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 1997, 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 2009, rounded to the nearest whole number.
years since 1997 (x) new cases (y)
0 925
1 878
2 819
3 846
4 751
5 748
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answer attempt 2 out of 2
regression equation: y = 35.40x + 916.33
final answer:

Explanation:

Step1: Determine x - value for 2009

The year 2009 is \(2009 - 1997=12\) years since 1997, so \(x = 12\).

Step2: Substitute x into regression equation

The regression equation is \(y=- 35.40x + 916.33\). Substitute \(x = 12\) into it: \(y=-35.40\times12 + 916.33\).
First, calculate \(-35.40\times12=-424.8\). Then \(y=-424.8+916.33 = 491.53\).

Step3: Round the result

Rounding \(491.53\) to the nearest whole - number gives \(y = 492\).

Answer:

492