2. A colleague of yours shows you a simple linear regression model he ran that aims to explain the percentage of correctional officers reporting self-harm on the basis of the number of prisoners they are assigned to. His prediction equation looks as follows: y = 0.05 + 1.31x.

a) Interpret this prediction equation in the context of the problem.

b) You criticize your friend's model for not incorporating anything but the constant and a single explanatory variable. Other variables that could have real explanatory power (e.g. past history of mental illness, working conditions) are entirely left out. He replies that that is technically inaccurate. How could he be correct in making that assessment?

c) Assuming he persuaded you of the validity of that assessment, should you then conclude as a result that his model is sound? Justify your answer

d) How would you interpret an R2 for this model with a value of 0.12 in the context of the problem?

3. You read a report purposing to show that a prisoner's age (in years) is associated with the length of his/her prison sentence - in other words, the older he/she is, the longer the sentence he/she is currently serving. Is there anything potentially problematic with limiting this association to these two variables alone? Justify your answer.