Reference no: EM132845239
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).
x 19.8 15.0 19.4 18.3 17.9 15.5 14.7 17.1
y 88.0 73.0 94.9 85.3 82.0 75.2 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
(1) Calculate the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
r =
(2) Find the equation of the least-squares line y = a + bx. (Round your answers for a and b to three decimal places.)
y = ? + ?x
(3) 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 %
(4) What is the predicted temperature when x = 17.0 chirps per second? (Round your answer to two decimal places.)