Consider the subsequent situation

The general manager of a mass merchandising chain trusts that sales of a product are influenced by the amount of space the product is allotted on the shelves. But the manager apprehends that sales volume would likely rise with extra space only up to a certain point. Beyond that point the change in sales would probable flatten besides perhaps even become negative because customers may be dismayed by large exhibits?

To test his confidence the manager records the sales of a product during 1 week in 75 stores in the chain. For each store he as well records the shelf space (in inches) allocated to the product.

(i) Suggest a population model that allows for this theory as well as explain why you've chosen this model form.

(ii) What coefficients signs would be essential to see the type of relationship the manager believes to be true?