The time it takes for a planet to complete its orbit around the sun is called the planet's sidereal year. Johann Kepler studied the relation between the sidereal year of a planet and its distance from the sun in 1618. The following data show the distances that the planets are from the sun and their sidereal years.

(a) Determine the least-squares regression equation, treating distance from the sun as the explanatory variable.
(b) A normal probability plot of the residuals indicates that the residuals are approximately normally distributed. Test whether a linear relation exists between distance from the sun and sidereal year.
(c) Draw a scatter diagram, treating distance from the sun as the explanatory variable.
(d) Plot the residuals against the explanatory variable, distance from the sun.
(e) Does a linear model seem appropriate based on the scatter diagram and residual plot?
(f) What is the moral?

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