Timeline for R-squared result in linear regression and "unexplained variance"
Current License: CC BY-SA 2.5
10 events
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| Jan 10, 2011 at 13:29 | comment | added | Wayne | @Carcal: I think your point B is pretty important: the distinction between $\hat{Y}$ versus $Y$. I'm wanting to compare $\sum_t{b_i} p_{it}$ to $\sum_{t=1}^n{\sum_i{b_i p_{it}}} + n a$ where the intercept is $a$ and predictor $i$ at time $t$ is $p_{it}$. Not comparing coefficients, but rather how much that predictor contributed to the sum. Does that make sense? | |
| Jan 10, 2011 at 12:52 | vote | accept | Wayne | ||
| Jan 10, 2011 at 9:25 | comment | added | caracal |
@Wayne You need to calculate the semi-partial correlation between your DV elec and each of your predictors. Taking the coefficients as a measure of "influence" doesn't seem like a good idea to me: a) the coefficients are scale dependend b) for a coefficient $b_{i}$, it is $\hat{Y}$ that changes by $b_{i}$ units when predictor $i$ changes 1 unit, not $Y$ itself. Before delving further into regression theory, I'd take the increase in $R^{2}$ as a measure for the improvement in prediction wenn adding a predictor.
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| Jan 9, 2011 at 23:17 | comment | added | Wayne | One more question: this illustrates how each predictor contributes to the R-squared "variance accounted for". Is it legitimate to use the coefficients & intercept as I mentioned (in the edited version of) the original posting, to talk about each component's contribution to a yearly total? If so, how do you see the R-squared playing into this? | |
| Jan 9, 2011 at 21:17 | comment | added | chl | (+1) A nice step-by-step illustration. | |
| Jan 9, 2011 at 6:25 | comment | added | Wayne | OK, I have two predictors (hdd and cdd), and the squared semi-partial correlations for cdd ~ hdd is 0.755, and for hdd ~ cdd is 0.055, for a total of 0.810 versus the R-squared of 0.845. | |
| Jan 9, 2011 at 5:28 | vote | accept | Wayne | ||
| Jan 9, 2011 at 6:25 | |||||
| Jan 8, 2011 at 22:10 | history | edited | caracal | CC BY-SA 2.5 |
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| Jan 8, 2011 at 21:11 | history | edited | caracal | CC BY-SA 2.5 |
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| Jan 8, 2011 at 20:05 | history | answered | caracal | CC BY-SA 2.5 |