It shouldn't really take a pollster to show you that going after The Terminator is a bad idea. But new polling data from YouGov contains an important lesson for Donald Trump: If you attack Arnold Schwarzenegger you're going to come off worse.

President Trump's tweet attacking Schwarzenegger, the bodybuilding film star and former Republican governor of California, was among those that angered Americans most of all his social media outbursts.

YouGov has launched TweetIndex, a website which analyses the public's reaction to tweets. To demonstrate how it works, YouGov polled a representative sample of 1,000 Americans for their thoughts on Trump's tweets.

At the end of each day, these Americans would be shown the president's tweets from the past 24 hours and asked to rate them on a scale of 'great', 'good', 'OK', 'bad' and 'terrible'. Each rating adds or subtracts points. Great equals +2, while terrible equals -2.

And it was a catty tweet by Trump aimed at Schwarzenegger that was among the most unpopular. Schwarzenegger has been critical of Trump's controversial early presidency. He also said he would decline an offer of presenting a second series of The Celebrity Apprentice because Trump's involvement in the show leaves people with "a bad taste", he told Empire.

"Arnold Schwarzenegger isn't voluntarily leaving the Apprentice, he was fired by his bad (pathetic) ratings, not by me," Trump tweeted on March 4, hitting back. "Sad end to great show."

That tweet got a rating of -69, the second worst score of all his tweets. The next worst score was -65 for Trump's tweet accusing the former president Barack Obama of wiretapping his phones. "How low has President Obama gone to tapp [sick] my phones during the very sacred election process," Trump tweeted on March 4. "This is Nixon/Watergate. Bad (or sick) guy!"

But the most unpopular of all was his tweet in response to the tech billionaire Mark Cuban, who had himself tweeted: "It's time we accept @POTUS for who he is. He is entertaining. He is oblivious. He isn' smart enough to be dangerous."

Trump fired back on February 12: "I know Mark Cuban well. He backed me big-time but I wasn't interested in taking all of his calls. He's not smart enough to run for president!"

And that scored -81 among those polled. Ouch.

"Twitter is a platform like no other – allowing people to communicate their outlook unfiltered to the world," said Stephan Shakespeare, YouGov's global CEO and co-founder. "And no one showcases this better than President Trump.

"Everyone knows what he says on Twitter, but YouGov is providing unique data on how people are responding to his tweets. Some think they're great while others think they're terrible, but very few sit on the fence.

"YouGov will be the chronicler of Trump's America, allowing us to look at how each of his pronouncements resonate with different groups. Given their power, the president's tweets deserve to be assessed – and measured – alongside his other public statements."