webassign.net/web/Student/Assignment-Responses/last?dep=33426111 hwoodschools.org bookmarks Classes SIS K-12360 Launch \( [-/ 22 \) Points] DETAILS MY NOTES BBUNDERSTAT12HS 9.R.010.DEFECTIVE ASK YOUR TEACHER Let \( x \) be a random variable representing percentage change in neighborhood population in the past few years, and let \( y \) be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information. \begin{tabular}{|c|cccccc|} \hline\( x \) & 30 & 5 & 11 & 17 & 7 & 6 \\ \hline\( y \) & 173 & 37 & 132 & 127 & 69 & 53 \\ \hline \end{tabular} In this setting we have \( \Sigma x=76, \Sigma y=591, \Sigma x^{2}=1420, \Sigma y^{2}=72,421 \), and \( \Sigma x y=9787 \). (a) Find \( \bar{x}, \bar{y}, b \), and the equation of the least-squares line. (Round your answers for \( \bar{x} \) and \( \bar{y} \) to two decimal places. Round your least-squares estimates to four decimal places.) \[ \begin{array}{l} \bar{x}=\square \\ \bar{y}=\square+\square \\ b=\square \\ \hat{y}=\square \end{array} \] (b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point \( (\bar{x}, \bar{y}) \). Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties.
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Given \(\Sigma x = 76\) and \(\Sigma y = 591\), and knowing there are 6 observations: \[ \bar{x} = \frac{\Sigma x}{6} = \frac{76}{6} \approx 12.67 \] \[ \bar{y} = \frac{\Sigma y}{6} = \frac{591}{6} \approx 98.50 \] Show more…
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Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information. x 28 3 11 17 7 6 y 172 36 132 127 69 53 Σx = 72; Σy = 589; Σx2 = 1,288; Σy2 = 72,003; Σxy = 9,336 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. (c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) % (d) For a neighborhood with x = 21% change in population in the past few years, predict the change in the crime rate (per 1000 residents). (Round your answer to one decimal place.) crimes per 1000 residents
Ivan K.
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). 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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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. Education: Violent Crime The following data are based on information from the book Life in America's Small Cities (by G. S. Thomas, Prometheus Books). Let $x$ be the percentage of $16-$ to 19 -year-olds not in school and not high school graduates. Let $y$ be the reported violent crimes per 1000 residents. Six small cities in Arkansas (Blytheville, El Dorado, Hot Springs, Jonesboro, Rogers, and Russellville) reported the following information about $x$ and $y:$ Complete parts (a) through (e), given $\Sigma x=112.8, \Sigma y=32.4$ $\Sigma x^{2}=2167.14, \Sigma y^{2}=290.14, \Sigma x y=665.03,$ and $r \approx 0.764$ (f) If the percentage of $16-$ to 19 -year-olds not in school and not graduates reaches $24 \%$ in a similar city, what is the predicted rate of violent crimes per 1000 residents?
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