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 2.6 3.7 3.3 4.5 2.6 3.2 3.4 y 4.7 9.9 11.2 10.0 7.9 3.9 5.5 LA USE SALT (a) Make a scatter diagram of the data. Then visualize the line you think best fits the data. 10 y (depth (in kilometers)) y (depth (in kilometers) 7 3.0 3.5 4.0 4.5 30 3.5 4.0 4.5 (magnitude of an earthquake x (magnitude of an earthquake O on the Richter scale) (on the Richter scale)) 4.5 4.0 depth (in kilometers)) y (depth (in kilometers)) 53. 3.0 2.5 2.5 6 10 11 6 7 8 9 10 11 x (magnitude of an earthquake x (magnitude of an earthquake O (on the Richter scale)) (on the Richter scale)) (b) Use a calculator to verify that Ex = 23.3, Ex2 = 80.15, Zy = 53.1, Ey2 = 453.41 and Exy = 182.53. Computer. (Round your answer to four decimal places.) As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer. O Given our value of r, we can not draw any conclusions for the behavior of y as x increases. O Given our value of r, y should tend to decrease as x increases O 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. 5. [-/5.31 Points] DETAILS BBUNDERSTAT12 9.2.005.MI. MY NOTES ASK YOUR TEACHER We use the form y = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor SE COBF Constant 15.54 28.31 11 .24 0.002 Elevation -28-680 3.51 -8 . 79 0.003 S - 11.8603 R-Sq - 94.80 Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the e (a) Use the printout to write the least-squares equation. (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Round your answer to three decimal places.) (c) The printout gives the value of the coefficient of determination . What is the value of r? Be sure to give the correct sign for r based on the sign of b. (Round your answer to four decimal places.) (d) What percentage of the variation in y can be e bonding variation in x and the least-squares line? 19% What percentage is unexplained