You need to maintain about 3v minimum across your regulator. This means the unregulated voltage should never dip below 15v. With 4700uF, you will get about 4v of ripple, which means the peaks of your unregulated voltage will have to be 19v. You will lose about 1.5v in your bridge rectifier, which means the peak voltage from your transformer needs to be at least 20.5v. This is 15v RMS. If your transformer secondary is rated at less than 15v, you need a bigger capacitor.
Sherif's equation will give you about a volt of ripple. If you can tolerate more, you can use a smaller capacitor.