Some researchers claim that exclusive breastfeeding of infants from birth to six months of age can boost a child's intelligence. Others are skeptical and believe that previous findings to this effect may be attributable to confounding by maternal socioeconomic status. That is, higher socioeconomic status mothers may be more likely to practice exclusive breastfeeding through six months of age; and high material socioeconomic status may contribute to the development of intelligence in the child through mechanisms other than breastfeeding. An investigator studying these issues has a dataset on 1422 mother-child dyads. The dataset contains the following key variables: CHILDIQ, the intelligence of the child as measured via the Stanford-Binet IQ test age age 6 years, with higher scores indicating greater intelligence; BRSTFD, the mother's self-report of whether or not she breastfed the child exclusively through six months of age (0 = no, 1 = yes); and MOMSES, an index of maternal socioeconomic status derived from information about educational attainment, income, and her own parents' occupations. The investigator finds that the mean score on Stanford-Binet IQ test was 107.32 among the 454 children who were exclusively breastfed for six months; and 102.55 for the 968 children who were not exclusively breast fed through six months of age. Thus, the average breastfed child had an IQ 4.77 points higher than the average non-breastfed child. To determine the extent to which this difference could attributable to confounding by maternal socioeconomic status rather than to an actual effect of breastfeeding on intelligence, the investigator next runs the following linear regression model:
CHILDIQi = b0 + b1BRSTFDi + b2MOMSESi +ei.
If the difference is due in part to confounding by maternal SES, how would the value of the coefficient b1 in this model likely compare to the raw difference of 4.77?