## Let's try to predict beak width using middle toe length and island
## the data set https://roualdes.us/data/finches.csv
## First, ensure there is statistically different mean beak widths
## amongst the islands. Write out the hypotheses and conclude the
## test, using alpha=0.05.
## Calculate the correlation between beak width and middle toe length.
## Based on this calculation, what do you expect the sign of the slope
## coefficient to be?
## Fit multiple linear regression using intercepts for each island and
## a shared (amongst all the islands) slope. Write the fitted
## regression equation.
## Check the assumptions of your linear model.
## Why are only two of the three levels of island obviously displayed
## in the output?
## Interpret the coefficient estimate of floreana in the context of
## these data.
## Each coefficient is being tested with a default hypothesis test.
## Set up one such hypothesis test, using appropriate subscripts, and
## conclude the hypothesis test in statistical language.
## Interpret the slope in the context of these data. Is this variable
## significantly different from zero?
## Interpret the adjusted $R^2$ value in the context of these data.
## Why is the $R^2$ value larger than the adjusted $R^2$?
## Predict average beak width for the island San Cristobal when middle
## toe length is equal to 20.
## Hint: ?predict.lm # the examples within should help
## Calculate the residuals for the third observation of your original
## data. Does your answer match the third element of the residuals?
## Did you over/under predict the third residual?