How is the distance from the sun for planets in our solar system related to the mean temperature of each planet? To find out, a scatterplot that relates the natural log of the distance of each planet (including Pluto) from the sun in millions of miles and the natural log of the mean planetary temperature in Kelvin was created. A graph titled l n (Temperature) versus l n (distance) has l n (distance) on the x-axis, and l n (temperature) on the y-axis. Points are in a line with negative slope.

A 5-column table with 2 rows. Column 1 is labeled Predictor with entries constant, l n distance. Column 2 is labeled coefficient with entries 7.9009, negative 0.4536. Column 3 is labeled S E Coefficient with entries 0.4381, 0.0706. Column 4 is labeled T with entries 18.03, negative 6.42. Column 5 is labeled P with entries 0.000, 0.004. S = 0.3446, r square = 85.5 percent, r square adjusted = 83.2 percent.

Based on the scatterplot and computer output, a reasonable estimate of mean temperature in Kelvin for Saturn, which is 886.7 million miles away from the sun is:

4.822 degrees Kelvin because ŷ = −0.4536(In 886.7) + 7.9009 = 4.822.
124.2 degrees Kelvin because and e4.822 = 124.2.
709.0 degrees Kelvin because and e6.564 = 709.0.
0.05 degrees Kelvin because and e−3.008 = 0.0494.