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function pred = regress_interval_pred(price, quantity, interval)
assert(mod(size(price, 1), interval) == 0);
assert(mod(size(quantity, 1), interval) == 0);
days = size(price, 1) - size(quantity, 1);
product_count = size(price, 2);
test_count = size(quantity, 1);
test_interval_count = size(quantity, 1) / interval;
pred_interval_count = days / interval;
test_base = [0:test_interval_count-1] * interval;
pred_base = [0:pred_interval_count-1] * interval;
pred = zeros(days, product_count);
for i = 1:product_count
for j = 1:interval
test_set = test_base + j;
pred_set = pred_base + j;
regress_quad = @(x, y) [ log(x) x.^0 ] \ y;
abc = regress_quad(price(test_set, i), quantity(test_set, i));
pred(pred_set, i) = polyval(abc, log(price(test_count+pred_set, i)));
end
end
endfunction
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