, then you can usually make it linear by transforming IVs or the DV so that there is a linear relationship between them. Sometimes transforming one variable won't work; the IV and DV are just not linearly related. If there is a curvilinear relationship between the DV and IV, you might want to dichotomize the IV because a dichotomous variable can only have a linear relationship with another variable (if it has any relationship at all). Alternatively, if there is a curvilinear relationship between the IV and the DV, then you might need to include the square of the IV in the regression (this is also known as a quadratic regression).
The failure of linearity in regression will not invalidate your analysis so much as weaken it; the linear regression coefficient cannot fully capture the extent of a curvilinear relationship. If there is both a curvilinear and a linear relationship between the IV and DV, then the regression will at least capture the linear relationship.
