Question

Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information.

x	30	3	11	17	7	6
y	170	35	132	127	69	53

Σx = 74; Σy = 586; Σx² = 1,404; Σy² = 71,248; Σxy = 9,617

(a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.)

x

=

y

=

b

=   

+ x(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)

r =
r2 =

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)
%

(d) For a neighborhood with x = 15% change in population in the past few years, predict the change in the crime rate (per 1000 residents). (Round your answer to one decimal place.)
crimes per 1000 residents

Answer 1

\

a)]

X̅=ΣX/n =	12.33
Y̅=ΣY/n =	97.67

b=4.864

ŷ =

37.682+4.864x

c)

r=Cov/(Sx*Sy)=

0.911

coefficient of determination r2 =

0.829

percentage of variation in y is explained by the least-squares model =82.9 %

d)

predicted value =37.682+4.864*15=

110.6