Questions 1 through 6 work with the length of the sidereal year vs. distance from the sun. The table of data is shown below.
Planet |
Distance from Sun |
Years (as a |
ln(Dist) |
ln(Year) |
Mercury |
36.19 |
0.2410 |
3.5889 |
-1.4229 |
Venus |
67.63 |
0.6156 |
4.2140 |
-0.4851 |
Earth |
93.50 |
1.0007 |
4.5380 |
0.0007 |
Mars |
142.46 |
1.8821 |
4.9591 |
0.6324 |
Jupiter |
486.46 |
11.8704 |
6.1871 |
2.4741 |
Saturn |
893.38 |
29.4580 |
6.7950 |
3.3830 |
Uranus |
1,794.37 |
84.0100 |
7.4924 |
4.4309 |
Neptune |
2,815.19 |
164.7800 |
7.9428 |
5.1046 |
Pluto |
3,695.95 |
248.5400 |
8.2150 |
5.5156 |
Enter the original data in L1 and L2 (that is, the Distance from the Sun and Years).
Make L3 = ln(L1) and L4 = ln(L2). Verify that this matches the columns given above. Don't worry about the small discrepancies you may find due to rounding and the number of decimal places shown on your calculator. If your results differ from the values above, double-check your original entries!
(Note that the explanatory variable is always some form of "Distance.") To get the most out of this Assignment, look at a scatterplot of each of these combinations.
Which transformation yields the highest correlation coefficient (Pearson's r)? Sketch a scatterplot of this transformation and show the least-squares line. What is the value of r and r^{2} for that transformation, and what regression equation does it yield? (3 points)
Using the equation from number 3, make a residual graph. Create a residual plot on your calculator and interpret it; you don't need to draw the plot. (Note: You'll probably need to turn off the plot in Y1 to display the scatterplot correctly.) (2 points)
. Using algebra, convert your regression equation to a power equation (show your work below). Enter this equation in Y2 (press Y= and enter the equation) and make a scatterplot of L1, L2, with Y2, verifying that the power equation is a good fit for this data. Finally, summarize, in plain English, what you've done in questions 1-4. (3 points)
As you set up your regression equation, keep in mind that the variables are ln9 and lnx .
Get Answers For Free
Most questions answered within 1 hours.