The Minister of National Security in Trinidad and Tobago is interested in determining the factors that influence the number of crimes that are reported. You are tasked to develop a model using the appropriate variables. The following variables are utilized: X1 = total overall reported crime rate per 100,000 residents X2 = reported violent crime rate per 100,000 residents X3 = % of people 25 years+ with 4 yrs. of high school X4 = % of 16 to 19-year-olds not in high school and not high school graduates. X5 = % of 18 to 24-year-olds in college X6 = % of people 25 years+ with at least 4 years of college
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
- The Minister of National Security in Trinidad and Tobago is interested in determining the factors that influence the number of crimes that are reported. You are tasked to develop a model using the appropriate variables. The following variables are utilized:
X1 = total overall reported crime rate per 100,000 residents X2 = reported violent crime rate per 100,000 residents
X3 = % of people 25 years+ with 4 yrs. of high school
X4 = % of 16 to 19-year-olds not in high school and not high school graduates. X5 = % of 18 to 24-year-olds in college
X6 = % of people 25 years+ with at least 4 years of college
|
X1 |
X2 |
X3 |
X4 |
X5 |
X6 |
|
478 |
184 |
74 |
11 |
31 |
20 |
|
494 |
213 |
72 |
11 |
43 |
18 |
|
643 |
347 |
70 |
18 |
16 |
16 |
|
341 |
565 |
71 |
11 |
25 |
19 |
|
773 |
327 |
72 |
9 |
29 |
24 |
|
603 |
260 |
68 |
8 |
32 |
15 |
|
484 |
325 |
68 |
12 |
24 |
14 |
|
546 |
102 |
62 |
13 |
28 |
11 |
|
424 |
38 |
69 |
7 |
25 |
12 |
|
548 |
226 |
66 |
9 |
58 |
15 |
|
506 |
137 |
60 |
13 |
21 |
9 |
|
819 |
369 |
81 |
4 |
77 |
36 |
|
541 |
109 |
66 |
9 |
37 |
12 |
|
491 |
809 |
67 |
11 |
37 |
16 |
|
514 |
29 |
65 |
12 |
35 |
11 |
|
371 |
245 |
64 |
10 |
42 |
14 |
|
457 |
118 |
64 |
12 |
21 |
10 |
|
437 |
148 |
62 |
7 |
81 |
27 |
|
570 |
387 |
59 |
15 |
31 |
16 |
|
432 |
98 |
56 |
15 |
50 |
15 |
|
619 |
608 |
46 |
22 |
24 |
8 |
|
357 |
218 |
54 |
14 |
27 |
13 |
|
623 |
254 |
54 |
20 |
22 |
11 |
|
547 |
697 |
45 |
26 |
18 |
8 |
|
792 |
827 |
57 |
12 |
23 |
11 |
|
799 |
693 |
57 |
9 |
60 |
18 |
|
439 |
448 |
61 |
19 |
14 |
12 |
|
867 |
942 |
52 |
17 |
31 |
10 |
|
912 |
1017 |
44 |
21 |
24 |
9 |
|
462 |
216 |
43 |
18 |
23 |
8 |
|
859 |
673 |
48 |
19 |
22 |
10 |
|
805 |
989 |
57 |
14 |
25 |
12 |
|
652 |
630 |
47 |
19 |
25 |
9 |
|
776 |
404 |
50 |
19 |
21 |
9 |
Using SPSS
- Determine the multiple regression equation for the data.
- Interpret the coefficient of determination.
- At the 10% significance level, determine if the model is useful for predicting the number of crimes that are reported in Trinidad and Tobago. In responding, construct and test any appropriate hypothesis.
- At the 10% significance level, does it appear that percent of people 25 years+ with 4 yrs. of high school, percent of 16 to 19-year- olds not in high school and not high school graduates or percent of 18 to 24-year-olds in college can be removed from the model as unnecessary? In responding, construct and test any appropriate hypothesis.
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