# 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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### Regression equation passing through the origin

I'm going through Multiple Choice Questions of Basic Econometrics by Gujarati. There is a question which states that: It is a simple two-variable regression: Any regression equation written in its ...
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### OLS R-Squared Drops by 15% When Constant / Intercept is Removed?

I ran an Ordinary Least Squares model and found the constant / intercept is the more significant than all the other features. When constant is included, the R-squared is 45%, when I remove the ...
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### R/S-Analysis: Hurst Coefficient Using Least Squares Method

The application I am working on (it is an image processing program) needs to calculate, given an m-by-m matrix of integers, the so-called Hurst coefficient for that matrix, considering it as a time-...
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### Role of random sample assumption in consistency of OLS estimator

I guess in part what this all amounts to is what does the assumption {(x_i,y_i) : i=1,2,...,n} being i.i.d. imply about the i.i.d-ness of functions of it? I am confused because for example I have ...
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### Measurement error in one regressor amongst k regressors

Above I have set out the assumptions and a true claim made by Wooldridge (2002). I am having trouble proving that claim and was wondering if anyone could provide a step-by-step solution of the claim. ...
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### In LLSE $e_i$ are orthogonal random variables

If we have a sequence of zero-mean random variables $(y_0,y_1,...,y_{i-1})$ and $$e_i =y_i-\hat{y}_{i|i-1},\ \ \&\ \ \ \hat{y}_{0|-1}=0$$ $\hat{y}_{i|i-1}=$ LLSE (Linear least square estimate) ...
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### Linear Least square estimate of $x^3$ given $x$ and the moments

I have been struggling to find a direction on how to proceed with the following problem. Given that $x$ is a zero mean (non-Gaussian) random variable with moments E$(x^n)=\mu_n$. I need to find the ...
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### Calculation of intercept in multiple linear regression (OLS)

While researching OLS, I found out the equation to calculate coefficients as: $$\beta = (X^\top X)^{-1}X^\top y$$ (Ref: https://en.wikipedia.org/wiki/Linear_least_squares) However it does not ...
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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 ...
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 ...