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This is an anthropomorphism, which according to The New Jerome Biblical Commentary, 77:20, page 1288:
21. (the first of three paragraphs on the subject) The attribution of human features and behavior to nonhuman beings (along with anthropopathism - the attribution of human feelings) is common in both religious and profane literature of all cultures. What makes anthropomorphism worthy of special attention in the OT is the difficulty of reconciling it with the prohibition of images and the explicit denials that Yahweh is like any created being. The fear of a plastic image of Yahweh is in marked contrast to the lack of restraint in employing verbal images. Yahweh has a countenance, eyes, ears, mouth nostrils, hands, feet. He speaks, hears, smells, laughs, hisses, whistles, strikes, writes, walks. He feels delight, joy, anger, hatred, love, disgust, compassion (see e.g., T. E. Fretheim, The Suffering of God [OBT 14; Ph, 1984]. The OT never speaks of Yahweh without attributing human traits to him. There is scarcely any OT anthropomorphism that cannot be paralleled in other ancient Semitic literature; for the gods of other ancient Semitic peoples were personifications of natural forces or social realities to whom were attributed human features and behavior.
So it should be clear God does not literally regret, but this is an anthropomorphism to express an inexpressible idea.
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If God is omniscient how can he regret?
The ability to know things would not exclude the possibility of having an emotional reaction.
A parent may know that his child is going to fall down, however, that parent still encourages the child to learn to walk. The child that bangs his head on the coffee table can cause regret in the heart of the parent.
The regret of God is not the surprise event he didn't anticipate. It is the sorrow in the heart of a parent for a child that makes wrong decisions.
We have an example of God repenting (changing his mind) in reaction to an emotional perception.
1 Chronicles 21:15 And God sent an angel unto Jerusalem to destroy it: and as he was destroying, the LORD beheld, and he repented him of the evil, and said to the angel that destroyed, It is enough, stay now thine hand. And the angel of the LORD stood by the threshingfloor of Ornan the Jebusite.
Even though the three days of pestilence had not been fulfilled, the reaction to the death of 70,000 men was sufficient to cause God to stop the punishment.