function [rmsvars lowndx rmstrain rmstest] = a2_00000000
% [RMSVARS LOWNDX RMSTRAIN RMSTEST]=A3 finds the RMS errors of
% linear regression of the data in the file “AIRQUALITY.CSV” by treating
% each column as a vector of dependent observations, using the other
% columns of the data as observations of independent varaibles. The
% individual RMS errors are returned in RMSVARS and the index of the
% smallest RMS error is returned in LOWNDX. For the variable that is
% best explained by the other variables, a 5-fold cross validation is
% computed. The RMS errors for the training of each fold are returned
% in RMSTEST and the RMS errors for the testing of each fold are
% returned in RMSTEST.
% none
% OUTPUTS:
% RMSVARS – 1xN array of RMS errors of linear regression
% LOWNDX – integer scalar, index into RMSVALS
% RMSTRAIN – 1×5 array of RMS errors for 5-fold training
% RMSTEST – 1×5 array of RMS errors for 5-fold testing
filename = ‘airquality.csv’;
[rmsvars lowndx] = a2q1(filename);
[rmstrain rmstest] = a2q2(filename, lowndx)
function [rmsvars lowndx] = a2q1(filename)
% [RMSVARS LOWNDX]=A2Q1(FILENAME) finds the RMS errors of
% linear regression of the data in the file FILENAME by treating
% each column as a vector of dependent observations, using the other
% columns of the data as observations of independent varaibles. The
% individual RMS errors are returned in RMSVARS and the index of the
% smallest RMS error is returned in LOWNDX.
% FILENAME – character string, name of file to be processed;
% assume that the first row describes the data variables
% OUTPUTS:
% RMSVARS – 1xN array of RMS errors of linear regression
% LOWNDX – integer scalar, index into RMSVALS
% Read the test data from a CSV file; find the size of the data
% % STUDENT CODE GOES HERE: REMOVE THIS COMMENT
% Compute the RMS errors for linear regression
% % STUDENT CODE GOES HERE: REMOVE THE NEXT 2 LINES AND THIS COMMENT
rmsvars = 0.1*(1:16);
lowndx = 1;
% Find the regression in unstandardized variables
% % STUDENT CODE GOES HERE: REMOVE THIS COMMENT
% Plot the results
% % STUDENT CODE GOES HERE: REMOVE THIS COMMENT
function [rmstrain rmstest] = a2q2(filename,lowndx)
% [RMSTRAIN RMSTEST]=A3Q2(LOWNDX) finds the RMS errors of 5-fold
% cross-validation for the variable LOWNDX of the data in the file
% FILENAME. The RMS errors for the training of each fold are returned
% in RMSTEST and the RMS errors for the testing of each fold are
% returned in RMSTEST.
% FILENAME – character string, name of file to be processed;
% assume that the first row describes the data variables
% LOWNDX – integer scalar, index into the data
% OUTPUTS:
% RMSTRAIN – 1×5 array of RMS errors for 5-fold training
% RMSTEST – 1×5 array of RMS errors for 5-fold testing
% Read the test data from a CSV file; find the size of the data
% % STUDENT CODE GOES HERE: REMOVE THIS COMMENT
% Create Xmat and yvec from the data and the input parameter,
% accounting for no standardization of data
% % STUDENT CODE GOES HERE: REMOVE THIS COMMENT
% Compute the RMS errors of 5-fold cross-validation
% % STUDENT CODE GOES HERE: REMOVE THE NEXT 2 LINES AND THIS COMMENT
rmstrain = 0.5*ones(1,5);
rmstest = 0.6*ones(1,5);
function [rmstrain,rmstest]=mykfold(Xmat, yvec, k_in)
% [RMSTRAIN,RMSTEST]=MYKFOLD(XMAT,yvec,K) performs a k-fold validation
% of the least-squares linear fit of yvec to XMAT. If K is omitted,
% the default is 5.
% XMAT – MxN data vector
% yvec – Mx1 data vector
% K – positive integer, number of folds to use
% OUTPUTS:
% RMSTRAIN – 1xK vector of RMS error of the training fits
% RMSTEST – 1xK vector of RMS error of the testing fits
% Problem size
M = size(Xmat, 1);
% Set the number of folds; must be 1
k = max(min(round(k_in), M-1), 2);
% Initialize the return variables
rmstrain = zeros(1, k);
rmstest = zeros(1, k);
% Process each fold
for ix=1:k
% % STUDENT CODE GOES HERE: replace the next 5 lines with code to
% % (1) set up the “train” and “test” indexing for “xmat” and “yvec”
% % (2) use the indexing to set up the “train” and “test” data
% % (3) compute “wvec” for the training data
xmat_train = [0 1];
yvec_train = 0;
wvec = [0 0];
xmat_test = [0 1];
yvec_test = 0;
rmstrain(ix) = rms(xmat_train*wvec – yvec_train);
rmstest(ix) = rms(xmat_test*wvec – yvec_test);