## Consider the dataset opossum (google it). This dataset records 104
## opossums from Australia and New Guinea, for which a number of
## variables were recorded. We'll pretend to be interested in the
## linear relationship between age and totalL. Put the variable that
## is more likely to explain the other, namely the explanatory
## variable, on the x axis. Put the variable that is doing the
## responding, namely the response variable, on the y axis.
## These data can be found at the following link: https://raw.githubusercontent.com/roualdes/data/master/possum.csv
## Make an appropriate plot for the variables age and totalL.
## Does simple linear regression seem reasonable for these data? Explain.
## As there are missing data in this dataset, use the following code
## to create a new dataframe that has the missing data removed. You
## have to change the dataframe names to match your code.
library(dplyr)
new_df <- old_df %>%
select(age, totalL) %>%
na.omit
## 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 totalL using an age of 6.5.
## 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(2003, shape=1, rate=1/40), probs=c(0.02, .5, 0.98))
## What percentage confidence interval would the $3$\% and $97$\%
## quantiles make?
## Which direction of skew does this distribution appear to have?