Question

Given the information below, interpret the correlation coefficient, check the significance and, assess the relationship between X (months on probation) and Y (risk to re-offend), include the strength, direction along with the r-squared interpretation, and what this means for the variables.

R= - 0.71 (Negative -.71)

N= 10

At the 0.05 level of significance the critical value is 0.6319.

Given the above information. Calculate the coefficient of determination (r-squared) and interpret what this means. How much can you reduuce the error predicting risk to reoffend if you know how many months of probation someone has been on?

Answer 1

We want to test that there is a significant correlation between the risk to re-offend & months on probation

Ho:- There is no significant correlation between the risk to re-offend & months on probation

vs

Ha:- There is a significant correlation between the risk to re-offend & months on probation

r = -0.71

So there is a negative correlation between the risk to re-offend & months on probation

|r| = 0.71 > 0.70

So we can say that there is a strong correlation between them.

So There is a strong & negative correlation between the risk to re-offend & months on probation.

The critical value = 0.6319

we reject Ho if |r| > 0.6319

Here |r| = 0.71 > 0.6319

So we reject Ho

We may conclude that there is a significant correlation between the risk to re-offend & months on probation.

b) coefficeint of determination = R2 = (r) ^2 = (-0.71)^2 = 0.5041

interpretation:

50.41 % of total variation in the risk to offend explained by the months of probation.

unexplained variance = 1- 0.5041 = 0.4959

49.59% of unexplained variation in risk to offend.

How much can you reduce the error predicting risk to re-offend if you know how many months of probation someone has been on?

We can reduce the 49.59% of the r predicting risk to re-offend if you know how many months of probation someone has been on.