Jerilyn Ross, a New York City psychologist, specializes in treating patients who are phobic and afraid to leave their homes. The following table indicates how many patients Dr. Ross has seen each year for the past ten years. It also indicates what the robbery rate was in New York City during the same year.

YEAR NUMBER OF PATIENTS CRIME RATE (ROBBERIES
PER 1,000 POPULATION)
1 36 58.3
2 33 61.6
3 40 73.4
4 41 75.7
5 40 81.1
6 55 89.0
7 60 101.1
8 54 94.8
9 58 103.3
10 61 116.2

a). Using the three month moving average, three month weigh average, exponential smoothing(α= 0.5), trend analysis, how many patients do you think Dr. Ross will see in years 11, 12, and 13? Which method is the best?

b). Apply linear regression to study the relationship between the crime rate and Dr. Ross's patient load. If the robbery rate increases to 131.2 in year 11, how many phobic patients will Dr. Ross treat? If the crime rate drops to 90.6, what is the patient projection? Constitute the test hypothesis (F test) to verify if there is a relationship between the crime rate and Dr. Ross's patient load with α= 0.05 significant level