Gross Profit The gross profit of a business is the difference between what a retailer charges for what it sells (net sales) and the cost of the items sold. For example, in the first quarter of 2010, net sales at Lowe’s (the chain of hardware megastores) were $12.388 billion. The items that it sold cost Lowe’s $8.030 billion, so its operating income for this quarter was 12.388 - 8.030 = $4.358 billion. The following simple regression model describes the gross profit at Lowe’s in terms of loans made for real estate by commercial banks.
Estimated Operating Income t = b0 + b1 Loans t
The idea is that more home loans mean more busy homeowners shopping for hardware at Lowe’s. The data for this example are quarterly and run from 1990 through the end of 2011. The gross profit in the data table is given in millions of dollars; the amount of bank loans for real estate is in billions of dollars.
(a) Estimate the simple regression equation. What is the interpretation of the estimated intercept and slope?
(b) Does the equation ft in part (a) meet the conditions for the simple regression model? Use color codes or symbols to distinguish the quarter 11, 2, 3, or 42 in the plot of the residuals on time.
(c) Are the residuals for the different quarters similar, or do you find systematic differences in the different quarters? (Comparison boxplots may be helpful.)
(d) Regardless of problems from violating conditions, would this equation nonetheless be useful for forecasting the gross profit at Lowe’s?
(e) Here’s an alternative model. If bank loans for real estate are truly related to the gross profit at Lowe’s in some fundamental way, then the percentage changes in the bank loans ought to be related to percentage changes in Lowe’s operating income. Are they? Regress the percentage changes in the operating income at Lowe’s on the percentage changes in bank loans for real estate. Summarize the ft of this simple regression. Does this regression meet the conditions for the simple regression model?
(f) What’s your conclusion about the relationship between the gross profit at Lowe’s and the level of lending for real estate?