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# Questions tagged [least-squares]

Refers to a general estimation technique that selects the parameter value to minimize the squared difference between two quantities, such as the observed value of a variable, and the expected value of that observation conditioned on the parameter value. Gaussian linear models are fit by least squares and least squares is the idea underlying the use of mean-squared-error (MSE) as a way of evaluating an estimator.

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### Linear regression prediction interval

If the best linear approximation (using least squares) of my data points is the line $y=mx+b$, how can I calculate the approximation error? If I compute standard deviation of differences between ...
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### Regression when the OLS residuals are not normally distributed

There are several threads on this site discussing how to determine if the OLS residuals are asymptotically normally distributed. Another way to evaluate the normality of the residuals with R code is ...
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### OLS vs. logistic regression for exploratory analysis with a binary outcome

In the idealized logistic model, we obtain an S-shaped curve linking each continuous IV to the DV. But in practice this S-shape infrequently occurs, making the logistic approach seem a little less ...
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### Could logistic regression be used to detect large errors in least squares regression?

I have the following linear model: $$w^*=\text{arg min}_w\sum_{i=1}^N \bigg(Y_i-\sum_{j=1}^M X_{i,j}\times w_j\bigg)^2$$ Let $T \in N^*$ and $e_i=|Y_i-\sum_{j=1}^M X_{i,j}\times w_j|$. It's ...
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### Standard errors in weighted least squares

My data is a panel of countries by year. Suppose my main RHS variable is a country's GDP and my main LHS variable classifies countries by whether the country is a democracy. Is it desirably to ...
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### MLE vs least squares in fitting probability distributions

The impression that I got, based on several papers, books and articles that I've read, is that the recommended way of fitting a probability distribution on a set of data is by using maximum likelihood ...
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### Does including both raw and per capita measures as predictors reduce significance of either predictor?

I'm running a regression on independent variables, some of which are measured in different units, for example: The amount of broadband connections in a country The amount of broadband connections in ...
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