What causes a faulty Linear Voltage regulator to output wrong voltage
LM/KA78xx regulators are almost impossible to get to oscillate (unlike many other types such as LM1117, LM7905 etc). Others are either repeating folklore or are much (un)luckier in this regard than I have been (and I've tried to get them to ring). 

We shipped approximately 30,000 units with no output capacitor, for example, and zero problems. And some 78xx datasheets explicitly state that the output capacitor is not required for stability. One of the advantages (along with price) of non-LDO positive regulators. Usually you want a cap on the output for transient response on a digital circuit, but typically nothing bad will happen other than poor regulation if you omit it. The internal voltage divider is more than sufficient minimum load at normal temperatures. 



If the ground pin connection is not in place your output will go too high, so it's definitely not that. 

You could have a defective part. You could have a (possibly fraudulently) remarked 7805. But, I suspect your problem is that you have a mains-frequency transformer followed by a rectifier and either no capacitor or insufficient capacitance. This is not a stability issue, but a filter capacitor/ripple voltage issue. if the input voltage is above about 9.5V you'll get 8V out, but if it dips down to say 3V, you'll get very little out, so the output would be a clipped version of the input waveform, plausibly with an average that was 4.8V. 







simulate this circuit &ndash; Schematic created using CircuitLab