Let x be a random variable representing percentage change in

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   33   3   11   17   7   6
y   167   39   132   127   69   53

In this setting we have x = 77, y = 587, x2 = 1593, y2 = 70,533, and xy = 10040.
(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 four decimal places.)
x   =   

y   =   

b   =   

y   = + x


(b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y).

(c) 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 one decimal place.    crimes per 1000 residents

Solution

x bar = Mean of x = 12.83

y bar=97.83

b = slope = 4.145

a = Intercept = 44.643

Regression equation is

y = 4.145x+44.643

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Scatter Plot:

Variation = R^2 where R is correlation coefficient.

= 0.8904²= 0.7928

When x = 16, plug in this value to get predicted value of y

y = 44.643+4.145(16)

= 110.963