[levocardia]

Non-constant variance does not actually bias the coefficients of a linear regression model -- thus, its predictions will be just fine. What it does is underestimate the standard errors; your p-values will typically be too small. Sometimes a log-transform or similar can help, but otherwise you can use weighted least-squares.

This kind of problem is actually a good intro to iterative refitting methods for regression models: How do you know what the weights should be? Well, you fit the initial model with no weights, get its residuals, use those to fit another model, rinse and repeat until convergence. A good learning experience and easy to hand-code.