Antibiotic resistance represents a major public health challenge. Although bacteria naturally develop advantageous mutations over time, overuse of antibiotics accelerates the evolutionary process, resulting in the proliferation of bacteria capable of resisting even multiple antibiotic drugs. In the United States, at least 2.8 million people annually are infected with antibiotic-resistant bacteria or fungi. Currently, cases of resistance have been identied in nearly all antibiotics that have been developed since the discovery of penicillin in the 1940s. Overuse of antibiotics in clinical settings is thought to be a major contributor to increased antibiotic resistance. Rates of antibiotic use may dier by region due to variation in the incidence of infectiousdisease,availabilityofantibiotics,andsocioeconomicdeterminantssuchasincomeand education levels. 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. Prior to January 1, 2011, purchase of antibiotics without a prescription from a physician was allowed at private pharmacies, but not the public pharmacies operated by the government. After the law was passed, medical prescriptions were required for purchase of antibiotics in all pharmacies. Thestudyteamcollecteddataonaveragemonthlyantibioticconsumptionin621countiesin2010 and 2011, in addition to information on socioeconomic determinants such as percentage of population living in urban areas and percentage of population over 25 years old who had completed higher education. Antibiotic consumption is measured in units of dened daily dose per 1,000 inhabitants per day (DID); higher DID indicates a higher level of antibiotic consumption. The data from 2010 and 2011 are in antibiotics_2010.Rdata and antibiotics_2011.Rdata, respectively. The datasets have the same variables with the exception of the variable predicted, which is present only in the 2011 dataframe. Variable Description county.id Unique ID number corresponding to a county public Number of public clinics per 100,000 people private Number of private clinics per 100,000 people illiteracy Percentage of population illiterate urban Percentage of population living in urban area popdensity Population density (1,000 people/km2) edu Percentage of population over 25 years old with higher education meancon Average monthly antibiotic consumption over 2008-2010 female Percentage of population female metro Coded Yes if within metropolitan area of province capital and No if otherwise gini Gini index in percentage infect Hospital admittances due to infectious disease per 1,000 people lifeexp Life expectancy in years consumption Average monthly antibiotic consumption in DID predicted Predicted average monthly antibiotic consumption (in DID) Some additional background on certain variables: - TheGiniindexisameasureofincomeinequality, withhighernumbersrepresentinggreater income inequality. For example, Sweden has a Gini index of 29.2% (2015) while the United States has a Gini index of 41.5% (2016).

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- The predicted antibiotic consumption values are calculated using a prediction model built with data from 2010. The specics of this model are not provided; those details are not needed to answer the following questions. The dataset antibiotics_overall.Rdata contains average antibiotic consumption over all counties in the study per month, from January 2008 to December 2012. The months are sequentially labeled 1 - 60; month 1 corresponds to January 2008 and month 60 corresponds to December 2012. Antibiotic consumption is recorded in DID. Use these datasets to answer the following questions. a) (20 pts.) Investigate how average monthly antibiotic consumption has changed between 2010 and 2011. i. Describe the distribution of average monthly antibiotic consumption in 2010, with reference to appropriate numerical and graphical summaries. ii. Compute the proportion of counties in which there was a decrease in antibiotic consumption after the passage of the law forbidding OTC sales of antibiotics in private pharmacies. iii. Create graphical summary of the relationship between monthly antibiotic consumption in 2010 and 2011. Describe what you see in relation to a y =x line. iv. Suppose a trend line were t to summarize the relationship between monthly antibiotic consumption in 2010 and 2011. Identify the counties that represent the two most extreme outliers and comment on whether either observation is potentially inuential. v. Analyzewhetherthereisastatisticallysignicantdierenceinaveragemonthlyantibiotic consumption between 2010 and 2011.