Simple Regression

 A CEO of a   large plastics manufacturing company would like to determine if she should be   placing more money allotted in the budget next year for television   advertising of a new baby bottle marketed for controlling reflux and reducing   gas. She wonders whether there is a strong relationship between the amount of   money spent on television advertising for this new baby bottle called Gentle   Bottle and the number of orders received. The manufacturing process of this   baby bottle is very difficult and requires advanced quality control so the   CEO would prefer to generate a stable number of orders.

The cost of   advertising is always an important consideration in the phase I roll-out of a   new baby bottle. Data that have been collected over the past 20 months indicate   the amount of money spent of television advertising and the number of orders   received.   The use of   linear regression is a critical tool for a manager’s decision-making ability.   Please carefully read the example below and try to answer the questions in   terms of the problem context.

The results are as follows:   Month Advertising Cost Number of Orders   1 77,430 2,902,000   2 62,620 1,800,000   3 69,580 1,299,000   4 50,670 1,430,000   5 69,180 1,367,000   6 73,140 2,011,000   7 83,370 3,888,000   8 78,880 2,935,000   9 64,990 1,555,000   10 77,230 3,654,000   11 61,380 1,598,000   12 62,900 1,967,000   13 63,270 1,899,000   14 89,190 3,245,000   15 60,030 1,934,000   16 79,210 2,853,000   17 65,770 1,625,000   18 84,530 3,778,000   19 79,760 2,999,000   20 82,640 3,834,000      

  a. Set up a   scatter diagram and calculate the associated correlation coefficient.

b. Discuss   how strong you think the relationship is between the amount of money spent on   television advertising and the number of orders received.    

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