The number of newly reported crime cases in a county in New York State is shown in the accompanying table,...

Question

The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 2011, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the calendar year in which the number of new cases would reach 1230.

SnapAndSolve AI · Accepted Answer

To find the linear regression equation, we first calculate the slope (m) and y-intercept (b) using the given data points: (0, 911), (1, 907), (2, 915), and (3, 981).

Calculate the slope (m):
m = (mean of x * mean of y - mean of xy) / (mean of x^2 - (mean of x)^2)
Using the data points:
mean of x = (0 + 1 + 2 + 3) / 4 = 1.5
mean of y = (911 + 907 + 915 + 981) / 4 = 928.5
mean of xy = (0*911 + 1*907 + 2*915 + 3*981) / 4 = 2265.5
mean of x^2 = (0^2 + 1^2 + 2^2 + 3^2) / 4 = 2.5
m = (1.5 * 928.5 - 2265.5) / (2.5 - 1.5)
m = (1392.75 - 2265.5) / 1
m = 73.75
Calculate the y-intercept (b):
b = mean of y - m * mean of x
b = 928.5 - 73.75 * 1.5
b = 928.5 - 110.625
b = 817.875
Therefore, the linear regression equation is:
y = 73.75x + 817.88
To estimate the year when the number of new cases reaches 1230:
1230 = 73.75x + 817.88
73.75x = 1230 - 817.88
73.75x = 412.12
x = 412.12 / 73.75
x ≈ 5.59
Since x represents years since 2011, the estimated calendar year is:
2011 + 6 = 2017

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The number of newly reported crime cases in a county in New York State is shown in the accompanying table,...

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