This is surely possible. I have been doing this for 3 complete seasons now :)
First, your records shall be the current seasons' Player-GW records which are collected by visiting the FPL summary page of each player, (for instance, Harry Kane's FPL summary page is: https://fantasy.premierleague.com/drf/element-summary/372, which is a JSON object. Under the JSON array named "history", you will find the Player-GW records for this player). By the end of this step, you will have your training data.
Now each records has got lots of attributes/features as seen in the JSON object of a Player-GW record. It is up to you which features to include, and which to exclude. You may also want to create some historical features, like the player's total points in past 5 matches..etc). Also note that not all features of GW should be included to determine the player's total point in this GW. For instance, Threat, Creativity, ICT index, and a couple of other features are only populated after the game. This means you cannot train based on these as you will not have them when trying to predict the player's score for the next GW.
As to the output - which is what you are trying to predict - does it have to be the very next GW? I mean, if a player is in good form, based on his previous GWs performance, it is still very hard to predict his score for only the next GW, since different GW and different matches have their own conditions/circumstances. But it is easier and more logical to predict a player's combined score for the next - let's say - 3 games. That makes it more logical and increases the prediction accuracy.
Now as to which regression algorithms to use, well there are a plethora of them. You have to try different ones and measure the accuracy of each.
Which brings me to the last point, accuracy. How do you measure the accuracy of a model? Maybe RMSE, maybe correlation, maybe other custom created functions (like I do). Remember, the model scoring function should reflect in a way how you are going to use the mode. I mean, why use RMSE for all players? After all what you'll probably end up doing is to select the let's say 20 highest scoring players in your model and try to buy some of them. Then your model scoring function should only evaluate the top 20 predicted players, not all 500-600 players in the Permier League.
In short, you will need to try and make some runs to be able to determine:
- what is your feature set?
- what should be the output?
- what regression algorithm you will use?
- what model scoring function you will use to select the best regression algorithm and to fine tune its parameters?
Good luck :)