## The dataset hospital is a sample of 113 hospitals from four
## anonymized regions of the United States. You can find the CSV of the
## dataset at the following link:
## https://raw.githubusercontent.com/roualdes/data/master/hospital.csv
## You can find the help file for this dataset at the following link:
## https://github.com/roualdes/data/blob/master/hospital.txt
## Read in the dataset using the funciton read.csv.
## Using ggplot2, make a scatter plot of the variables
## stay and infection_risk with points colored by
## region.
## Use the likelihood method together with optim to predict
## infection_risk using a multiple linear regression model with one
## intercept for all regions and unique slopes across stay for each
## region.
## Write 1 complete English sentence describing the estimated intercept
## for all regions.
## Write 1 complete English sentence describing the estimated slope for
## region 4.
## Usethe bootstrap method to calculate $R = 999$ bootstrapped estimated
## coeficients from your model.
## Write 1 complete English sentence describing an $89$\% confidence
## interval for the intercept for all regions.
## Write 1 complete English sentence describing an $89$\% confidence
## interval for the slope for region 4.
## Write 1 complete English sentence describing an $89$\% confidence
## interval for the predicted infection_risk when stay is equal to its
## maximum for region 2.
## Write 1 complete English sentence describing an $89$\% confidence
## interval for the predicted infection_risk when stay is equal to its
## maximum for region 4.
## Comment on the difference between the predicted infection_risk at
## the maximum of stay for regions 2 and 4. Is infection risk
## significantly greater in one region than the other at this value
## for stay?