Question 3: (Minitab or Excel – Excel is easiest) The table below shows the average distance...

Question 3: (Minitab or Excel – Excel is easiest)

The table below shows the average distance of each of the nine planets from the sun, and the length of the year (in earth years). Note that Pluto is not considered a planet anymore (check it out on Wikipedia).

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 the Distance from the Sun (the explanatory variable). Describe the scatterplot.

b) Fit a linear model that will help predict the Length of Year a planet from its Distance from the Sun. Does the model provide a good 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 improve the model by re-expressing both distance and length of year in the logarithmic scale. This approach is indicated by the large amount of variance in both variables as well as strong positive skewness of their distributions (you can check both of these facts for yourself by making stemand-leaf plots and obtaining summary statistics—no need to include this step in your paper).

d) Take the base ten logarithm of the distance and length of year variables. We will refer to the new variable as the Log(distance) and Log(length). Follow the Minitab directions below on how to proceed.

e) Fit a regression line to predict Log(length) from Log(distance).

f) Obtain the residual plot for the model.

g) Did we improve the model?

Solutions

Expert Solution

orchestra answered 1 year ago

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