5 Flexible Teaching-Learning Modality emote (asynchronous) Module, exercises, problem sets, PowerPoint lessons 6 Assessment Task irection. Answer the following items. 1. The table below shows the students' involvement in community service (in hours) and their general weighted average (GWA). Community service (in General Weighted Average hours) Page 13 of 15 \( \begin{array}{ll}37 & 1.75 \\ 35 & 3.00 \\ 24 & 2.35 \\ 15 & 2.00 \\ 28 & 2.50 \\ 35 & 1.63 \\ 32 & 2.80 \\ 38 & 2.52 \\ 30 & 2.95 \\ 27 & 1.95 \\ 29 & 2.13 \\ 30 & 2.42 \\ 24 & 2.53 \\ 39 & 2.85 \\ 35 & 2.50\end{array} \) a. Compute the correlation coefficient of the two variables. b. Find the equation of the least-squares line. 7 References: Beaver, B.M. and Beaver R.J. (1999). Introduction to Probability and Statistics. \( 10^{\text {th }} \) ed. New York: Duxbury Press. Bluman, A. (1998) Elementary Statistics: A Step by Step Approach. \( 3^{\text {rd }} \) ed. McGraw-Hill Book Co. Deuna, Melecio C. (1996), Elementary Statistics for Basic Education. Quezon City: Phoenix Publishing House, Inc. ebre, F.A. and Virginia F. Cawagas (Consultant)(1987) Introduction to Statistics. Metro Manila, Pheonix Publishing House, Inc. ierguson G. (1981) Statistical Analysis in Psychology and Education. \( 5^{\text {th }} \) ed. New York: McGraw-Hill Book Company. adua, R. N., E.G. Adanza and R.T. Guinto (1986) Statistics: Theory and Applications. Metro Manila: Hermil Printing Services. Reyes, C.Z. and Saren, L.L. (2003). Metro Manila. M.G. Reprographics. Spiegel, M. and Stephens, L. (1999). Schaum's Outline Theory and
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Mean of community service hours (X): \( \bar{X} = \frac{37 + 35 + 24 + 15 + 28 + 35 + 32 + 38 + 30 + 27 + 29 + 30 + 24 + 39 + 35}{15} = \frac{442}{15} = 29.47 \) Mean of GWA (Y): \( \bar{Y} = \frac{1.75 + 3.00 + 2.35 + 2.00 + 2.50 + 1.63 + 2.80 + 2.52 + 2.95 + Show more…
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For Problems $7-18$, 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 $\sum x y$ 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 $y$ : $$ \begin{array}{l|lrrrrr} \hline x & 24.2 & 19.0 & 18.2 & 14.9 & 19.0 & 17.5 \\ \hline y & 13.0 & 4.4 & 9.3 & 1.3 & 0.8 & 3.6 \\ \hline \end{array} $$ 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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