Each box of one brand of breakfast cereal contains a coupon entitling purchasers to a free package of vegetable seeds. At the home office, they use the weight of the incoming mail to determine the number of employees to be assigned to collecting coupons and sending out seed packages each day. (The company policy is that all mail received will be answered the same day.) Following is the data for a random sample of 8 days:

Weight of mail (pounds) 11 20 16 6 12 18 23 25

Number of employees 6 10 9 5 8 14 13 16

(a) Draw a scatter diagram for the data-discuss its shape (5 marks)

(b) Using Excel conduct the following regression models for the data

I. Linea

III. Third degree polynomial

IV. Exponential

V. Logarithmic

VI. Power

(c) Determine which model is the best-state the reason for your belief. (5 marks)

(d) What percentage of the variation in the number of employees is explained by the regression model chosen.

(e) If the company receives 15 pounds of mail, how many employees should be assigned mail duty?

2.Explore non-linear regression. Determine a possible data set that would most likely not have a linear relationship, but would have a non-linear relationship. Discuss the type of data (find an example) and the relationship that the data would have. Also discuss why you think it would have this type of relationship