Please be very careful with the rounding and use all the decimals when needed

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

part a Multiple Choice

Decide which variable should be the independent variable and which should be the dependent variable.

a) Independent: year; Dependent: time

b) Independent: time; Dependent: year

part b

Make a Scatter plot of the data

part c Multiple Choice

Does it appear from inspection that there is a relationship between the variables? Why or why not?

a) Yes, it appears that the time decreases as the year increases.

b) No, there is no visible relationship between the variables.

part d

Calculate the least squares line. Put the equation in the form of:=a+bx.

(Round your answers to three decimal places.)

=______+______x

part e

Find the correlation coefficientr. (Round your answer to four decimal places.)

r=________

Is the decrease in times significant?

a) Yes

b) No

part f

Find the estimated gold medal time for1924. (Use your equation from part (d). Round your answer to two decimal places.)

________sec

Find the estimated gold medal time for1984. (Use your equation from part (d). Round your answer to two decimal places.)

________ sec

part j Multiple Choice

Why are the answers from part (f) different from the chart values?

a) The answers are different because the chart values are based on observations and the estimated values are based on the least squares line.

b) The answers are different because swimmers were slower years ago.

c) The answers are different because of errors in recording the swimming times.

d) The answers will be different each time you calculate a least squares line.

part h Multiple Choice

Does it appear that a line is the best way to fit the data? Why or why not?

a) A line is the best way to fit the data because the slope of the line is negative and the linear correlation is negative.

b) A line is not the best way to fit the data because it does not touch all the data points.

c) A line does appear to be the best way to fit the data because the data points follow a negative linear trend.

d) A line is the best way to fit the data because there is only one correct line that will fit a data set.

part i

Use the least squares line to estimate the gold medal time for the2012Summer Olympics. (Use your equation from part (d). Round your answer to two decimal places.)

___________sec

Do you think that your answer is reasonable? Why or why not?

a) Yes, because the estimate is positive.

b) No, because 2012 is outside the domain of the least squares line.

I know its a lot but Im very confused. Thank you for any help you can give.