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 2002, 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 2011, rounded to the nearest whole number. years since 2002 (x) new cases (y) 0 1130 1 1172 2 1180 3 1279 4 1275 answer regression equation: final answer:

Explanation:

Step1: Enter data into calculator

Use a graphing calculator or statistical software. Enter the \(x\) - values (\(0,1,2,3,4\)) and \(y\) - values (\(1130,1172,1180,1279,1275\)).

Step2: Calculate linear regression

On a TI - 84 Plus (for example), go to STAT > CALC > LinReg(a + bx) (or LinReg(ax + b) depending on the calculator model). The calculator will output the values of \(a\) (the \(y\) - intercept) and \(b\) (the slope).
For the given data, \(a\approx1123.77\) and \(b\approx37.03\). So the linear regression equation is \(y = 37.03x+1123.77\).

Step3: Find \(x\) for 2011

Since \(x\) represents the number of years since 2002, for 2011, \(x = 2011 - 2002=9\).
Substitute \(x = 9\) into the equation \(y=37.03x + 1123.77\).
\(y=37.03\times9+1123.77\)
\(y = 333.27+1123.77\)
\(y=1457.04\approx1457\)

Answer:

Regression Equation: \(y = 37.03x+1123.77\)
Final Answer: \(1457\)