Nonlinear regression. The following data gives the distance from the sun (in millions of miles) and the length of year (in earth years) for the traditional 9 planets in the solar systems (including pluto, which is technically a dwarf-planet as it is smaller than the dwaft-planet Eris).

Distance to the Sun 36 67 93 142 484 887 1784 2796 3666

Year (in earth-years).24 .61 1.00 1.88 11.86 29.46 84.07 164.82 247.68

a) show the scatterplot for this data with the least squares regression line. Find R^2. How much of the variation is explained by the regression line?

b)NOw fit a quadratic equation of the form y=ax^2+bx+c to the data by using the calculator and "5: QuadReg".

c)Investiage a few other regression curves:

CubicReg ExpReg PwrReg

For each, show the scatterplot with the regression curve and give R^2. Comment on which curve fits the data best.

d)Use the method of "Using least-ssquares to Fit a power Model" to manually find an equation of the form y=ax^b that models the data. Show all steps in the process. Compare your equation with those found in c).

e)Choose a regression equation to predict the length of year for a planet in the aseroid belt at 260 million miles from the sun. and "year length", which model best explain the relationship? Why is it best? Expalin your reasoning in detail. Use Kepler's third law to support your reasoning.

a