Regression Equations and Meanings
Scenario: Regression equations are created by modeling data, such as the following:
Sales = (Cost Per Item – Number of Items) – Constant Charges
In this equation, constant charges may be rent, salaries, or other fixed costs. This includes anything that you have to pay for periodically as a business owner. This value is negative because this cost must be paid each period and must be paid whether you make a sale or not.
Your company may wish to release a new e-reader device. Based on data collected from various sources, your company has come up with the following regression equation for the sales of the new e-reader:
Sales = $0.15 – number of e-readers sold – $28
Or, assuming x = the number of e-readers sold, this would be the same regression equation:
Sales = 0.15x – 28
In this case, the values are given in thousands (i.e., the cost of making an individual e-reader will be $150 [0.15 – 1,000], with $28,000 [28 * 1,000] in constant charges).
Answer the following questions based on the given regression equation:
1.Using the graphing program that you downloaded from www.padowan.dk/graph, graph the sales equation. Discuss the meaning of the x- and y-axis values on the graph. (Hint: Label the axis with the Text tool in the graphing program.)
2.Based on the results of the graph and the sales equation provided, discuss the relationship between sales and number of e-readers produced. (Hint: Consider the slope and y-intercept.)
3.If the company does not sell a single e-reader, how much is lost in sales? Mathematically, what is this value called in the equation?
4.If the company sells 5,000 e-readers, how much will the company make (or lose) in sales?
5.If sales must equal 100 thousand, how many e-readers will your company need to sell? (Round up to the nearest e-reader.)
6.If your company is hoping to break even, how many e-readers will need to be sold to accomplish this? (Round up to the nearest e-reader.)