Timeline for Variability in the fitted values
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 5, 2021 at 8:36 | comment | added | Sergio | @InColorado: The concept has a name, and it is "analysis of variance". See Kutner, Nachtsheim, Neter & Li, Applied Linear Statistical Models, §2.7; Weisberg, Appplied Linear Regression, §2.6; Draper & Smith, Applied Regression Analysis, §1.3; Graybill & Iyer, Regression Analysis, §3.8 etc etc | |
| Feb 5, 2021 at 4:14 | comment | added | InColorado | @whuber, same request as above? I tried Galton per your comment but didn't yet find what I need. I understand that the basic issue is that a deterministic prediction doesn't reproduce the variability represented by each source observation's error term but my explanation isn't sufficient without citations. | |
| Feb 5, 2021 at 4:13 | comment | added | InColorado | @Sergio the only citation I've found that makes your sound argument is Farmer 2016, doi 10.1002/2016WR019129. I have looked (and looked, for hours…)! Suggestions pls? Does the concept have a name? I need cites for a skeptical reviewer for (1) the 'never can be greater' concept above, (2) if the predictions' variance IS higher than benchmark then at least one coefficient is overestimated, and (3) if the coefficient in a single-driver linear regression is misestimated by a multiplier k, then the variance of the predictions will change by a factor of k squared. | |
| Sep 14, 2020 at 16:27 | vote | accept | user149054 | ||
| Sep 13, 2020 at 8:03 | answer | added | Robert Long | timeline score: 1 | |
| Sep 12, 2020 at 15:01 | comment | added | Sergio | Variability of observed values: $\sum(y_i-\bar{y})^2$. Variability of fitted values: $\sum(\hat{y}_i-\bar{y})^2$. Variability around your model: $\sum(y_i-\hat{y})^2$. Since $$\sum(y_i-\bar{y})^2=\sum(y_i-\hat{y})^2+\sum(\hat{y}_i-\bar{y})^2$$ the variability of fitted values can never be greater than the variability of observed values, and they can be equal only if you model explains absolutely nothing. | |
| Sep 12, 2020 at 14:56 | comment | added | whuber♦ | In the 1880's, Francis Galton discovered this was a universal phenomenon. It is part of his theory of "regression to the mean." He illustrated it with his celebrated quincunx. | |
| Sep 12, 2020 at 14:34 | comment | added | user149054 | @Sergio Is it bad indication that the fitted values are not as spread as observed values? | |
| Sep 12, 2020 at 14:09 | comment | added | Sergio | That your model explains a part of the observed variability. | |
| Sep 12, 2020 at 12:44 | history | asked | user149054 | CC BY-SA 4.0 |