1. Write a function that uses OLS to estimate the coefficients and standard errors of a linear regression model.
The function should
- accept two arguments:
yandX(both matrices) - output estimated coefficients
- output estimated standard errors
Your function should only use matrix operations (e.g., %*%) and basic summary statistics (e.g., sum). Do not use more complex functions.
Hint: The function named function() allows you to write a function. For example,
function(a,b) {
a + b
}
2. Show that your function works using the mtcars dataset in R. Specifically: Use your function to regress mpg on an intercept, the number of cylinders (cyl), horsepower (hp), and weight wt.
Compare your results to those of lm.
3. What assumptions do your standard errors rely upon (to be approximately correct)?
4. What assumptions do your coefficient estimates need to be causal?