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 2006, and y represents number of new cases. write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. using this equation, find the projected number of new cases for 2014, rounded to the nearest whole number.

years since 2006 (x)	new cases (y)
1	825
2	855
3	806

answer attempt 1 out of 2

regression equation: y = - 8.1x + 844.4

final answer:

Explanation:

Step1: Determine x - value for 2014

Since x represents years since 2006, for 2014, $x=2014 - 2006=8$.

Step2: Substitute x into regression equation

The regression equation is $y=-8.1x + 844.4$. Substitute $x = 8$ into it: $y=-8.1\times8+844.4$.
First, calculate $-8.1\times8=-64.8$. Then, $y=-64.8 + 844.4$.
$y=779.6$.

Step3: Round to nearest whole number

Rounding 779.6 to the nearest whole number gives 780.

Answer:

780