As Massachusetts voters prepare to pick the state's next governor, most feel good about the job outgoing Gov. Charlie Baker has been doing, a new poll shows.

In the University of Massachusetts Amherst/WCVB poll, 68% of voters surveyed in late October said they approved of how Baker is handling the job. That's up from the 60% approval rating Baker received in June, and higher than the latest approval numbers for Sens. Ed Markey and Elizabeth Warren and the state Legislature.

“These are some big shoes to step into, figuratively and literally,” said Tatishe Nteta, a UMass Amherst political science professor and director of the UMass Poll. “It's going to be difficult to resemble the approval of Charlie Baker, and I think that's one of the reasons why you see both candidates, both of the major party candidates at least, attempting in their varying ways to embrace the legacy of Charlie Baker rather than run away from it.”

Baker opted not to seek reelection after two terms in the corner office. Findings the pollsters released last week showed Attorney General Maura Healey, the Democratic nominee for governor, solidly ahead in the race to succeed Baker, with a 28-point lead over Republican Geoff Diehl.

One-third of respondents said they were "very concerned" about the idea of Democrats controlling both the state Legislature and the governor's office in Massachusetts, a figure Nteta said was fueled by concerns among Republicans and people who describe themselves as conservative. Thirty-two percent said they were not concerned at all.

Nteta said voters have connected with Baker’s leadership style and, in some ways, see him as a moderating force against more progressive inclinations of the Democratic supermajorities in the Legislature.

Democrats, along with liberals, people of color and women — all demographic groups have historically been connected to the Democratic Party — were among those who gave Baker high marks, Nteta said.

"I think it's a reflection of the fact that the governor has done a really good job in terms of shepherding the state over the course of the last eight years through some really hard times, whether that be the pandemic, for some the Trump presidency, and for others, I mean, just keeping the ship moving," he said.

Respondents viewed Massachusetts’ economy and overall trajectory more positively than the country’s as a whole. Two-thirds of voters said the country is on the wrong track, but only 36% of poll respondents feel that way about Massachusetts.

When it comes to particular issues Baker has handled since taking office in 2015, 71% approved of how he managed the COVID-19 pandemic, while only 34% said he'd performed well on transportation and transit. But voters in counties served by the MBTA largely appear not to blame Baker for the transit agency's recent safety woes — only 11% said he was most responsible for the safety problems, compared to 48% who said it's MBTA general manager Steve Poftak.

“I think this is also a reflection of Charlie Baker's innate ability to sidestep scandal and to be viewed not as the cause of the problems in the state, but to be seen as the solution to them,” Nteta said.

If problems persist at the T, Nteta said it will be interesting to see if the next governor is seen as liable.

Asked whether they'd support the federal government taking temporary control of the MBTA, respondents were split, with 32% in favor, 30% against, and 38% saying they'd neither support or oppose it.

The poll of 700 registered voters was conducted by YouGov from Oct. 20-26, and it has a margin of error of 4.3%.