question the number of newly reported crime cases in a county in new york state is shown in the accompanying…

Explanation:

Step1: Calculate sums

Let $n = 5$ (number of data - points). $\sum_{i = 1}^{n}x_i=0 + 1+2 + 3+4=10$ $\sum_{i = 1}^{n}y_i=1130 + 1172+1180+1279+1275 = 5936$ $\sum_{i = 1}^{n}x_i^2=0^2 + 1^2+2^2 + 3^2+4^2=0 + 1+4 + 9+16 = 30$ $\sum_{i = 1}^{n}x_iy_i=0\times1130+1\times1172 + 2\times1180+3\times1279+4\times1275=0 + 1172+2360+3837+5100 = 12469$

Step2: Calculate slope $m$

The formula for the slope $m$ of the regression line is $m=\frac{n\sum_{i = 1}^{n}x_iy_i-\sum_{i = 1}^{n}x_i\sum_{i = 1}^{n}y_i}{n\sum_{i = 1}^{n}x_i^2-(\sum_{i = 1}^{n}x_i)^2}$ $m=\frac{5\times12469-10\times5936}{5\times30 - 10^2}=\frac{62345-59360}{150 - 100}=\frac{2985}{50}=59.70$

Step3: Calculate y - intercept $b$

The formula for the y - intercept $b$ is $b=\frac{\sum_{i = 1}^{n}y_i-m\sum_{i = 1}^{n}x_i}{n}$ $b=\frac{5936-59.7\times10}{5}=\frac{5936 - 597}{5}=\frac{5339}{5}=1067.80$

The linear regression equation is $y = 59.70x+1067.80$

Step4: Find $x$ value for 2011

Since $x$ represents the number of years since 2002, for 2011, $x = 2011 - 2002=9$

Step5: Predict number of new cases

Substitute $x = 9$ into the regression equation: $y=59.70\times9+1067.80=537.3+1067.80 = 1605.1\approx1605$

Answer:

The linear regression equation is $y = 59.70x+1067.80$ and the projected number of new cases for 2011 is 1605.