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I am not sure if I am doing this problem correctly. I have to use simple linear regression to either prove or disprove the Big Bang Theory (Y = TX), using the data, I fit a regression line without an intercept term and found a 95% confidence interval of (.00152641, .002131719) for the slope. For the model, I let x = recession velocity (km/sec) and y = distance between earth and some nebula (in megaparsecs). The question is asking me what the units of measure are on B1, and I am having trouble on figuring out how to convert these numbers into years to determine what the age of the universe is.

bob jones
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  • The units of slope are units of y divided by units of x. So in your case, this would be Mpc/(km/sec). Google conversion between Mpc and km and between seconds and years and simplify. – Golden_Ratio Feb 04 '22 at 00:32
  • Ok should I plugged those values in and got the interval to be converted to about 1.4 billion to 2.2 billion. Since the Big Bang Theory suggests that the age of the universe is 13 billion years old, does this disprove the theory in the case of the problem? – bob jones Feb 04 '22 at 00:49
  • The Big Bang model is about an expanding universe, but does not think that expansion was linear, so linear regression is unlike to prove or disprove it – Henry Feb 04 '22 at 00:59
  • You may also want to report the median of all ratios Yi/Xi which is a robust estimate of the slope. You may wish to add an intercept term and argue you have a linear approximation to a non-linear process. – AJKOER Feb 04 '22 at 01:36
  • @Henry I suspect what OP means is examining Hubble's law https://en.wikipedia.org/wiki/Hubble%27s_law – Golden_Ratio Feb 04 '22 at 04:18
  • @AJKOER if it's Hubble's law, there's no intercept term – Golden_Ratio Feb 04 '22 at 04:19
  • @bobjones Fitting data to Hubble's law would have recessional velocity as the y variable. Any particular reason you chose y to be distance? – Golden_Ratio Feb 04 '22 at 04:23

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