Task Background: Regression is a very powerful tool for making predictions. For example, the number of hours that you put into a course ultimately should reflect your final grade average. That is, the more hours you study, the higher your grade. Regression is often used in businesses to make predictions for the sales of goods and services. Graphs of regression equations help to make these predictions by providing a visual relationship between two variables. Assignment Windows Based Computers: Download the graphing program from www.padowan.dk/graph. The instructions for using this program can be found in the Instructor’s Files of your Virtual Classroom. Apple (Mac) Based Computers: Download the graphing program from http://www.geogebra.org/cms/. (NOTE: You are free to use Excel as well if preferred). Scenario: Regression equations are created by modeling data, such as the following: Profit = (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 profit of the new e-reader: Profit = $0.15 × number of e-readers sold – $28 Or, assuming x = the number of e-readers sold, this would be the same regression equation: Profit = 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, graph the profit equation. Discuss the meaning of the x- and y-axis values on the graph. (Hint: Be sure to label the axis) 2.Discuss the meaning of the slope of the equation that you have just graphed. How is it related to the cost of each e-reader? 3.Based on the results of the graph and the profit equation provided, discuss the relationship between profits and number of e-readers produced. (Hint: Consider the slope and y-intercept.) 4.If the company does not sell a single e-reader, how much is lost ? Mathematically, what is this value called in the equation? 5.If the company sells 5,000 e-readers, how much will the company make (or lose)? 6.If profit must equal 100 thousand, how many e-readers will your company need to sell? (Round up to the nearest e-reader.) 7.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.)
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