1) The weight gains (kilograms) during pregnancy for 30 pregnant women are recorded in data WeightGain.dta together with their race (1 "White" 2 "Black" 3 "Hispanic" 4 "Asian"). a. Graph a box plot for the variable WeightGain over different race categories. What do you observe in terms of the medians and the IQRs of weight gain over different race categories? b. What are the sample means of weight gains for each race group? What are the sample standard deviations for weight gains for each race group? c. Perform a one-way ANOVA in Stata. What is the pvalue of the test, and what is your conclusion? 2) Personal health care expenditures by state for the years 1966-1982 have been examined in an attempt to understand issues related to rising healthcare costs. We are interested in understanding the relationship between expense per admission and the average length of stay in a community hospital. The dataset hospital.xlsx contains information for each state in the U.S. for the year 1982. Mean expense per admission (dollars) and length of stay (days) for each state are saved under variable names expadm and los. Conduct the following: a. Obtain numerical summary statistics (mean, standard deviation, minimum and maximum) for the expense and length of stay variables. b. Construct a twoway scatter plot of expense vs. length of stay, and add a lowess curve to the graph. What does the scatter plot suggest about the relationship between the two variables? c. Using expense as the response and length of stay as the explanatory variable, fit a simple linear regression model. Write the equation of the regression line. What does the estimated slope of the line mean in words? d. Construct a 95% confidence interval for the slope. Explain the 95% confidence interval in words. e. What is the value of the F-test statistics and associated pvalue? What does it tell you about the model? f. What is the value of the unadjusted R2 and what does it tell you about the model? g. What is the Pearson correlation coefficient? Verify the relationship between the Pearson correlation coefficient and the Coefficient of Determination (unadjusted 2 ).