a. A battery manufacturer was interested in predicting the annual maintenance cost of the battery…

a. A battery manufacturer was interested in predicting the annual maintenance cost of the battery manufacturing machines based upon the age of the machine. A sample of ten machines revealed the following ages and maintenance costs during the previous year.

i. Fit the linear regression model to the data using the least squares method.

(7 marks )

ii. Interpret the meaning of the slope in the linear regression model in part (ii).

(1 mark ) iii. Predict the maintenance cost of a machine that is 10 years old. (1 marks )

b. State Bayes’ theorem(2 marks )

c. An economist believes that during periods of high economic growth, the U.S. dollar appreciates with probability 0.70; in periods of moderate economic growth, the dollar appreciates with probability 0.40; and during periods of low economic growth, the dollar appreciates with probability 0.20. During any period of time, the probability of high economic growth is 0.30, the probability of moderate growth is 0.50, and the probability of low economic growth is 0.20. Suppose the dollar has been appreciating during the present period. What is the probability we are experiencing:

i.	A period of high economic growth?	(3 marks )
ii.	A period of moderate economic growth?	(3 marks )
iii.	A period of low economic growth	(3 marks )