The marketing division of a major food store chain designed the following study to evaluate three different promotions for its low-fat breakfast cereals. The promotions are as follows:
The company wants to determine which of the three promotions produces the largest average increase in sales. Thirty stores were selected for participation in the 1-month promotion period, with 10 stores randomly assigned to one of the three promotions. The company collected data on the increase in sales (y, in hundreds of units sold) and the average monthly sales for the 12 months prior to the promotion (x, in hundreds of units). The data are given here.
a. Write a model for this experiment. Make sure to identify all variables and parameters in your model.
b. Provide a scatterplot of the data with regression lines that would allow a visual assessment of whether there is a significant relationship between the increase in sales and the average monthly sales figures.
c. From your scatterplot in part (b), do the lines associated with the three promotions appear to have similar slopes?