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 answer the following 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-yearolds 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.
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 answer the following
- 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-yearolds 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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