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function pred = log_regress_pred(price, quantity)
days = size(price, 1) - size(quantity, 1);
product_count = size(price, 2);
test_count = size(quantity, 1);
test_set = 1:test_count;
pred_set = test_count+1:size(price, 1);
pred = zeros(days, product_count);
for i = 1:product_count
[a,b] = regress_log(price(test_set, i), quantity(test_set, i));
pred(:, i) = a * log(price(pred_set, i)) + b;
end
endfunction
function [a,b] = regress_log(x, y)
ab = [ log(x) ones(length(x), 1) ] \ y;
a = ab(1);
b = ab(2);;
endfunction
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