7  Practical One

NOTE: the answers to the questions below should be placed into their own qmd file in a Quarto project on GitHub. This Quarto project (the rendered document itself, as well as the source code on GitHub) will be peer-assessed next week.

1. Find all rows in “airquality” that have missing values. Note that the airquality dataset in R is always available (just type airquality in the console to see it).
2. Find mean, sd, min, max for each of temperature and ozone level.
3. For linear regression, parameter estimates can be found as follows. \(\hat{\beta} = (X^TX)^{-1}X^TY\) Here, Y is the response variable, and X is the design matrix. The cars data (an R data set, also always available in R) contains two variables: speed and distance to stop. Fit a simple linear regression model to these data, i.e. find the \(\beta\) estimates, using the equation above, and matrix calcuations in R.
4. Check that you get the same \(\beta\) estimates as when fitting the linear regression model using lm() in R.