Question

Dr. Lillian Fok, a New Orleans psychologist, specializes in treating patients who are agoraphobic (i.e., afraid to leave their homes). The following table indicates how many patients Dr. Fok has seen each year for the past 10 years. It also indicates what the robbery rate was in New Orleans during the same year: 

Year	1	2	3	4	5	6	7	8	9	10
Number of Patients	36	32	39	40	40	56	60	55	59	61
Robbery Rate per 1,000 Population	57.8	61.4	73.0	75.7	81.1	88.6	101.5	94.2	103.2	116.2

The simple linear regression equation that shows the best relationship between the number of patients and the robbery rate is (round your responses to three decimal places):

\(\hat{y}=\square+\square x\)

where \(\hat{y}\) = Number of Patients and x = Robbery Rate. 

In year 11, if the robbery rate increases to 132.50, using trend analysis, the number of patients Dr. Fok will see = _______ patients (round your response to two decimal places). 

In year 11, if the robbery rate decreases to 87.6, using trend analysis, the number of patients Dr. Fok will see = _______ patients (round your response to two decimal places). 

Answer 1

x	y	x*y	x*x	y*y
36	57.8	2,080.8	1,296.00	3,341
32	61.4	1,964.8	1,024.00	3,770
39	73.0	2,847.0	1,521.00	5,329
40	75.7	3,028.0	1,600.00	5,730
40	81.1	3,244.0	1,600.00	6,577
56	88.6	4,961.6	3,136.00	7,850
60	101.5	6,090.0	3,600.00	10,302
55	94.2	5,181.0	3,025.00	8,874
59	103.2	6,088.8	3,481.00	10,650
61	116.2	7,088.2	3,721.00	13,502
478	852.7	42,574.20	24,004.00	75,926.03

n		10.00
n*Sum(xy) =10*42574.20		425,742.00
Sumx*Sumy =478*852.7		407,590.60
n*sumx2 =10*24004		240,040.00
(Sumx)2 = 478^2		228,484.00

b = (425742-407590.6)/(240040-228484) = 1.57

a = (852.7-1.57*478)/10 = 10.19

y = 10.19 + 1.57*x

For y = 132.50:

132.50 = 10.19 + 1.57*x

x = 77.87

For y = 87.6:

87.6 = 10.19 + 1.57*x

x = 49.28