one 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,xis a random variable representing chirps per second andyis a random variable representing temperature (F).x20.315.320.817.917.315.514.717.1y89.471.892.983.181.475.269.782.0

x15.416.215.017.216.017.014.4y69.483.379.682.680.683.576.3Complete parts (a) through (e), givenx=250.1,y=1200.8,x²=4220.07,y²=96,751.18,xy=20,174.54,andr0.867.(a) Draw a scatter diagram displaying the data.

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Submission Data

(b) Verify the given sumsx,y,x²,y²,xy, and the value of the sample correlation coefficientr. (Round your value forrto three decimal places.)x=

y=

x²=

y²=

xy=

r=

(c) Findx, andy. Then find the equation of the least-squares line=a+bx. (Round your answers forxandyto two decimal places. Round your answers foraandbto three decimal places.)x=

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 determinationr². What percentage of the variation inycan beexplainedby the corresponding variation inxand the least-squares line? What percentage isunexplained? (Round your answer forr²to three decimal places. Round your answers for the percentages to one decimal place.)r²=

explained%unexplained%

(f) What is the predicted temperature whenx=18.2chirps per second? (Round your answer to two decimal places.)

F