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In: Statistics and Probability

A store manager believes items with discounts (10% off, 20% off, etc.) sell better than items...

A store manager believes items with discounts (10% off, 20% off, etc.) sell better than items offered at full price. She also believes items with well-known brand names sell better than items not associated with a well-known brand. Furthermore, she believes that when the prices of brand-name items are discounted sales are much higher than normal.

You think this sounds like she is describing an interaction between brand-named and discounts and you want to use regression to test the effects of discounts, brands, and their interaction.

Assume that the manager provides the following IVs:

  • sales                     number of sales (the DV
  • item_cost            cost of the item (a continuous IV)
  • brand (0,1)          brand=1 for items associated with a well-known brand and 0 otherwise
  • discount (0,1)      discount = 1 for items with discounted prices and 0 otherwise

Question: Write out the regression equation(s) you would use to test the hypothesis that there is an interaction between brands and discounts. Describe the procedure you would use to test the hypothesis.

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