The time it takes for a planet to complete its orbit around the sun is called the planet's sidereal year. In 1618, Johannes Kepler discovered that the sidereal year of a planet is related to the distance the planet is from the sun. The following data show the distances of the planets, and the dwarf planet Pluto, from the sun and their sidereal years.

(a) Draw a scatter diagram of the data treating distance from the sun as the explanatory variable.
(b) Determine the correlation between distance and sidereal year. Does this imply a linear relation between distance and sidereal year?
(c) Compute the least-squares regression line.
(d) Plot the residuals against the distance from the sun.
(e) Do you think the least-squares regression line is a good model? Why?

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Planet Distance from Sun, r (millions of miles) Sidereal Year, y Mercury 36 0.24 Venus 67 0.62 93 Earth 1.00 Mars 142 1.88 Jupiter 483 11.9 Saturn 887 29.5 1785 84.0 Uranus Neptune 2797 165.0 Pluto 3675 248.0