Please do the following. (a) Draw a scatter diagram...

Please do the following. (a) Draw a scatter diagram displaying the data. (b) Verify the given sums $\Sigma x, \Sigma y, \Sigma x^{2}, \Sigma y^{2},$ and $\Sigma x y$ and the value of the sample correlation coefficient $r$. (c) Find $\bar{x}, \bar{y}, a,$ and $b .$ Then find the equation of the least-squares line $\hat{y}=a+b x$. (d) Graph the least-squares line on your scatter diagram. Be sure to use the point $(\bar{x}, \bar{y})$ as one of the points on the line. (e) Interpretation Find the value of the coefficient of determination $r^{2} .$ What percentage of the variation in $y$ can be explained by the corresponding variation in $x$ and the least-squares line? What percentage is unexplained? Answers may vary slightly due to rounding. Does prison really deter violent crime? Let $x$ represent percent change in the rate of violent crime and $y$ represent percent change in the rate of imprisonment in the general U.S. population. For 7 recent years, the following data have been obtained (Source: The Crime Drop in America, edited by Blumstein and Wallman, Cambridge University Press). $$\begin{array}{c|ccccccc}\hline x & 6.1 & 5.7 & 3.9 & 5.2 & 6.2 & 6.5 & 11.1 \\\hline y & -1.4 & -4.1 & -7.0 & -4.0 & 3.6 & -0.1 & -4.4 \\\hline\end{array}$$ Complete parts (a) through (e), given $\Sigma x=44.7, \Sigma y=-17.4, \Sigma x^{2}=315.85, \Sigma y^{2}=116.1$ $\Sigma x y=-107.18,$ and $r \approx 0.084$. (f) Critical Thinking Considering the values of $r$ and $r^{2}$, does it make sense to use the least-squares line for prediction? Explain.

Please do the following.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums $\Sigma x, \Sigma y, \Sigma x^{2}, \Sigma y^{2},$ and $\Sigma x y$ and the value of the sample correlation coefficient $r$.
(c) Find $\bar{x}, \bar{y}, a,$ and $b .$ Then find the equation of the least-squares line $\hat{y}=a+b x$.
(d) Graph the least-squares line on your scatter diagram. Be sure to use the point $(\bar{x}, \bar{y})$ as one of the points on the line.
(e) Interpretation Find the value of the coefficient of determination $r^{2} .$ What percentage of the variation in $y$ can be explained by the corresponding variation in $x$ and the least-squares line? What percentage is unexplained?
Answers may vary slightly due to rounding.
Does prison really deter violent crime? Let $x$ represent percent change in the rate of violent crime and $y$ represent percent change in the rate of imprisonment in the general U.S. population. For 7 recent years, the following data have been obtained (Source: The Crime Drop in America, edited by Blumstein and Wallman, Cambridge University Press).
$$\begin{array}{c|ccccccc}\hline x & 6.1 & 5.7 & 3.9 & 5.2 & 6.2 & 6.5 & 11.1 \\\hline y & -1.4 & -4.1 & -7.0 & -4.0 & 3.6 & -0.1 & -4.4 \\\hline\end{array}$$
Complete parts (a) through (e), given $\Sigma x=44.7, \Sigma y=-17.4, \Sigma x^{2}=315.85, \Sigma y^{2}=116.1$ $\Sigma x y=-107.18,$ and $r \approx 0.084$.
(f) Critical Thinking Considering the values of $r$ and $r^{2}$, does it make sense to use the least-squares line for prediction? Explain.

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