Question

Using the data below about level of risk for juvenile detention (from 1 to 5 with 5 being high risk), number of at-risk factors (i.e., poverty, truancy from school), and progress for 25 juveniles, measured on a scale from 1 to 100, 10 years after the introduction of a program. What conclusion might you be able to draw from your results?

Risk	# of Factors	Progress
4	3	42
10	1	98
4	3	43
4	3	73
10	2	17
3	3	71
10	2	39
3	2	68
3	2	50
6	1	36
6	2	56
6	1	42
10	1	22
9	2	25
8	1	31
7	2	3
1	2	42
4	2	39
3	1	56
1	2	2
6	2	97
3	3	54
2	2	1
1	2	4
3	3	10

Answer 1

Let's first find out that if the Risk of juvenile detention is related to the No. of risk factors. For this, we will run a correlation test between the first two variables.

The results of the correlation test are:

Coefficient of determination = R^2 = 0.18

p-value = 0.38

This shows that there is no such relationship between the two variables (but ideally there should be)

Now we can find the result of the following hypothesis:

Ho: There is no relationship between the risk of juvenile detention and their progress after 10 years

H1: There is a relationship between the risk of juvenile detention and their progress after 10 years

This will tell us if the progress of a juvenile is deterred by the risk factor

The value of R^2 comes out to be 0.0122 which is no relationship between the two variables. Hence, we cannot reject the null hypothesis.

We can perform the same with No. of factors and Progress. The coeff. of determination is again very low. Hence, there is no such relationship between the variables.