At a meeting of the International Astronomical Union (IAE) in Prague in 2006, Pluto was determined not to be a planet, but rather the largest member of the Kuiper belt of icy objects. Let's examine the

relationship between the distance from the sun for the 9 sun-orbiting objects (including Pluto) and their length of years (earth years) for one complete orbit around the sun.

Distance the distance from the sun is in millions of miles and

length is the length of a year in earth years.) Use these data to answer the following questions:

1. Describe the relationship between these two variables.

2.Include the properly labeled scatterplot here that best straightens the relationship between the two variables here. (That is, if transforming only the response variable straightens the relationship, include that scatterplot here. If transforming both variables best straightens the relationship, include that scatterplot here.

3.Write the least-squares regression equation from the model that best straightens the relationship. Don't forget to define the terms in the equation.

4. It has been suggested that the asteroid belt between Mars and Jupiter may be the remnants of a failed planet. Suppose that failed planet was 400 million miles from the sun. Predict its length of year (in earth years) using the best-fitting model. Show work

DATA

planet position distance length

Mercury 1 36 0.24

Venus 2 67 0.61

Earth 3 93 1

Mars 4 142 1.88

Jupiter 5 484 11.86

Saturn 6 887 29.46

Uranus 7 1784 84.07

Neptune 8 2796 164.82

Pluto 9 3707 247.68