a) For each of the two, plot (scatterplot) Prices (on y-axis) against Sales (on x-axis), and fit a straight line and a quadratic line into the data in the graph.
b) What is the main difference that you observe between the product and the brand? What do you think is the reason for the difference?
c) Demean the Prices and Sales data from the brand with the most observations at the product (upc) level. In other words, take the average of price and sales for each upc from that brand, and subtract them from the Price and Sales data from that brand. Plot the demeaned prices against the demeaned Sales. Does the graph differ from the graph for the largest brand in 1.a? Why do you think that could be the case?
d) Add a line to the graph from 1.c that shows the distribution of observations along the x-axis. How do you interpret the fitted quadratic line in the graph from 1.c?
e) Using again the data from the brand with the most observation, take the log of Price and the log of Sales, and regress log Sales on log Prices. How would you interpret the coefficient you estimate on log price? Is it a useful estimate? Can you think of a way to improve the estimation of the coefficient? If yes, show the regression output.
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