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Fitting Lines to Data

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Cool Blue Planet?

Can you imagine a blue planet with daytime temperatures of 2000 degrees Fahrenheit and winds howling at 4500 mph? Researchers also believe that planet HD 189733b rains molten glass!

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An international team of scientists has determined the color of an extra solar planet using the Hubble Space Telescope. Planet HD 189733b, discovered in 2005, is 63 million light-years away. It is among a class of planets called “hot Jupiters,” which orbit close to their parent stars. HD 189733b is also deep blue in color thanks to silicate droplets, which scatter blue light in its atmosphere.

The scatter plot below compares the colors of the planets in our solar system to that of HD 189733b in terms of the blue light versus the green light they reflect.

While this graph might appear to represent just a bunch of random ordered pairs, all of the planet points can actually be described by the equation of a single line. By fitting a line that comes as close to all the planet points as possible—a process known as linear regression—we can describe the data linearly. And this is exactly how researchers draw conclusions about planets.

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The line of best fit for the data has been drawn in the graph below. Using the given scale of the graph’s coordinate axes, estimate the equation of the fitted line.

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