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 neighborhoods gave the following information.

x	29	4	11	17	7	6
y	176	40	132	127	69	53

Σx = 74, Σy = 597, Σx² = 1352, Σy² = 73,699, and Σxy = 9,676

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

x	=
y	=
b	=
ŷ	=	+ x

Plot the line on the scatter diagram of part (a).

(c) Find the sample correlation coefficient r and the coefficient of determination r ². (Round your answers to three decimal places.)

r =
r 2 =

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 = 19% change in population in the past few years, predict the change in the crime rate (per 1000 residents). (Round your answer to two decimal places.)
crimes per 1000 residents

Answer 1

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