roblem 4.30 Dr. Lilian Fok, a New Orleans psychologist, specializes in treating
ID: 390990 • Letter: R
Question
roblem 4.30 Dr. Lilian Fok, a New Orleans psychologist, specializes in treating patients who are agoraphobic (i e, atraid to leave thieir 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 10 62 33 411 4 58 Number of Patients Robbery Rate per 1,000 Population 35 57 58.0 606 730 761 78.5 89.5 996 94.8 1032 1156 The simple linear regression equation that shows the best relationship between the number of patients and year is (round your responses to three decimal places where y- Dependent Variable and x Independent Variable.Explanation / Answer
Solution:
Intercept can be calculated as
a = summation(y)*summation(x^2) - summation(x) summation(xy) / n*summation(x^2) - (summation(x))^2
a = 848.9*23595 - 475*42088.8 / 10*23595 - 475*475 = 3.643
X
Y
X2
Y2
XY
35
58
1225
3364
2030
33
60.6
1089
3672.36
1999.8
39
73
1521
5329
2847
41
76.1
1681
5791.21
3120.1
41
78.5
1681
6162.25
3218.5
54
89.5
2916
8010.25
4833
58
99.6
3364
9920.16
5776.8
55
94.8
3025
8987.04
5214
57
103.2
3249
10650.24
5882.4
62
115.6
3844
13363.36
7167.2
475
848.9
23595
75249.87
42088.8
Slope of the line can be calculated as
b =n*summation(XY) - summation(x) summation(y) / n*summation(x^2 ) - (summation(x))^2
b= 10*42088.8 - 475*848.9 / 10*23595 - 475*475 = 1.170
So linear regression line Y = 1.71046X + 3.64315
In year 11 no. of patients = 1.71046*11 + 3.64315 = 22.46
In year 12 no. of patients = 1.71046*12 + 3.64315 = 24.17
If coeffiecient of determination for linear regression model is 0.8640 which shows that show that 86.40% variablity in dependent variable explained by this model. So we can say that there is strong relationship between the no. of patients and year.
X
Y
X2
Y2
XY
35
58
1225
3364
2030
33
60.6
1089
3672.36
1999.8
39
73
1521
5329
2847
41
76.1
1681
5791.21
3120.1
41
78.5
1681
6162.25
3218.5
54
89.5
2916
8010.25
4833
58
99.6
3364
9920.16
5776.8
55
94.8
3025
8987.04
5214
57
103.2
3249
10650.24
5882.4
62
115.6
3844
13363.36
7167.2
475
848.9
23595
75249.87
42088.8
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