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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).
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