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 1998, 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, find the projected number of new cases for 2008, rounded to the nearest whole number.

years since 1998 (x) new cases (y)
0 703
1 675
2 706
3 643
4 660
5 605

copy values for calculator
open statistics calculator

regression equation:
final answer

Explanation:

Step1: Input data into calculator

Input the \(x\) - values (\(0,1,2,3,4,5\)) and \(y\) - values (\(703,675,706,643,660,605\)) into a statistics calculator.

Step2: Find the linear regression equation

Using the linear regression function on the calculator, we get the equation \(y = - 12.89x+699.77\) (rounded to the nearest hundredth).

Step3: Find \(x\) for 2008

Since \(x\) represents the number of years since 1998, for 2008, \(x=2008 - 1998=10\).

Step4: Substitute \(x = 10\) into the equation

Substitute \(x = 10\) into \(y=-12.89x + 699.77\). So \(y=-12.89\times10+699.77\).

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Rounding \(570.87\) to the nearest whole number gives \(y = 571\).

Answer:

Regression Equation: \(y=-12.89x + 699.77\)
Projected number of new cases for 2008: \(571\)