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 (Source: Neighborhood Facts, The Piton Foundation).

Σx = 72; Σy = 589; Σx² = 1340; Σy² = 72,277; Σxy = 9499

(a) Draw a scatter diagram for the data.

(b) Find x, y, b, and the equation of the least-squares line. Plot the line on the scatter diagram of part (a).

(c) Find the sample correlation coef­ficient r and the coeffi­cient of determination. What percentage of the variation in y is explained by the least-squares model?

(d) Test the claim that the population correlation coef­ficient r is not zero at the 1% level of signifi­cance.

(e) For a neighborhood with x = 12% change in population in the past few years, predict the change in the crime rate (per 1000 residents).

(f) Verify that S_e ≈ 22.5908.

(g) Find an 80% con­fidence interval for the change in crime rate when the percentage change in population is x = 12%.

(h) Test the claim that the slope b of the population least-squares line is not zero at the 1% level of signi­ficance.

(i) Find an 80% con­fidence interval for b and interpret its meaning.

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