Question

The following table gives the gold medal times for every other Summer Olympics for the women's 100 meter freestyle (swimming).

Year	Time (seconds)
1912	82.2
1924	72.4
1932	66.8
1952	66.8
1960	61.2
1968	60.0
1976	55.65
1984	55.92
1992	54.64
2000	53.8
2008	53.1

d) Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. (Round your answers to three decimal places.)

ŷ =____+____x

e) Find the correlation coefficient r. (Round your answer to four decimal places.)

r = ______

f) Find the estimated gold medal time for 1924. (Use your equation from part (d). Round your answer to two decimal places.)

_____ sec

Find the estimated gold medal time for 1992. (Use your equation from part (d). Round your answer to two decimal places.)

_____ sec

i) Use the least squares line to estimate the gold medal time for the 2012 Summer Olympics. (Use your equation from part (d). Round your answer to two decimal places.)

_____ sec

Answer 1

d) from above y^ =603.430+(-0.276)*x

e)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

-0.9512

f)

for x=1924

predicted value=603.43+1924*-0.276=

72.41

for x =1992

predicted value=603.43+1992*-0.276=

53.64

i)

for x =2012:

predicted val=603.43+2012*-0.276=

48.12