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

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}=957 + 988+1000+1106+1109 = 5160) (\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_{i}y_{i}=0\times957+1\times988 + 2\times1000+3\times1106+4\times1109=0 + 988+2000+3318+4436 = 10742)

Step2: Calculate slope (m)

The formula for the slope (m) of the regression - line is (m=\frac{n\sum_{i = 1}^{n}x_{i}y_{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}}) Substitute the values: [ \begin{align*} m&=\frac{5\times10742-10\times5160}{5\times30 - 10^{2}}\ &=\frac{53710-51600}{150 - 100}\ &=\frac{2110}{50}\ & = 42.20 \end{align*} ]

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}) Substitute (m = 42.20), (\sum_{i = 1}^{n}x_{i}=10), (\sum_{i = 1}^{n}y_{i}=5160) and (n = 5) [ \begin{align*} b&=\frac{5160-42.20\times10}{5}\ &=\frac{5160 - 422}{5}\ &=\frac{4738}{5}\ &=947.60 \end{align*} ]

The linear regression equation is (y=42.20x + 947.60)

Step4: Predict for 2014

Since (x) represents the number of years since 2004, for 2014, (x = 10) Substitute (x = 10) into the regression equation (y=42.20\times10+947.60) [ \begin{align*} y&=422+947.60\ &=1369.6\approx1370 \end{align*} ]

Answer:

Regression Equation: (y = 42.20x+947.60) Final Answer: (1370)