

Astronomy 23/223 InClass Exercise:
X Data
X_{i} 
X_{i}^{2} 
Y Data
Y_{i} 
Y_{i} ^{2} 
X_{i}·Y_{i} 

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 = 4.136x10^{9} years 
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