1.   [8] Make a binary infix operator called %ols% that takes thearguments x and y and returns the ordinary least squares regressioncoefficients for regressing y on x.  Inthis function x and y may any combination of vectors or matrices. Rather thanusing a built in R function, use the equation we saw in Question 2d) of thesecond assignment. This function should add a column of 1s to x so that anintercept is fit.  For examplex<-1:10; y<-2+3*x; y%ols%x returns: the vector 2, 3.

i)                  Regress ozone on temperature.  

ii)                Try replicating the model in Q1 f) by setting y to ozoneand x to a matrix where the first column contains radiation and the next twocolumns contain wind and temperature, respectively. Do this part in oneexpression.

2d)题目如下：

Assume that thereis an approximate linear relationship between Illiteracy and Murder rates.Given the design matrix defined above, we can define a simple linear modelas y=Xb+e where y (Murder) is the dependent variable, X is thedesign matrix (or matrix of independent variables), b is the vector ofparameters and e is the error term. The least squares estimate of b is:  bhat=(XtX) -1Xt y.Write an expression to calculate bhat in R. Note that Xt is thetranspose of X.

ozone 和 temperature 来自于下表：