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

Homework Answers

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
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