In R-

Write a function that takes in a string response, two vectors of string covariates, a dataset, and returns the covariate from the second set that decreases the AIC most when added to a model containing the first set of covariates. If none decrease the AIC, the function should return NULL or a length-zero vector.

Use these functions to write a function implementing the forward selection algorithm on the Ames housing data, using both Sale_Price and log Sale_Price as the response. Your forward selection function should take in a response string, a character vector of candidate covariates (in case you don't want to test all the covariates, or want to try some interactions), a data frame, and return the vector of selected covariates. Your function should check whether the candidate covariates are available in the data frame, and return an error with an informative error message if not.