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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