of Pine Bluffs is considening increasing the number of police in an effort to re
ID: 379808 • Letter: O
Question
of Pine Bluffs is considening increasing the number of police in an effort to reduce crime Before making a final decision, the council asked the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information 17 Oxdord Starksille 17 Darmille Holgate Carey 25 a. Determine the standar d error of estimate. (Round your answer to 3 decimal places.) b. Determine the coeficient of determination. (Round your answer to 2 decimal places.) 0.76 c. Interpret the coefficient of determination. (Round your answer to the nearest whole number.) References eBook & Resources equation's ablity to Worksheet OVExplanation / Answer
First calculate the regression equation
a. Formula for the standard error of the estimate from a sample
Standard error of the estimate = {Sum (Y-Y’) ^2 / N-2}
Where N is number of samples = 8 (cities)
Therefore,
Standard error of the estimate = (68.48/8-2)
= 3.38
b. Coefficient of determination = 0.76
c. Percent of variation of number of crimes can be explained by variation in number of police.
City Police (x) Number of crime (Y) x - x bar y - y bar (x-xbar)*(y-ybar) (x-xbar)^2 (y-ybar)^2 1 15 17 -3.25 5.13 -16.66 10.6 26.2656 2 17 13 -1.25 1.13 -1.41 1.6 1.2656 3 25 5 6.75 -6.88 -46.41 45.6 47.2656 4 27 7 8.75 -4.88 -42.66 76.6 23.7656 5 17 7 -1.25 -4.88 6.09 1.6 23.7656 6 12 21 -6.25 9.13 -57.03 39.1 83.2656 7 11 19 -7.25 7.13 -51.66 52.6 50.7656 8 22 6 3.75 -5.88 -22.03 14.1 34.5156 Mean 18.25 11.88 x bar ybar Sum -231.75 241.50 290.88 slop b = Sum of {(x-xbar)*(y-ybar)}/ Sum of {(x-xbar)^2} -0.96 Intercept a = ybar - b * x bar 29.39 Equation Y = a + bx = 29.39-0.96*x coefficient of determination 0.76 (use excel formula: =RSQ(value of y, value of x)Related Questions
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