Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to u n was studied in detail by George W. Pierce, a physics professor at Harvard. In the following data, x is a random variable representing chirps per second and y is a random variable representing temperature (OF). * 19.1 1 17.0 19.4 18.2 2 17.6 15.5 14.7 17.1 y 87.2 72.8 91.7 82.7 82.4 69.7 82.0 x 15.4 16.2 15.0 17.2 16.0 17.0 14.4 y 69.4 83.3 79.6 82.6 80.6 83.5 76.3 LA USE SALT Complete parts (a) through (e), given Ex = 249.8, Zy = 1199, Ex = 4192.72, Zy = 96,383.22, Exy = 20,070.63, and / * 0.7748. (a) Draw a scatter diagram displaying the data. 90 19 85 18 18 17 y (temperature (in degrees Fahrenheit)) 17 y (temperature (in degrees Fahrenheit)) y (temperature (in degrees Fahrenheit)) y (temperature (in degrees Fahrenheit) 80 80 16 16 . . 75 75 15 15 70 70 15 16 17 18 10 75 80 85 15 16 17 18 19 75 80 85 90 O x (chirps per second) O x (chirps per second) x (chirps per second) x (chirps per second) b) Verify the given sums Ex, Zy, Ex", Ey , Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex ? Ey 2 EXY Find x, and y. Then find the equation of the least-squares line y = a + bx. (Round your answer to four decimal places.) * = y= 9 = (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. 90 8 18 85 y (temperature (in degrees Fahrenheit)) y (temperature (in degrees Fahrenheit)) y (temperature (in degrees Fahrenheit)) y (temperature (in degrees Fahrenheit)) 80 80 16 16 75 15 70 70 OL 75 80 85 90 15 16 17 18 19 15 16 17 18 19 75 80 85 90 x (chirps per second) O x (chirps per second) O x (chirps per second) O x (chirps per second) (e) Find the value of the coefficient of determination . 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 r to four decimal places. Round your answers for the percentages to two decimal place.)18 8 17 y (temperature (in degrees Fahrenheit)) y (temperature (in degrees Fahrenheit)) . . 80 y (temperature (in degrees Fahrenheit)) 16 y (temperature (in degrees Fahrenheit)) 16 75 - 15 75 15 85 90 19 70 75 80 16 17 18 85 06 15 x (chirps per second) - 70 75 80 x (chirps per second) 16 18 19 15 17 x (chirps per second) x (chirps per second) correlation coefficient r. (Round your value for r to four decimal places.) b) Verify the given sums Ex, Ey, Ex?, Ey?, Exy, and the value of the Ex Ey? Exy (c) Find x, and y. Then find the equation of the least-squares line y = a + bx. (Round your answer to four decimal places.) * = 9 = (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. 8 90 85 y (temperature (in degrees Fahrenheit)) y (temperature (in degrees Fahrenheit)) y (temperature (in degrees Fahrenheit) 80 y (temperature (in degrees Fahrenheit)) 75 15 16 75 75 80 85 70 19 15 16 17 18 16 17 18 19 x (chirps per second) JO 15 x (chirps per second) O 70 75 80 x (chirps per second) x (chirps per second) O explained? (Round your answer for 2 to four decimal places. Round your answers for the percentages to two decimal place.) (e) Find the value of the coefficient of determination . What percentage of the variation in y can be explained by the corresponding variation in x and the leas explained unexplained f) What is the predicted temperature when x = 17.0 chirps per second? (Round your answer to two decimal places.) Need Help? Read It