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.

1,629 questions
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Multicollinearity confusion

so for my master's thesis, I am examining the influence of union density (% of the workforce in a union) and top marginal tax rates on pre-tax CEO pay. These two independent variables are very highly ...
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Parameter errors in linear least squares

I would like to help my (Chemistry) students understand the math behind linear regression.(1) The generally accepted approach for my discipline is to omit any use of calculus and introduce matrix ...
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Enzyme kinetics: Bootstrapping parameter estimates

First things first - this is kind of a mixed problem from biological data analysis, I hope I am in the right place to ask my question(s). Context I have data from a fluorescence assay of binding of ...
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Correlation coefficients and range of residuals

I've generated these plots: The upper two scatter plots show linear regressions of two different combinations of three variables ($W2$, $K$ and $R$), both against $log(z)$, with their ...
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What are the advantages of a random effects model versus a pooled OLS regression with cluster–robust standard errors?

Both models allow for explanatory variables that are time-invariant. I had thought that the advantage of a random effects model might be related to the fact that random effects models mitigate ...
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Measure of error for non-linear systems?

I am trying to model a system that is ideally explained by the formula Q=Qi*(1+Di*b*t)^(-1/b), where: ...
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Confidence interval around weighted sum of regression coefficient estimates?

Let's say you have $N$ random variables $Y_i$, where $Y_i = \beta_i X + \epsilon_i$. $X$ values are the same for all $Y_i$, but the error terms have different variance. I estimate each $\beta_i$ with ...
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divergence of beta estimates between OLS and regression with ARIMA error

I have physiological time-series data: ~60k observations per channel, ~100 Hz sampling. I will model individual channels with ~20 regressors. Under OLS, given temporal autocorrelation in the data, ...
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confusion with frisch lovell type situation

Suppose I am trying to run a regression as follows: $y= a_1+ b_1*x_1 +b_2*x_2 + e_1$ To study the relation between $y$ and $x_2$ net of their correlation with $x_1$, I run the following model first: ...
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How can I find the k-nearest neighbors for a collection of linear time series data?

I need to figure out how to determine the nearest neighbors of an "optimal" line, as illustrated in a simplified figure, linked below. The blue, orange, green, and purple lines represent the best fit ...
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Interpret orthogonal design

I am dealing with orthogonal matrices in regressions, so every regressor has $x_j'x_k=0, if \ j \neq k \\ x_j'x_k=1, if \ \ j=k$ The first one told us that the correlation between two predictors ...