Astronomy 23/223 In-Class Exercise:

Solution: How Old is our Solar System?

 X Data Xi Xi2 Y Data Yi Yi 2 Xi·Yi Sample 1 0.03298 0.001088 0.70127 0.491780 0.023128 Sample 2 0.04614 0.002129 0.70209 0.492930 0.032394 Sample 3 0.02414 0.000583 0.70060 0.490840 0.016912 Sample 4 0.17130 0.029344 0.70954 0.503447 0.121544 Sample 5 0.15250 0.023256 0.70840 0.501831 0.108031 Sample 6 0.13800 0.019044 0.70748 0.500528 0.097632 Sample 7 0.13650 0.018632 0.70758 0.500669 0.096585 Sample 8 0.12680 0.016078 0.70733 0.500316 0.089689 Sample 9 0.09050 0.008190 0.70497 0.496983 0.063800 Sample 10 0.07280 0.005300 0.70373 0.495236 0.051232 SUM 0.99166 0.123644 7.05299 4.97456 0.700948

 = 0.99166 = 7.05299 = average X = 0.099166 = average Y = 0.705299 = 0.123644 = 4.97456 = 0.700948 Now, solve either form of the following two equations, and you’ll know the equations of your line!

 slope = 0.060497 intercept = 0.6993 Equation for regression line is: Y = slope · X + intercept Y = 0.060497 X + 0.6993 Age = ln(slope+1)/1.42x10-11 Age = 4.136x109 years

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