Question

# Let x be a random variable representing percentage change in neighborhood population in the past few...

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

\

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