Chapter 9.2, Problem 15P

(a)

To determine

Construct a scatter diagram for the data.

(b)

To determine

Verify the values of ${\displaystyle \sum x}$, ${\displaystyle \sum x^2}$, ${\displaystyle \sum y}$, ${\displaystyle \sum y^2}$, ${\displaystyle \sum xy}$ and r.

(c)

To determine

Find the value of $\overline{x}$.

Find the value of $\overline{y}$.

Find the value of a.

Find the value of b.

Find the equation of the least-squares line.

(d)

To determine

Construct a scatter diagram with least squares line.

Locate the point $\left(\overline{x},\overline{y}\right)$ on the line.

(e)

To determine

Find the value of the coefficient of determination $r^2$.

Mention percentage of the variation in y that can be explained by variation in x.

Mention percentage of the variation in y that cannot be explained by variation in x.

(f)

To determine

Find the predicted rate of violent crimes per 1,000 residents for the 24% of 16- to 19-year-olds not in school and not graduates.