University Of Georgia > Math, Statistics and Probability - STAT 6320 > Week 8 Exam Guide + Explanations (2019/2020) - Already Graded A+

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Question 1) Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth ... (in kilometers) of the quake below the surface at the epicenter. x 2.9 4.7 3.3 4.5 2.6 3.2 3.4 y 4.6 10.3 11.2 10.0 7.9 3.9 5.5 (b) Use a calculator to verify that Σx = 24.6, Σx2 = 90.20, Σy = 53.4, Σy2 = 460.56 and Σxy = 195.43. Compute r. (Round to 3 decimal places.) 2) In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player, and let y represent the player's home run percentage (number of home runs per 100 times at bat). A random sample of n = 7 professional baseball players gave the following information. x 0.251 0.251 0.286 0.263 0.268 0.339 0.299 y 1.2 3.7 5.5 3.8 3.5 7.3 5.0 b) Use a calculator to verify that Σx = 1.957, Σx2 = 0.553, Σy = 30.0, Σy2 = 150.36 and Σxy = 8.710. Compute r. (Round to 3 decimal places.) 3- You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms). x 3 4 8 16 26 36 y 43 46 75 100 150 200 Complete parts (a) through (e), given Σx = 93, Σy = 614, Σx2 = 2317, Σy2 = 82,090, Σxy = 13,613, and r ≈ 0.998. (a) Draw a scatter diagram displaying the data. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = ________ y = _______ y ^ = _______ + ________ x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. (e) Find the value of the coefficient of determination r2. 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? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.) r2 = explained % unexplained % (f) The calves you want to buy are 22 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.) ________ kg _______________________________________________________________________________________________________________________________________ 2- In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player, and let y represent the player's home run percentage (number of home runs per 100 times at bat). A random sample of n = 7 professional baseball players gave the following information. x 0.235 0.259 0.286 0.263 0.268 0.339 0.299 y 1.4 3.1 5.5 3.8 3.5 7.3 5.0 (a) Make a scatter diagram of the data. Then visualize the line you think best fits the data. (b) Use a calculator to verify that Σx = 1.949, Σx2 = 0.549, Σy = 29.6, Σy2 = 146.80 and Σxy = 8.612. Compute r. (Round to 3 decimal places.) _______ As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer. • Given our value of r, y should tend to increase as x increases. • Given our value of r, y should tend to remain constant as x increases. • Given our value of r, we can not draw any conclusions for the behavior of y as x increases. • Given our value of r, y should tend to decrease as x increases. [Show More]

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