To Warm Up, Let Us Start with a Problem That

Essay

To warm up, let us start with a problem that has a "perfect" regression line. Assume that the state prison wants to encourage prisoners to get involved in education. Thus, the prison administration offers that for every hour spent on education, inmates receive 5 additional minutes in the prison yard.
a. Compute beta and interpret your finding.
b. Compute the constant (y intercept or a) and interpret your finding.
$$\begin{array} { | l | r | r | } \hline & { \boldsymbol { x } } & {y } \\\hline & 0 & 0 \\\hline & 1 & 5 \\\hline & 2 & 10 \\\hline & 3 & 15 \\\hline & 4 & 20 \\\hline & 5 & 25 \\\hline & 6 & 30 \\\hline & 7 & 35 \\\hline & 8 & 40 \\\hline & 9 & 45 \\\hline & 10 & 50 \\\hline \text { Totals } & & \\\hline \text { Means } & & \\\hline\end{array}$$
c. Assume that John (inmate) has studied 17 hours in the previous week; how many minutes of additional yard time did he earn? Use the classic algebraic equation (y = a + bx) to calculate the amount of minutes earned and interpret your result.
d. Next, you want to predict the total time an inmate is allowed to spend in the yard (weekly allowance + additional time earned). The weekly allowance regarding yard time is (without additional time earned) 630 minutes (10.5 hours).
$$\begin{array} { | l | r | r | } \hline & x & y \\\hline & 0 & 630 \\\hline & 1 & 635 \\\hline & 2 & 640 \\\hline & 3 & 645 \\\hline & 4 & 650 \\\hline & 5 & 655 \\\hline & 6 & 660 \\\hline & 7 & 665 \\\hline & 8 & 670 \\\hline & 9 & 675 \\\hline & 10 & 680 \\\hline \text { Totals } & & \\\hline \text { Means } & & \\\hline\end{array}$$
i. Compute beta.
ii. Compute the constant (a or y-intercept).
iii. How many minutes (total) is John allowed to spend in the prison yard if he has studied for 21 hours? Use the classic algebraic equation (y = a + bx).