Final answer:
The correlation coefficient between police response time and poverty is approximately 1.654, indicating a strong positive linear relationship between the two variables. The decrease in times is not significant.
Step-by-step explanation:
The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. To find the correlation coefficient, you can use the formula:
r = (n∑xy - (∑x)(∑y)) / sqrt((n∑x^2 - (∑x)^2)(n∑y^2 - (∑y)^2))
Using the given data, we can calculate the correlation coefficient:
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- Find the sum of the products of x and y: 11*2 + 25*5 + 52*5 + 65*6 + 13 = 1235
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- Find the sum of x and y: ∑x = 11 + 25 + 52 + 65 + 13 = 166, ∑y = 2 + 5 + 5 + 6 + 13 = 31
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- Find the sum of squares of x and y: ∑x^2 = 121 + 625 + 2704 + 4225 + 169 = 7844, ∑y^2 = 4 + 25 + 25 + 36 + 169 = 259
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- Calculate n: n = 5
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- Substitute the values into the formula: r = (5*1235 - 166*31) / sqrt((5*7844 - 166^2)(5*259 - 31^2))
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- Calculate the numerator: 5*1235 - 166*31 = 6175 - 5146 = 1029
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- Calculate the denominator: sqrt((5*7844 - 166^2)(5*259 - 31^2)) = sqrt((39220 - 27556)(1295 - 961)) = sqrt(1164*334) = sqrt(388056) = 622.85
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- Calculate the correlation coefficient: r = 1029 / 622.85 ≈ 1.654
Therefore, the correlation coefficient between police response time and poverty is approximately 1.654.
The decrease in times is not significant because the correlation coefficient is positive, indicating a positive linear relationship between the two variables. A correlation coefficient of 1.654 indicates a strong positive relationship.