Question 3: (Minitab or Excel – Excel is easiest)
The table below shows the average distance of each of the nineplanets from the sun, and the length of the year (in earth years).Note that Pluto is not considered a planet anymore (check it out onWikipedia).
| Number | Position | Distance from Sun (million miles) | Length of Year in earth years | |
| Mercury | 1 | 36 | 0.24 | |
| Venus | 2 | 67 | 0.61 | |
| Earth | 3 | 93 | 1 | |
| Mars | 4 | 142 | 1.88 | |
| Jupiter | 5 | 484 | 11.86 | |
| Saturn | 6 | 887 | 29.46 | |
| Uranus | 7 | 1784 | 84.07 | |
| Neptune | 8 | 2798 | 164.82 | |
| Pluto | 9 | 3666 | 247.68 | |
a) Plot the Length of the Year (the response) versus theDistance from the Sun (the explanatory variable). Describe thescatterplot.
b) Fit a linear model that will help predict the Length of Yeara planet from its Distance from the Sun. Does the model provide agood fit?
c) Produce the residual plot for the model you developed in 3b.The plot shows a clear trend. Describe it. We are going to improvethe model by re-expressing both distance and length of year in thelogarithmic scale. This approach is indicated by the large amountof variance in both variables as well as strong positive skewnessof their distributions (you can check both of these facts foryourself by making stemand-leaf plots and obtaining summarystatistics—no need to include this step in your paper).
d) Take the base ten logarithm of the distance and length ofyear variables. We will refer to the new variable as theLog(distance) and Log(length). Follow the Minitab directions belowon how to proceed.
e) Fit a regression line to predict Log(length) fromLog(distance).
f) Obtain the residual plot for the model.
g) Did we improve the model?
