A sociologist investigating the recent upward shift in homicide trends throughout the country studied the extent to which the homicide rate per 100 000 people (y) is associated with population size in thousands (x), the rate of unemployment (x,), and the percentage of families with annual incomes less than R24 000 (x3). Data are provided in the table for a sample of 20 cities. A regression analysis was performed on the data and the results indicated that the interaction model E(v) = B, + B + Bx+ Bx; + B,xx2+ B;xX3 + Bx,x3 was a good model to fit to the data. %3D However, the residual plot for this model indicates that heteroscedasticity may exists for the percentage of families with annual incomes less than R24 000.
A sociologist investigating the recent upward shift in homicide trends throughout the country studied the extent to which the homicide rate per 100 000 people (y) is associated with population size in thousands (x), the rate of unemployment (x,), and the percentage of families with annual incomes less than R24 000 (x3). Data are provided in the table for a sample of 20 cities. A regression analysis was performed on the data and the results indicated that the interaction model E(v) = B, + B + Bx+ Bx; + B,xx2+ B;xX3 + Bx,x3 was a good model to fit to the data. %3D However, the residual plot for this model indicates that heteroscedasticity may exists for the percentage of families with annual incomes less than R24 000.
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Chapter1: Starting With Matlab
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Question
Transcribed Image Text:y
11.2
13.4
40.7
5.3
24.8
587
643
635
692
1248
643
1964
1531
713
749
7895
762
2793
6.2
6.4
16.5
20.5
26.3
16.5
19.2
16.5
9.3
5.3
7.3
5.9
6.4
7.6
4.9
6.4
6.0
7.4
12.7
20.9
23.2
35.7
8.7
21.3
17.2
14.3
18.1
9.6
14.5
26.9
15.7
36.2
18.1
28.9
14.9
25.8
21.7
23.1
19.1
24.7
28.6
24.9
17.9
22.4
20.2
16.9
5.8
741
8.6
625
854
716
921
595
3353
6.5
8.3
6.7
8.6
8.4
6.7
25.7
Transcribed Image Text:A sociologist investigating the recent upward shift in homicide trends throughout the country
studied the extent to which the homicide rate per 100 000 people (v) is associated with population
size in thousands (x ), the rate of unemployment (x,), and the percentage of families with annual
incomes less than R24 000 (x3). Data are provided in the table for a sample of 20 cities. A
regression analysis was performed on the data and the results indicated that the interaction model
E(y) = B,+ Bx + Bx, + Bx; + B,xqx,+ B;xx; + Bzxzx; was a good model to fit to the data.
%3D
However, the residual plot for this model indicates that heteroscedasticity may exists for the
percentage of families with annual incomes less than R24 000.
How do I Conduct a test for heteroscedasticity by dividing the data into two subsamples,
x,21 and x, > 21 using MSE for the first subsample = 582.3, MSE for the second subsample =
364.7 and a= 0.05. And how do I explain my conclusion.
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