Question

An amateur astronomer is researching statistical properties of known stars using a variety of databases. They collect the absolute magnitude or MV and stellar mass or M⊙ for 30 stars. The absolute magnitude of a star is the intensity of light that would be observed from the star at a distance of 10 parsecs from the star. This is measured in terms of a particular band of the light spectrum, indicated by the subscript letter, which in this case is V for the visual light spectrum. The scale is logarithmic and an MV that is 1 less than another comes from a star that is 10 times more luminous than the other. The stellar mass of a star is how many times the sun's mass it has. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets, rounding to two decimal places.

Absolute Magnitude V Stellar Mass

15.71 0.11

4.35 1.09

5.61 0.89

13.28 0.18

16.92 0.09

10.23 0.48

1.52 2.05

11.27 0.52

15.09 0.11

16.32 0.10

13.59 0.18

14.48 0.12

5.95 0.83

9.67 0.52

13.20 0.16

16.06 0.10

16.25 0.11

16.96 0.10

2.53 1.63

13.34 0.48

7.51 0.70

8.27 0.64

11.03 0.35

11.62 0.26

10.05 0.50

13.17 0.16

6.59 0.78

16.46 0.09

5.61 0.96

15.62 0.11

Answer #1

Using Excel, (Data -> Data Analysis -> Correlation), we get

The correlation coefficient r = -0.9312

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