12
votes
Accepted
Model reduction in linear regression by stepwise elimination of predictors with "non-significant" coefficients
This procedure looks like standard backward elimination based on p-values except for the "smallest absolute value" selection, which only makes sense if predictors are standardised. The major ...
- 26.8k
11
votes
Accepted
Assumptions of Linear Regression (homoscedasticity and normality of residuals)
The questions themselves are interesting and nontrivial enough that I believe you may have some basic knowledge about assumption testing already, so I'm not telling you what to do in particular (for ...
- 26.8k
5
votes
Accepted
What I have to do more to improve my regression model in r
First off, the transformation of the dependent variable is just odd. I'm guessing there is no way to meaningfully interpret the dependent variable if it is converted in this fashion, and its not clear ...
- 16.2k
3
votes
Accepted
Deriving MSE($\hat{\beta}$) under Linear regression
This uses a decomposition of the expected value of the squared-norm
This MSE result is a particular application of a decomposition of the expected value of the squared-norm of a random vector. Start ...
- 130k
2
votes
Standardized regression coefficient
The standardized coefficient can be higher than 1, or lower than -1.
It's nothing to do with whether some of the variance in Y is still explained by the other predictors. It typically happens in the ...
- 18.6k
2
votes
Deriving MSE($\hat{\beta}$) under Linear regression
When the parameter $\boldsymbol \theta\in\mathbb R^p, $ one is supposed to work with the matrix-valued squared error loss function $$\mathrm L(\boldsymbol \theta,\delta(\mathbf X))=(\delta(\mathbf X)- ...
- 9,597
2
votes
Does ceiling effect of outcome variable violate linearity assumption of linear regression
Those values at the ceiling represent a lower limit to the true outcome values. The technical term for that is right censoring. Linearity of response and normality of errors around predictions from a ...
- 97.9k
2
votes
Statistical models with values in non-freely generated R-modules
The definitions are a bit weird (e.g. no reason for observations to be real numbers, you'd typically speak of likelihood rather than error), but I think there are some real-world examples where the ...
- 2,974
2
votes
Multiple regression correlated predictors
Unfortunately, the short answer is no. The point of multicollinearity is that when two variables are strongly correlated, you have little information with which to differentiate them. As a result, ...
1
vote
Accepted
Sequential sum of squares with svd
There is no easy way to get this from SVD. This is because Cholesky and QR decompositions are directly connected to the columns of the original $\mathbf{X}$ matrix, in the sense that if we take the ...
- 126
1
vote
How to visualise the value of one predictor in a multiple linear regression
Well, start by looking at your model summary if you are using R: summary(mod)
You should see a column "Estimate" and you can look at the value of the ...
- 343
1
vote
Why estimates of data via residuals has 50/50 effect on significance compared to original data?
I'll focus on the second model with fixed coefficients. In that case, it's because the estimate of I based on the residuals of ...
- 97.9k
1
vote
Accepted
Assumptions of linear regression, when its results are input for a ranking based algorithm
The usual p-values for a linear regression are based on assumptions that the model is correctly specified and that the residual errors are uncorrelated and normally distributed, with zero mean and ...
- 97.9k
1
vote
How to prove an OLS estimator is inconsistent under simultaneity
Note that $Y_i = X_i - Z_i$ gives
\begin{align}
&X_i - Z_i = \beta_0 + \beta_1 X_i + \epsilon_i \\
\iff &(1 - \beta_1) X_i = \beta_0 + Z_i + \epsilon_i \\
\overset{\beta_1 \neq 1}{\iff} &...
- 6,355
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