Question

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)
1	675
2	706
3	643
4	660
5	605

answer attempt 1 out of 2
regression equation: $y=-17.09x + 708.05$
final answer:

Explanation:

Step1: Determine the value of x for 2008

The year 2008 is \(2008 - 1998=10\) years since 1998, so \(x = 10\).

Step2: Substitute x into the regression equation

We have the regression equation \(y=-17.09x + 708.05\). Substitute \(x = 10\) into it: \(y=-17.09\times10+708.05\).
First, calculate \(-17.09\times10=-170.9\). Then \(y=-170.9 + 708.05\).
\(y = 537.15\).

Step3: Round the result

Rounding \(537.15\) to the nearest whole - number gives \(y = 537\).

Answer:

537