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# Tag Info

## New answers tagged least-squares

1 vote

### Different Transformation of the same IV

I agree with everything Nick said here (except that I still use "independent variable"). I'd just add that, unless you have strong substantive reasons for your somewhat unusual choice, then ...
• 125k
2 votes

### Different Transformation of the same IV

Naturally it's possible. You did it. Your question is presumably whether it's a good idea. Question in turn: Why did you choose different transformations in different models? There are many myths ...
• 58.6k
0 votes

### Help clarify the implication of normality in an Ordinary Least Square (OLS) Regression

The original claim probably implied or mentioned elsewhere that the conditional distributions have constant variance. However, without that assumption, the claim is false, as the below simulation ...
• 65k
0 votes

### OLS vs MLE when errors are not normally distributed (Laplace distributed)

OLS is BLUE regardless of the distribution of the errors, as long as they have a finite variance. However, the "Best" in BLUE refers to a specific criterion: variance, or, equivalently in ...
• 40.5k
8 votes

### A model suffering from omitted variable bias can be said to be unidentified?

From the tag: A model is identifiable if a single set of parameters can be found that will yield the best fit. Unidentifiability is typically used to mean the model can't uniquely assign values to ...
• 12.9k
2 votes

### Deriving $k_i$ for $\hat{\beta} = \sum_{i=1}^n k_i y_i$ where $\hat{\beta}$ is the OLS -estimator

Thank you all for the answers! I've come up with a derivation in scalar form after many trials and errors and decide to post my own attempt here. Now that I'm not entirely sure of my solution and I'm ...
4 votes
Accepted

### Deriving $k_i$ for $\hat{\beta} = \sum_{i=1}^n k_i y_i$ where $\hat{\beta}$ is the OLS -estimator

Using the vector approach in the linked question and answer, we can derive a general result for multiple linear regression and then derive the special case of interest for simple linear regression. ...
• 129k
2 votes

### Deriving $k_i$ for $\hat{\beta} = \sum_{i=1}^n k_i y_i$ where $\hat{\beta}$ is the OLS -estimator

I am not going to engage in vectorial arguments for they are already stated in other answers and primarily due to the fact that what OP asked warrants a simpler treatment. C&B offers a ...
• 9,427
2 votes

• 305
10 votes

### What does it mean for observations to be uncorrelated and have constant variance?

Random variables VS observations. Strictly speaking, there are random variables (which take values in $\mathbb{R}$) and realizations of these random variables (which are elements of $\mathbb{R}$). ...
• 431
0 votes

### Kalman Filter to minimize weighted errors on the states: what's wrong with my derivation

TL;DR: I think the mistake lies in the incorrect assumption that the weighting matrix $\Omega$ can be factored out and canceled in the optimisation. Rather, it should show how the weights directly ...
• 64.1k

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