Let x be the percentage of 16- to 19-years-olds not in school and not high school graduates. Let y be the reported violent crimes per 1000 residents. Six small cities in Arkansas (Blytheville, El Doraod, Hot Springs, Jonesboro, Rogers, and Russellville) reported the following information about x and y.
X 24.1 19.4 18.5 14.9 19.0 17.5
Y 12.9 4.8 9.0 1.3 0.8 3.6
Given Σx=113.4 Σy=32.4 Σx2=2188.68 Σy2=285.74 Σxy= 668.08 r= .7855
A) find x and y. Then find the equation of the least squares line y=a+bx. (Round your answer to four decimal places)
x=
y=
y=__+__x
b) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least squares line? What percentage is unexplained?(Round your answer for r2to four decimal places. Round your answers for the percentages to two decimal places)
r2=
explained=__%
unexplained=___%
c) If the percentage of 16- to 19- year-olds not in school and not graduates reaches 21.8% in a similar city, what is the predicted rate of violent crimes per 1000 residents? (Round your answer to two decimal places)
___ violent crimes per 1000 residents