Question

Suppose we have the following set of data points (Table 1) that describe the count rate, photons per sec, versus distance from the source. Further suppose these data points can be fit to a line with the equation Cratb(1/d2) where b is the slope and a is the y-intercept. find the slope, theerror in the slope (Th) , and relative error, ơn/b. Turn in your Excel spread sheet showing calculations and show your final answer. Finally, what are the units of b the slope? Table 1 (m2) (sec) (error) 25.0 0.2 901 30.0 0.3 11.11 443 0.45 4.94 281 16.8 0.602.78 220 14.8 0.751.78 180 13.4 1.0 1.0 154 12.4 21.0

Answer 1

Slope=30.7433 (rounded 4 decimal places)

SUMMARY OUTPUT 901 443 281 220 180 154 25 Rearession Statistics 4.94 2.78 1.78 MultipleR R Square Adjusted R Square Standard Error Observations 0.999101948 0.998204702 0.997755878 13.40200099 ANOVA I MS Significance F Regression Residual Total 1399468.3788 399468.379 2224.04267 1.20938E-06 4 718.4545217 179.61363 5 400186.8333 Coefficients Standard Errort Stat Lower 95% Upper 95% 124.342445 7.455283366 16.6784331 7.5717Е-05 103.64326 145.04163 30.743302510.651896967 47.1597569 1.2094E-06 28.93334637 32.5532587 P-value Intercept X Variable 1

$\sigma_b=0.6519~(rounded~4~decimal~places)\\ Relative~error=\sigma_b/b=0.6519/30.7433=0.0212~(rounded~4~decimal~places)\\ Since~b=\frac{Cov(C_i,1/d_i^2)}{Var(1/d_i^2)}~hence~unit~is~sec^{-1}*m^{-2}/m^{-4}=sec^{-1}m^{2}$