Exercise 1.2 gives the age x1, measured in years, as well as the selling price x2, measured in thousands of dollars, for n 10 used cars. These data are reproduced as follows: 1 2 3 3 4 5 6 8 9 11 18.95 19.00 17.95 15.54 14.00 12.95 8.94 7.49 6.00 3.99 (a) Use the results of Exercise 1.2 to calculate the squared statistical distances (x, x)'S'(x, x). j = 1,2,..., 10, where x = [1,2]. - (b) Using the distances in Part a, determine the proportion of the observations falling within the estimated 50% probability contour of a bivariate normal distribution. (c) Order the distances in Part a and construct a chi-square plot. (d) Given the results in Parts b and c, are these data approximately bivariate normal? Explain.

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter1: Introduction And Vectors
Section: Chapter Questions
Problem 25P: A sidewalk is to be constructed around a swimming pool that measures (10.0 0.1) m by (17.0 0.1) m....
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Exercise 1.2 gives the age x1, measured in years, as well as the selling price x2, measured
in thousands of dollars, for n 10 used cars. These data are reproduced as follows:
1
2
3
3 4 5 6 8 9 11
18.95 19.00 17.95 15.54 14.00 12.95 8.94 7.49 6.00 3.99
(a) Use the results of Exercise 1.2 to calculate the squared statistical distances
(x, x)'S'(x, x). j = 1,2,..., 10, where x = [1,2].
-
(b) Using the distances in Part a, determine the proportion of the observations falling
within the estimated 50% probability contour of a bivariate normal distribution.
(c) Order the distances in Part a and construct a chi-square plot.
(d) Given the results in Parts b and c, are these data approximately bivariate normal?
Explain.
Transcribed Image Text:Exercise 1.2 gives the age x1, measured in years, as well as the selling price x2, measured in thousands of dollars, for n 10 used cars. These data are reproduced as follows: 1 2 3 3 4 5 6 8 9 11 18.95 19.00 17.95 15.54 14.00 12.95 8.94 7.49 6.00 3.99 (a) Use the results of Exercise 1.2 to calculate the squared statistical distances (x, x)'S'(x, x). j = 1,2,..., 10, where x = [1,2]. - (b) Using the distances in Part a, determine the proportion of the observations falling within the estimated 50% probability contour of a bivariate normal distribution. (c) Order the distances in Part a and construct a chi-square plot. (d) Given the results in Parts b and c, are these data approximately bivariate normal? Explain.
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