My dog was a nightmare to house train... so I'll let you know what I ended up doing.
Whenever he was in the house, he would have his leash on and would be tied to me. He was never able to get even four feet away. I would take him outside every hour and command him to go pee (he now pees on command). If he so much as started sniffing around, I would take him outside and tell him to do his business. Once he stopped having accidents that way, I let him off his leash in a confined area. I trained him to ring a bell whenever he wanted to go outside (it's easy - hang a bell on the door, and every time you are going to take your pup outside, take his paw and hit the bell with it. Say, "Good boy!", give him a quick pet, and take him outside. Keep in mind that you must let your dog out EVERY time he rings the bell. He will annoy the heck out of you at first, but eventually he'll get the idea and will only ring it to actually go out). The bell thing eliminates the dog's lack of ability to communicate his needs to you.
At this point, I moved to crate training. If the dog had an accident in the house, I would say, "No!" and take him outside. If he finished outside, he would get a mini party with treats and praise. If he didn't do the rest of his business outside, we would go inside and he would go in the crate. I would take him outside every 20 minutes or so. If he didn't go, he would come back in the house and go in the crate. If he did go, he would get his mini party and be allowed to wander around his area of the house again.
With my dog, it got to the point where he would go outside when it suited him, but if he was upset with me for saying no, or for not playing with him, he would wander away and eliminate somewhere else in the house. I know all the "experts" say not to put the dog's nose in it, but I sure as heck did, and then he would go in the crate. The attitude stopped just about instantly (goldens are not stupid!).
Most goldens are about love and fun, so make your dog's house training enjoyable. Throw a party every time your dog does his business outside, with lots of petting and loving and a treat.
Keep in mind that 4.5 months really is not that old. Some pups will continue to have the occasional accident in the house until they're a year old. Don't despair - it happens. As long as it doesn't become a regular pattern, all is good.
Be patient, and be firm!