## Consider the dataset petrol, which records various variables
## relating to gas consumption for each of the 48 contiguous states in
## 1980. Pretend you're interested in the variables tax (cents per
## gallon) and highway (miles of paved road). We'll investigate
## whether or not increased taxes is linearly related to the number of
## paved miles of road a state has.
## These data can be found at the following link: https://raw.githubusercontent.com/roualdes/data/master/petrol.csv
## Make an appropriate plot for the variables tax (x) and highway (y).
## Does simple linear regression seem reasonable for these data? Explain.
## Provide an estimate for $\beta_0$. Interpret this estimated
## coefficient in context of the data.
## Does $\hat{\beta}_0$ make sense in the context of these data?
## Explain.
## Provide an estimate of $\beta_1$. Interpret this
## estimated coefficient in context of the data.
## Predict the value of highway for a state with tax equal to $7$
## cents.
## Calculate a $95$\% confidence interval for $\beta_0$. Interpret
## this confidence interval in context of the data.
## Calculate a $95$\% confidence interval for $\beta_1$. Interpret
## this confidence interval in context of the data.
## The following questions do not necessarily pertain to the dataset
## above.
## The bootstrap proceduce has essentially two steps: resample, and on
## each resample, calculate something. What do we resample from?, how
## is the resampling done?, and what is being calculated on each resample?
## What is the conceptual goal of the bootstrap procedure? Say more
## than just to calculate confidence intervals.
## Supppose you calculated the following quantiles using the following code:
## quantile(rgamma(1001, shape=2, rate=1/20), probs=c(0.03, .5, 0.97))
## What percentage confidence interval would the $3$\% and $97$\%
## quantiles make?
## Which direction of skew does this distribution appear to have?