Antibiotic resistance represents a major public health challenge. Overuse of antibiotics in clinical settings is thought to be a major contributor to increased antibiotic resistance. A study was conducted across several regions in China to investigate the impact of a 2011 law prohibiting over-the-counter (OTC) sales of antibiotics in private pharmacies. The study team collected data on average monthly antibiotic consumption in 621 counties, in addition to information on socioeconomic determinants such as percentage of population illiterate. The following model was fit to investigate whether the relationship between monthly antibiotic consumption and percentage of population (over 25 years of age) with an advanced degree differs between counties that are located in a metropolitan area and those that are not.

(a) Interpret the model coefficients, including any relevant inferential results.

(b) Make a prediction of average monthly antibiotic consumption for a county in a metropolitan area where \(10 \%\) of the population over 25 years old has an advanced degree.

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Estimate Std. Error t value Pr(>|t|) (Intercept) 0.8482 0.3311 2.56 0.0107 metro Yes 2.3035 0.9612 2.40 0.0169 edu 0.5711 0.0319 17.90 0.0000 metro Yes:edu -0.1838 0.0752 -2.44 0.0148