1. Consider the following situation:
The general manager of a mass merchandising chain believes that sales of a product are influenced by the amount of space the product is allotted on the shelves. However, the manager realizes that sales volume would likely increase with extra space only up to a certain point. Beyond that point, the change in sales would likely flatten and perhaps even become negative (because customers may be dismayed by large exhibits).
To test his belief, the manager records the sales of a product during 1 week in 75 stores in the chain. For each store, he also records the shelf space (in inches) allotted to the product.
(i) Propose a population model that allows for this theory, and explain why you’ve chosen this model form.
(ii) What coefficients signs would be necessary to see the type of relationship the manager believes to be true?
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