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 2000, and y represents number of new cases. write the linear regression equation that represents this set of dat rounding all coefficients to the nearest tenth. using this equation, find the projected number of new cases for 2008, rounded to the nearest whole number. years since 2000 (x) new cases (y) 0 998 1 1047 2 1106 3 1084 copy values for calculator open statistics calculator answer attempt 3 out of 3 regression equation: final answer: submit answer

Explanation:

Step1: Input data into calculator

Input the \(x\) - values (\(0,1,2,3\)) and \(y\) - values (\(998,1047,1106,1084\)) into a statistics calculator.

Step2: Find the linear regression equation

Using the linear regression function on the calculator, we get the equation \(y = 25.5x+994.3\) (rounded to the nearest tenth).

Step3: Find \(x\) for 2008

Since \(x\) represents the number of years since 2000, for 2008, \(x = 2008 - 2000=8\).

Step4: Substitute \(x = 8\) into the equation

Substitute \(x = 8\) into \(y = 25.5x+994.3\). So \(y=25.5\times8 + 994.3\).
First, calculate \(25.5\times8=204\). Then \(y=204 + 994.3=1198.3\).

Answer:

Regression Equation: \(y = 25.5x + 994.3\)
Final Answer: \(1198\)