Chapter B.2, Problem 53E

Satellite Orbits. Each issue of the magazine Ad Astra presents a list of space satellites that are launched into earth orbit during a two-month period. Also provided are the period of the satellite (time required to make one orbit of the earth), the apogee of the satellite (maximum distance from the earth), and the perigee of the satellite (minimum distance from the earth). The table below displays data on satellites placed in earth orbit from November 1998 through April, 1999 (Ad Astra, 11, Numbers 2, 3, 4). Multiple satellites placed in the same orbit during a single launch are listed as one observation only. We want to develop a second-order polynomial regression equation relating satellite period to apogee and perigee. (Readers interested in astronomy should investigate why this is an appropriate model.) Use the technology of your choice to do the following.

1. a. Obtain a scatterplot matrix for the observed values of period, apogee, and perigee. What do these plots indicate about the relationship between period and apogee? between period and perigee?
2. b. Obtain a three-dimensional scatterplot of period versus apogee and perigee. What does this plot indicate about the relationship between period and the two predictor variables apogee and perigee?
3. c. Obtain the correlation coefficients between period and the first- and second-order terms in the centered predictor variables apogee_c and perigee_c. Which terms are most highly correlated with period? What are the correlation coefficients between the first- and second-order terms? Will these correlations adversely affect the ability to assess the effect of a term in the presence of the other terms? Explain your answer.
4. d. Perform a second-order polynomial regression analysis for period using the centered predictor variables apogee_c and perigee_c. Based on the t-tests for the individual utility of each term in the model, which terms would you retain in the regression equation? Is it appropriate to use the t-tests here?

1. e. Obtain plots of residuals versus fitted values, residuals versus apogee_C, and residuals versus perigee_c, and also a normal probability plot of the residuals. Assess the appropriateness of the second-order polynomial regression equation, the assumption of constant conditional standard deviations, and the assumption of normality of the conditional distributions. Check for outliers and influential observations.
2. f. Does your analysis in part (e) reveal any violations of the assumptions for regression inferences? Explain.
3. g. Would it be appropriate to use the second-order polynomial regression equation obtained here to predict the period of the moon? Explain your answer.