IDS: Exam solution 10/09/2026

Read the attached IDS_2026_SeptemberOUT.pdf and compare Exercise II with the textbook exercises referenced in the issue. The body includes a submitted MATLAB script but does not specify a change to make or what completion would look like.

IDS_2026_SeptemberOUT.pdf

Exercise II was identical to two exercises in the textbook. Therefore, anyone who did not complete it had evidently not even looked through the book.

As usual there was one student who submitted the following exam completely done by AI and completely wrong
INCREDIBLE

load citiesItaly.mat

% Numeric vars
PUL = varfun(@isnumeric, citiesItaly, 'OutputFormat','uniform');
numT = citiesItaly(:, PUL);

meds = varfun(@median, numT);
mads = varfun(@(x) mad(x,1), numT);

medVals = table2array(meds);
madVals = table2array(mads);
sigma = madVals / 0.6745;

names = numT.Properties.VariableNames;
Z = table(); 
for k = 1:numel(names)
    col = numT.(names{k});
    Z.( [names{k} '_robustz'] ) = (col - medVals(k)) ./ sigma(k);
end

citiesItalyRobust = [citiesItaly Z];

summaryStats = table(names', medVals', sigma', 'VariableNames', {'Variable','Median','UnbiasedMAD'});

robCols = endsWith(citiesItalyRobust.Properties.VariableNames,"_robustz");
Trob = citiesItalyRobust(:, robCols);
X = table2array(Trob);
names = Trob.Properties.VariableNames;
p = size(X,2);

figure;
hold on;
for k = 1:p
    h = boxchart(k*ones(size(X,1),1), X(:,k));  
    h.BoxFaceColor = [0.6 0.6 0.9];                
    h.MarkerStyle = 'none';
    h.DisplayName = names{k};                     
end
hold off;
xlim([0.5 p+0.5]);
set(gca, 'XTick', 1:p, 'XTickLabel', names, 'XTickLabelRotation', 45);

ylabel("addedval(1)");
title("addedval(1)");
legend("show", "Location", "bestoutside");

s = skewness(X,0);                 

% Find largest absolute skewness
[~, idxAbsMax] = max(abs(s));
varAbsMax = names{idxAbsMax};
skewAbsMax = s(idxAbsMax);

[skewPosMax, idxPosMax] = max(s);
[skewNegMin, idxNegMin] = min(s);
varPosMax = names{idxPosMax};
varNegMax = names{idxNegMin};

disp(table(names', s', 'VariableNames', {'Variable','Skewness'}));
fprintf('Largest absolute skewness: %s (skewness = %.4g)\n', varAbsMax, skewAbsMax);
fprintf('Largest positive skewness: %s (skewness = %.4g)\n', varPosMax, skewPosMax);
fprintf('Largest negative skewness: %s (skewness = %.4g)\n', varNegMax, skewNegMin);


load citiesItaly.mat   

want = {'addedval','depos'};
vars = citiesItaly.Properties.VariableNames;
if all(ismember(want,vars))
    sel = want;
else
    PUL = varfun(@isnumeric, citiesItaly, 'OutputFormat','uniform');
    numVars = citiesItaly.Properties.VariableNames(PUL);
    if numel(numVars) < 2
        error('Need at least two numeric variables in the table.');
    end
    sel = numVars(1:2);
end

x = table2array(citiesItaly(:,sel(1)));
y = table2array(citiesItaly(:,sel(2)));
XY = [x(:) y(:)];

if size(XY,2) ~= 2
    error('XY must be n-by-2.');
end
if size(XY,1) < 2 || all(var(XY)==0)
    error('Need at least two nonidentical observations.');
end

% Scatter
figure; hold on; axis equal;
scatter(XY(:,1), XY(:,2), 30, [0 0.4470 0.7410], 'filled');

mu = mean(XY,1);
S = cov(XY);

if ~isequal(size(S),[2 2])
    error('Covariance matrix is not 2-by-2. Check input data.');
end

k = chi2inv(0.99,2);

[V,D] = eig(S);

% Semi-axis lengths 
a = sqrt(k * D(1,1));
b = sqrt(k * D(2,2));

% Ellipse in eigen-coordinates and transform back
t = linspace(0,2*pi,300);
ellipse_eig = [a*cos(t); b*sin(t)];
ellipse = (V * ellipse_eig)' + mu;

% Plot ellipse and principal axes
plot(ellipse(:,1), ellipse(:,2), 'r-', 'LineWidth',1.5);
for i = 1:2
    vec = V(:,i) * sqrt(k * D(i,i));
    plot([mu(1)-vec(1), mu(1)+vec(1)], [mu(2)-vec(2), mu(2)+vec(2)], 'k--', 'LineWidth',1.2);
end

xlabel(sel{1}); ylabel(sel{2});
title(sprintf('Scatter of %s vs %s with 99%% Confidence Ellipse', sel{1}, sel{2}));
legend('Data','99% ellipse','Principal axes','Location','best');
grid on; hold off;


load citiesItaly.mat

% Select first two numeric variables
PUL = varfun(@isnumeric, citiesItaly, 'OutputFormat','uniform');
numVars = citiesItaly.Properties.VariableNames(PUL);
if numel(numVars) < 2
    error('Need at least two numeric variables in the table.');
end
x = table2array(citiesItaly(:,numVars{1}));
y = table2array(citiesItaly(:,numVars{2}));

figure('Name','Scatter with Bivariate (marginal) Boxplots','NumberTitle','off');

% Main scatter axes
mainPos = [0.15 0.15 0.65 0.65];
axMain = axes('Position',mainPos);
scatter(axMain, x, y, 30, [0 0.4470 0.7410], 'filled');
axis(axMain,'equal');
xlabel(axMain, numVars{1}); ylabel(axMain, numVars{2});
grid(axMain,'on');

% Top boxplot for X
topPos = [mainPos(1) mainPos(2)+mainPos(4)+0.02 mainPos(3) 0.12];
axTop = axes('Position',topPos);
boxplot(axTop, x, 'Orientation','horizontal','Labels',{''}, 'Colors','k');
set(axTop,'XAxisLocation','top','XTick',[],'YTick',[]);
xlim(axTop, xlim(axMain));

% Right boxplot for Y 
rightPos = [mainPos(1)+mainPos(3)+0.02 mainPos(2) 0.12 mainPos(4)];
axRight = axes('Position',rightPos);
boxplot(axRight, y, 'Orientation','vertical','Labels',{''}, 'Colors','k');
set(axRight,'YTick',[],'XTick',[]);
ylim(axRight, ylim(axMain));

% Link limits so they stay consistent when zooming/panning
linkaxes([axMain axTop], 'x');
linkaxes([axMain axRight], 'y');

box(axTop,'off'); box(axRight,'off');


load citiesItaly.mat   

% Pick first two numeric vars
PUL = varfun(@isnumeric, citiesItaly, 'OutputFormat','uniform');
numVars = citiesItaly.Properties.VariableNames(PUL);
if numel(numVars) < 2
    error('Need at least two numeric variables.');
end
X = table2array(citiesItaly(:, numVars(1:2)));

[robCov,robMean] = robustcov(X,'Method','fmcd');

md2 = sum(((X - robMean) / robCov) .* (X - robMean), 2);  

cut = chi2inv(0.99,2);

outIdx = find(md2 > cut);

if ~isempty(citiesItaly.Properties.RowNames)
    outNames = citiesItaly.Properties.RowNames(outIdx);
    disp('Rows outside robust bivariate boxplot (row names):');
    disp(outNames);
else
    disp('Rows outside robust bivariate boxplot (row indices):');
    disp(outIdx);
end