The defendant appeals from his conviction of murder in the second degree of his infant daughter. The defendant contends on appeal that the trial judge erred by (1) *509denying the defendant’s motion for a required finding of not guilty, (2) admitting evidence of prior bad acts, (3) allowing unduly prejudicial testimony on cross-examination, and (4) excluding proper testimony of defense witnesses. We affirm.
Viewing the evidence in the light most favorable to the Commonwealth, the jury reasonably could have found the following facts. The defendant began dating Lori Bakirakis in August, 1992, after meeting her at their mutual place of employment, Star Market. In November, 1992, the defendant moved into Lori’s condominium and began moonlighting at her father’s candy store. One month later, Lori became pregnant, much to the defendant’s surprise. The defendant, not wanting a child, asked her to have an abortion. Lori refused; she married the defendant on January 15, 1993.
On July 17, 1993, Lori gave birth to the victim, Victoria. The defendant’s negative attitude toward having a child continued after Victoria’s birth. He perceived the baby as fussy and always spitting up; he compared his parental babysitting responsibilities to being in jail. Nine days after Victoria’s birth, the defendant put Victoria on a department store shelf and walked away, telling Lori, “Let’s leave her here.” At home, the defendant antagonized the baby to tears by putting blankets over her head until she hyperventilated and by putting his face near hers. On one occasion the defendant angrily made Lori walk home with the baby and narrowly missed hitting them with his car in the driveway.
The first documented instance of harm to Victoria was on August 12, 1993, when Lori bumped Victoria’s head on the car door jamb as she removed her from the car seat. The next day, Lori bumped Victoria’s head in the same way. Lori immediately sought a doctor’s advice over the telephone for the resulting lump. The doctor indicated that an office visit was not necessary; the lump went away within a few days.
One week before the fatal incident, the defendant was alone with Victoria twice. Both days she was uncharacteristically fussy and crying after her time alone with the defendant. On August 20, 1993, Lori’s mother took care of Victoria, who was vomiting more than usual, even after ingesting Pedialyte, upon a doctor’s prescription. The next day Lori and the defendant took Victoria to her pediatrician, Dr. Delollis. After a full examination, including her stomach, ribs, back, legs, head, fontanel, eyes, and pupils, the doctor found no signs of discomfort or abnormality.
*510On August 23, 1993, Lori took care of Victoria from 7 a.m. to 4 p.m. while the defendant was at work. Lori testified that Victoria appeared well and she observed no abnormalities in her appearance and feeding pattern. Prior to Lori’s leaving for work, Victoria vomited on the defendant. The defendant was alone with Victoria from 4:30 p.m. to 9:30 p.m.2
When Lori arrived home from work she found the apartment was unusually neat and a small load of laundry had been washed. She also found the sleeper Victoria had been wearing when she left hanging on the back of the toilet to dry. As Lori checked on a sleeping Victoria, the defendant followed, put his hand on the baby’s back, and said, “Yep, she’s still breathing.” At 11 p.m., before going to bed, Lori and the defendant observed that Victoria was fine. The defendant lay awake until 2:30 a.m., at which time he took Victoria out of her crib and into the living room for about twenty minutes. Lori indicated that she did not hear Victoria cry and that the baby monitor was moved away from its place near her on the dresser to the window sill closer to the defendant.
After Lori observed about 4 a.m. on August 24 that the baby looked sick and was having trouble breathing, Lori and the defendant took Victoria to the emergency room. A CAT scan revealed two skull fractures and massive brain swelling and bleeding. Victoria’s right optic nerve was severed and the left optic nerve damaged as well. Dr. Newburger, head physician in the child abuse unit at Children’s Hospital, concluded that the injuries had been inflicted within twelve hours of Victoria’s 5:17 a.m. admission. Several bone scans the next day revealed that Victoria suffered several broken bones and fractured ribs. Victoria was transferred to a medical foster facility and remained in a permanent vegetative state until her death on February 10, 1996.
During Victoria’s hospitalization, the defendant spoke with the police and hospital staff, offering various explanations for Victoria’s injuries. The defendant stated that Lori had bumped her head. He also gave several other possible reasons for her injuries: he had slightly bumped her head on the bassinet; *511bouncing her on his knee may have broken her legs; emergency room personnel may have been a little rough and broken her ribs; and a birth defect could have caused her retinal hemorrhaging.
The defendant also exhibited behavior that the jury could have found demonstrated consciousness of guilt. The defendant became unusually close and supportive toward Lori, even demonstrating rare outward displays of affection. Shortly after Victoria’s hospitalization, the defendant offered to go to the Department of Social Services (DSS) and confess in exchange for Lori’s promise not to pursue a restraining order. The defendant later asked Lori to help him make up a he to tell DSS and asked her if she would wait for him if he went to jail.
1. Sufficiency of the evidence. The defendant asserts that the Commonwealth’s evidence was insufficient to establish him as the perpetrator. He argues that because the evidence failed to rule out his wife Lori as the perpetrator, he could not be found guilty beyond a reasonable doubt. We disagree. See Berry v. Commonwealth, 393 Mass. 793, 795 (1985); Commonwealth v. Woodward, 427 Mass. 659, 682 (1998).
“[T]he Commonwealth’s proof in a criminal trial need not exclude all possible exculpatory interpretations of the evidence. . . . Nor is it necessary for the Commonwealth to negate the possibility that someone else other than the defendant might have committed the crime charged.” Commonwealth v. Macey, 47 Mass. App. Ct. 42, 48 (1999), quoting from Commonwealth v. Russell, 46 Mass. App. Ct. 307, 311 (1999). Circumstantial evidence can establish guilt, and inferences drawn from circumstantial evidence “need only be reasonable and possible.” Commonwealth v. Roman, 427 Mass. 1006, 1007 (1998). “[W]hether an inference is warranted or is impermissibly remote must be determined, not by hard and fast rules of law, but by experience and common sense.” Ibid. If the evidence established a solid foundation of the defendant’s guilt and is not left to conjecture or surmise, a verdict of guilty must stand. See Berry v. Commonwealth, 393 Mass. at 795-796.
We conclude that the Commonwealth’s evidence of the defendant’s guilt was sufficient to warrant the judge’s denial of the defendant’s motion for a required finding of not guilty. The record reveals sufficient evidence to show that the defendant had opportunity and ability to kill Victoria. The jury heard testimony from Lori and had an opportunity to weigh her cred*512ibility. Compare Berry v. Commonwealth, 393 Mass. at 795 n.2, 796 (defendant’s conviction reversed where the mother could not be ruled out as a perpetrator and she did not testify and the jury did not get to weigh her credibility), with Commonwealth v. Avellar, 416 Mass. 409, 414-415 (1993). Lori testified that Victoria was fine when she left for work. There was credible medical evidence that the time of the fatal injury was within twelve hours of admission to the hospital. The defendant had sole custody of Victoria during many of those crucial hours.
The jury reasonably could have inferred that Lori was not disposed to harming Victoria. Lori routinely took Victoria to the pediatrician and sought medical attention after an incident in which Victoria’s head was bumped exiting a car. Subsequent visits to the pediatrician revealed no abnormalities after that incident. See Commonwealth v. Avellar, 416 Mass. at 415 (sufficient evidence to convict the defendant and rule out the mother where she was the regular caretaker and routine doctor visits had disclosed no abnormalities). The defendant’s actions before and after Victoria’s hospitalization demonstrate consciousness of guilt and provide additional support for the jury’s finding of guilt. See id. at 418 (admission, as evidence of consciousness of guilt, of defendant’s reaction upon finding the dying victim was not erroneous). The jury fairly could have concluded beyond a reasonable doubt that the evidence, albeit, for the most part, circumstantial, supports a reasonable inference that the defendant inflicted the fatal injury to Victoria. See, e.g., Commonwealth v. Macey, 47 Mass. App. Ct. at 44-48.
2. Bad act evidence. The defendant contends that the trial judge, over objection, improperly admitted evidence of the defendant’s prior bad acts. Specifically, the evidence included testimony that the defendant became violent and abusive toward his wife during her pregnancy. On one occasion the defendant began to drive away after Lori had taken a fall in a snowy restaurant parking lot. On another occasion the defendant yelled at Lori for over five hours because she arrived home before him. In another instance, the defendant angrily began to drive in an erratic manner, causing the seat belt to tighten sharply against Lori’s pregnant belly. Upon arriving home, the defendant narrowly avoided hitting Lori as he drove away, leaving her locked out of the house.
The defendant argues that this testimony was not relevant to his state of mind and unduly prejudicial as it merely tended to *513demonstrate his bad character. “It is well settled that the prosecution may not introduce evidence that a defendant previously has misbehaved, indictably or not, for the purposes of showing his bad character or propensity to commit the crime charged, but such evidence may be admissible if relevant for some other purpose.” Commonwealth v. Triplett, 398 Mass. 561, 562 (1986), quoting from Commonwealth v. Helfant, 398 Mass. 214, 224 (1986). Such evidence “may be admissible, if relevant, to show a common scheme or course of conduct, a pattern of operation, absence of accident or mistake, intent, or motive.” Commonwealth v. Barrett, 418 Mass. 788, 793-794 (1994). Evidence is relevant which “relates to a subsidiary issue, such as the state of mind of the defendant, and is not offered to prove his guilt but rather to prove a relevant subsidiary fact.” Commonwealth v. Triplett, 398 Mass. at 562, quoting from Commonwealth v. Trapp, 396 Mass. 202, 206 (1985), S.C., 423 Mass. 356, cert. denied, 519 U.S. 1045 (1996).
The trial judge in his discretion “must decide if such evidence is admissible by determining whether its probative value outweighs the risk of undue prejudice.” Commonwealth v. McClendon, 39 Mass. App. Ct. 122, 128 (1995). In order for the evidence to be sufficiently probative it must connect with the facts of the case. See Commonwealth v. Barrett, 418 Mass. at 794. Absent a connection to the facts, the evidence has the effect of merely “impugning the defendant’s character.” See Commonwealth v. Marrero, 427 Mass. 65, 67 (1998).
We do not decide whether the evidence of the defendant’s hostility toward Lori prior to the victim’s birth was relevant to the defendant’s state of mind vis-a-vis the victim, as the Commonwealth argues, or whether it showed only hostility toward Lori and not the victim, because there is nothing to show whether he would have been hostile to Lori anyway or whether the hostility was the result of the pregnancy, and because, in any event, the trial judge’s failure to exclude this testimony was harmless in light of the remaining evidence. The evidence revealed that the defendant was alone with the victim during the critical hours that the fatal injury was inflicted. The evidence also revealed that the defendant did not want Lori to have the baby and that after Victoria was bom he proposed abandoning her on a department store shelf. A reasonable juror could have come to the conclusion that the defendant was disposed to harming Victoria even without the evidence of the defendant’s hostil*514ity toward his wife while she was pregnant with the victim.
3. Improper cross-examination. Next, the defendant contends that the judge erred in allowing the prosecution to elicit testimony about (1) the defendant’s views on corporal punishment and (2) the defendant’s relationship with an ex-girlfriend. The defendant argues that the Commonwealth attempted to elicit this testimony on cross-examination, over objection, without a basis in admissible evidence, and that the admission of the testimony was prejudicial and warrants reversal. We disagree.
“Th[e] discretionary power of the judge is particularly well established in the case of cross-examination the scope of which, for the purpose of impeaching testimony, is subject to his control.” Commonwealth v. Fiore, 364 Mass. 819, 825 (1974). “We shall not overrule a trial judge’s determination as to the proper scope of cross-examination unless the defendant demonstrates that the judge abused his discretion and that the defendant was prejudiced thereby.” Commonwealth v. DeJesus, 44 Mass. App. Ct. 349, 352 (1998), quoting from Commonwealth v. Miles, 420 Mass. 67, 71-72 (1995).
We conclude that there is no basis for reversal. The defendant was not prejudiced by the prosecutor’s inquiry into the defendant’s views on corporal punishment. Contrary to the defendant’s argument, the trial judge could have found that the prosecutor had a good faith basis in wanting to show a pattern of conduct and intent. Compare Commonwealth v. Hubbard, 45 Mass. App. Ct. 277, 281-282 (1998). In any event, the defendant could not possibly conclude that he was prejudiced by this inquiry when the answer was favorable to him.3
Similarly, the defendant was not prejudiced by the inquiry into his relationship with his ex-girlfriend. The judge appropriately limited this inquiry, ruling that it could be used only to rebut the defendant’s testimony that he was happily married. The record does not show that the Commonwealth abrogated the judge’s instructions. The prosecutor used this testimony against the defendant on two occasions: (1) to impeach his testimony that he was ready to marry Lori in 1993, and (2) on *515cross-examination of the defendant’s mother to show her bias.4 We discern no prejudice.
4. Excluded testimony. The defendant claims that the trial judge incorrectly excluded testimony of two medical experts for the defense, Dr. O’Connor and Dr. Khalil-Togras. In an effort to contradict the testimony of Victoria’s pediatrician, defense counsel asked a question which Dr. O’Connor answered by saying that when the pediatrician examined Victoria during the August 21 office visit, at a time subsequent to when Lori had bumped her head, he should have detected skull fractures “if all the examinations were done as alleged, which would be a very unusual examination.” Dr. Khalil-Togras attempted to testify to the substance of a telephone conversation with Lori on the day Victoria’s head was bumped. The defendant claims that excluding this testimony was reversible error.
The judge within his discretion properly could have excluded Dr. O’Connor’s testimony as nonresponsive. When asked and directed by the judge to answer a direct question about whether the pediatrician would have detected the injuries,5 the witness responded essentially in the affirmative but “qualified” his answer, stating that such an exam “would be a very unusual examination.” Dr. O’Connor’s proposed testimony that such an exam usually was not as extensive was merely speculative as to whether the examining pediatrician had actually performed an examination of Victoria’s fontanel.6
Similarly, there was no error in the judge’s determination that Dr. Khalil-Togras’s proposed testimony was unauthenticated hearsay. The judge appropriately prevented the doctor from testifying about the telephone conversation because she could *516not identify Lori’s voice. See Liacos, Massachusetts Evidence § 12.4, at 694 (6th ed. 1994) (“when a witness has received an incoming call from a person claiming to be A, without more, this is insufficient evidence to admit the call as a conversation with A”).7 In any event, as no substantial prejudice has been made to appear, we conclude that there is no basis for reversal.
Judgment affirmed.
The defendant testified that he could not recall what he did from 4:30 p.m. to 6:30 p.m., but remembers that Victoria was restless. The defendant testified that at 6:30 p.m. he fed Victoria a bottle of Pedialyte and she appeared fine and fell asleep in her crib. Of course, as already stated, we view the evidence in the light most favorable to the Commonwealth.
Although the prosecution expected that the defendant’s mother would testify that the defendant advocated corporal punishment, she, in fact, answered to the contrary.
The testimony used to show the defendant’s mother’s bias included evidence that the ex-girlfriend spent the night at the mother’s house and rode with the family to the defendant’s father’s funeral.
The specific question was: “Doctor, do you have an opinion ... to a reasonable degree of medical certainty as to whether the eyes, skull and brain injuries would have been detected by that pediatrician giving that examination?”
We note in passing that the defendant’s counsel argued in closing' that the pediatrician’s lack of notation in the records about an examination of the fontanel meant that it was not done. (The pediatrician had testified on cross-examination that although he did not make a specific notation in his report that he had examined the fontanel, he did indicate that he had examined the head, using an abbreviation for “head, ears, eyes, nose, and throat,” and it was his practice usually to include the examination of the fontanel under that abbreviation.)
The defendant argues on appeal that the testimony was admissible because Lori herself had testified earlier to such a call. However, defense counsel did not point this out to the judge at the time admission was sought.