Timeline for How to tell if the slope of a line is 0 or there is just no relationship?
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| Dec 28, 2010 at 20:52 | comment | added | jebyrnes | Awesome, thanks, all. In summary, calculate t where $t=\frac{b1-b2}{se_{b1-b2}}$. To estimate the denominator, you can calculate this as $\sqrt{se_{b1}^2+se_{b2}^2}$. You can also use the sums of squares and a different formula if you like, but you'll get the same result. Then just pull out the df, and voila, answer. | |
| Dec 28, 2010 at 20:35 | comment | added | chl | Thanks for the clarification and added comment. I'm afraid to say that my initial ideas were not that advanced, but I definitively have to think about this last suggestion. | |
| Dec 28, 2010 at 18:53 | vote | accept | jebyrnes | ||
| Dec 28, 2010 at 18:33 | comment | added | whuber♦ | @chl You bring up an interesting question concerning equal intercepts. However, an intercept is an artifact of the origin of the x coordinate system. We can handle that problem by comparing two models in which a pair of linear splines (plus one common intercept) is nested within two slopes+two intercepts. The splines would of course have a "knot" at the transition from year 1 to year 2. Assuming the splines aren't a significantly worse fit than the bigger model, we can then test for equality of their coefficients to see whether the slope changed. | |
| Dec 28, 2010 at 18:27 | comment | added | whuber♦ | @chl I refrained from commenting on the option of computing a common slope because that implicitly assumes homoscedasticity in the combined year 1 + year 2 datasets. Given that the slope appears to have changed substantially I would want to check for a change in residual variance, which seems easiest to do by conducting a separate regression for each year--which the OP already has done. The advantage of modeling the combined datasets comes from the additional power it offers of evaluating serial correlation of the residuals. | |
| Dec 28, 2010 at 18:12 | comment | added | chl | (+1) I won't post my answer since it's basically your 2nd § (less well explained) + some digressions about an additional test for equal intercept (if we cannot reject the null for the test of the equality of slopes, compute a common slope for both regression lines and ask whether the new lines are parallel or identical)--but, it's always under the assumption that the sampled units are independent at the two time points. | |
| Dec 28, 2010 at 17:54 | history | answered | whuber♦ | CC BY-SA 2.5 |