Let x be a random variable representing percentagechange in neighborhood population in the past few years, and lety be a random variable representing crime rate (crimes per1000 population). A random sample of six Denver neighborhoods gavethe following information.

x	25	4	11	17	7	6
y	172	33	132	127	69	53

In this setting we have Σx = 70, Σy = 586,Σx² = 1136, Σy² = 71,796,and Σxy = 8844.

(a) Find x, y, b, and the equation ofthe least-squares line. (Round your answers for x andy to two decimal places. Round your least-squaresestimates to four decimal places.)

x	= Â
y	= Â
b	= Â
Å·	= Â	+   x

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

(c) Find the sample correlation coefficient r and thecoefficient of determination. (Round your answers to three decimalplaces.)

r =
r2 =

What percentage of variation in y is explained by theleast-squares model? (Round your answer to one decimalplace.)
%

(d) Test the claim that the population correlation coefficientρ is not zero at the 10% level of significance. (Roundyour test statistic to three decimal places and yourP-value to four decimal places.)

t =
P-value =

Conclusion

Reject the null hypothesis, there is sufficient evidence thatρ differs from 0.Reject the null hypothesis, there isinsufficient evidence that ρ differs from0.    Fail to reject the null hypothesis, thereis sufficient evidence that ρ differs from 0.Fail toreject the null hypothesis, there is insufficient evidence thatρ differs from 0.

(e) For a neighborhood with x = 19% change in populationin the past few years, predict the change in the crime rate (per1000 residents). (Round your answer to one decimal place.)
crimes per 1000 residents

(f) Find S_e. (Round your answer to threedecimal places.)
S_e =

(g) Find a 95% confidence interval for the change in crime ratewhen the percentage change in population is x = 19%.(Round your answers to one decimal place.)

lower limit   Â	crimes per 1000 residents
upper limit   Â	crimes per 1000 residents

(h) Test the claim that the slope β of the populationleast-squares line is not zero at the 10% level of significance.(Round your test statistic to three decimal places and yourP-value to four decimal places.)

t =
P-value =

Conclusion

Reject the null hypothesis, there is sufficient evidence thatβ differs from 0.Reject the null hypothesis, there isinsufficient evidence that β differs from0.    Fail to reject the null hypothesis, thereis sufficient evidence that β differs from 0.Fail toreject the null hypothesis, there is insufficient evidence thatβ differs from 0.

(i) Find a 95% confidence interval for β and interpret itsmeaning. (Round your answers to three decimal places.)

lower limit   Â
upper limit   Â

Interpretation

For every percentage point increase in population, the crimerate per 1,000 increases by an amount that falls within theconfidence interval.

For every percentage point increase in population, the crimerate per 1,000 increases by an amount that falls outside theconfidence interval.  

  For every percentage point decrease in population,the crime rate per 1,000 increases by an amount that falls withinthe confidence interval.

For every percentage point decrease in population, the crimerate per 1,000 increases by an amount that falls outside theconfidence interval.