A commercial bakery produces gluten-free pizza dough and sells it to chains of retail stores across Canada. The product is profitable, although some has to be discarded as spoilage since it is too close to its expiry date to be accepted by any of the retailers. Quarterly data over the past three years are as follows:

a) The logistics manager explains to the product manager that when sales volumes are small, it is difficult to deliver the product to the retailer on time. “The more product you can sell, the lower I can get the spoilage rate,” she says. Use a linear model to predict the spoilage rate from the volume shipped. Comment on the conditions.

b) If the volume shipped can be increased to 4 tonnes next quarter, what do you estimate the spoilage rate will be?

c) “Nonsense,” retorts the product manager. “It is because the spoilage rate is so high that I have dissatisfied customers who don’t want to order from us.” Use a linear model to estimate the volume shipped from the spoilage rate. Comment on the conditions.

d) If the spoilage rate can be reduced to 5% next quarter, what volume do you estimate will be shipped?

e) What fraction of the variability in the data is explained by these two models? Comment on whether the answer is the same for each model.

f) Interpret the meaning of the slope coefficient in the models you derived in (a) and (c).

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Volume Volume Shipped (tonnes) Spoilage (%) Shipped (tonnes) Spoilage (%) 2.73 1.98 10.40% 8.61% 2.16 9.26% 2.82 8.20% 8.71% 2.94 3.26 7.99% 2.92 8.19% 3.49 6.59% 2.64 9.06% 2.9 7.50% 2.39 9.53% 3.06 7.67%