Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon 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 (°F).
Extracted text: Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon 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 (°F). 19.2 15.0 20.4 17.8 16.5 15.5 14.7 17.1 y 87.8 73.4 93.1 84.7 82.2 75.2 69.7 82.0 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 n USE SALT Complete parts (a) through (e), given Ex = 247.4, Ey = 1203.4, Ex² = 4120.44, Ey² = 97,136.54, Exy = 19,983.11, and rx 0.8778. (a) Draw a scatter diagram displaying the data. Graph Layers 100 Clear All After you add an object to the graph you 96 Delete can use Graph Layers to view and edit its properties. 90 Fill 85 80 No Solution 75 70 66 O Help 13 14 15 16 19 20 21 17 18 22 WebAssign. Graphing Tool
Extracted text: (b) Verify the given sums Ex, Ey, Ex2, Ey2, Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex = Ey = Ex2 - Ey2 - Exy = (c) Find x, and y. Then find the equation of the least-squares line ý = a + bx. (Round your answer to four decimal places.) x = y = (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y y 120 120 100 100 80 80 60 60 40 40 20 20 5 10 15 20 5 10 15 20 120 120 100 100 80 80 60 60 40 40 20 20 5 10 15 20 5 10 15 20 (e) Find the value of the coefficient of determination 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? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal place.) 2 = explained % unexplained (f) What is the predicted temperature hen x = 17.8 chirps per second? (Round your answer to two decimal places.) oF