As I understand, your input dataset, “x” has size 1000 x 1 and the output, “y” has size 1000 x 1 and you are defining a regression model for predicting “y”.
In your model, the number of neurons in the last FC layer should match the dimension of “y”. Since, your output is 1-dimensional, the output size of the last Fully Connected (FC) layer used should also be 1. In case, your output “y” is of size 1000 x 2, then the output size of the FC layer should be 2.