Timeline for In multiple linear regression, why does a plot of predicted points not lie in a straight line?
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| S Aug 28, 2016 at 1:26 | history | bounty ended | Glen_b | ||
| S Aug 28, 2016 at 1:26 | history | notice removed | Glen_b | ||
| S Aug 25, 2016 at 4:19 | history | bounty started | Glen_b | ||
| S Aug 25, 2016 at 4:19 | history | notice added | Glen_b | Reward existing answer | |
| Sep 16, 2015 at 15:19 | history | tweeted | twitter.com/#!/StackStats/status/644168682084663296 | ||
| Sep 16, 2015 at 13:23 | comment | added | user83346 | @Klausos: if you say that there is a linear relationship between $y$ and $x_1$ that means that in the equation that defines $y$ you only find $x_1$, so no powers of it, no sinuses of it, ... just $x_1$. Similar, if you say that $y$ is linear in $\beta_1$ then in the equation for $y$ you only find only $\beta_1$ to the power $1$. | |
| Sep 16, 2015 at 12:53 | history | edited | Silverfish | CC BY-SA 3.0 |
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| Sep 16, 2015 at 12:52 | comment | added | Silverfish | Closely related question: What does linear stand for in linear regression? | |
| Sep 16, 2015 at 12:42 | vote | accept | Klausos | ||
| Sep 16, 2015 at 12:37 | comment | added | Silverfish | @klausos The relationship between $\hat y$ and $x_1$ is linear when $x_2$ is controlled for (i.e. for constant $x_2$, the relationship between $\hat y$ and $x_1$ is a straight line), which goes back to the "partialling out" thing I mentioned above. | |
| Sep 16, 2015 at 12:30 | answer | added | Silverfish | timeline score: 37 | |
| Sep 16, 2015 at 12:26 | comment | added | Klausos | @f coppens: Thanks. Then why does the literature say that a multiple linear regression model assumes linear relationships between Y and each of X (Y and X1, Y and X2)? | |
| Sep 16, 2015 at 12:20 | comment | added | Klausos | @Dawny33: posted. | |
| Sep 16, 2015 at 12:20 | comment | added | user83346 | I think the comment by @Silverfish is correct; in three dimensions $y=\beta_0+\beta_1 x_1 + \beta_2 x_2$ represents a plane $\mathcal{P}$. If you reduce to two dimensions then you 'project' the plane in three dimensions ($\mathcal{P}$) into the e.g. $(y,x_1)$ plane, this will be a line only if $\mathcal{P}$ is orthogonal to the $(y,x_1)$ plane. | |
| Sep 16, 2015 at 12:20 | history | edited | Klausos | CC BY-SA 3.0 |
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| Sep 16, 2015 at 12:05 | comment | added | Silverfish | You would only expect a line if either (i) the value of the other predictor $x_2$ is assumed to be the same for each predicted point (and if you try assuming different values of $x_2$ then you get a different line), or (ii) if you use predictions for your actual data, but "partial out" (i.e. compensate for) the variations in $x_2$, which is what a partial regression plot or added variables plot is for. Without knowing exactly how you have constructed this plot it's not possible to know what your issue is, as @dawny33 says | |
| Sep 16, 2015 at 11:57 | comment | added | Dawny33 | Can you post the code you used for the plot/analysis. The red and blue lines look like jitters of each other. So, the code behind this plot might help answer your problem better. | |
| Sep 16, 2015 at 11:50 | review | First posts | |||
| Sep 16, 2015 at 12:21 | |||||
| Sep 16, 2015 at 11:50 | history | asked | Klausos | CC BY-SA 3.0 |