# Tagged Questions

Questions on (linear or nonlinear) regression, the fitting of functions that best approximate empirical data.

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### Estimator for linear regression where data points have different variances

So in the case where data points have the same variance $\sigma^2$, the estimator (in normal equation form) can be written as $$\theta=(X^TX)^{-1}X^TY$$ I'm not sure how to derive a similar formula ...
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### When the predictor variable is so coded that $\bar X = 0$ and the normal error regression model applies, are $b_0$ and $b_1$ independent?

The Statement of the Problem: When the predictor variable is so coded that $\bar X = 0$ and the normal error regression model applies, are $b_0$ and $b_1$ independent? Are the joint confidence ...
I tried to do the F test for NLMs by myself and run into a dead-end. I have a linear model with normal distributed error $$Y = X\beta + e$$ I know that the test statistic $$F = \frac{n-r}{q}\frac{\|Q_{... 2answers 44 views ### Interpreting OLS Regression Coefficients with High Multicolinearity I am having trouble understanding the interpretation of OLS coefficients when predictors are highly correlated. My understanding of OLS coefficients is that they estimate a change in the expected ... 1answer 27 views ### standardised random variable least square regression X against Y, Y against X Let X and Y be mean 0 and variance 1 random variables such that we choose \alpha and \beta to minimise$$\mathbb{E}(X-\beta Y)^2$$and$$\mathbb{E}(Y-\alpha X)^2$$after not so difficult ... 0answers 34 views ### Please show that f(\beta_0,\beta_1)=\log(1+\operatorname{exp}(-y_1(\beta_0+\beta_1 x_1)))+\log(1+\operatorname{exp}(-y_2(\beta_0+\beta_1 x_2))) I would like to show that the following result is indeed true. I am very new with this subject, so I ask for a hint to get me started please. Please show that f(\beta_0,\beta_1)=\log(1+\... 0answers 42 views ### Estimating a probability distribution by fitting a function to a frequency histogram If I want to estimate a probability distribution, is it common practice to simply fit a function to a frequency histogram? So, I am training a classifier, the performance of which is evaluated by its ... 2answers 85 views ### Why is R^2=\rho^2 Considering y_i=\beta_1+\beta_2x_i+\epsilon_i \bar y_i=\hat\beta_1+\hat\beta_2\bar x_i+\bar\epsilon_i a linear equation of least square used when it seems that there is a like between two data, ... 0answers 13 views ### How to get the relative contribution of each variable in a difference that forms the numerator? I am facing a problem that may seem simple at first but with which I struggle. The question relates to economics where I try to see the effect of deficit at time t (D_t) onto Output at time t+h (... 0answers 31 views ### variances of the slope and intersect of an orthogonal / Deming) linear regression I am a humble tinkerer who tries to get a rover to run a SLAM (simultaneous localization and mapping) process in his house. I equipped the rover with a laser rangefinder which collect distance and ... 1answer 44 views ### Discrete version of continuous SIR model I'm working with a SIR infection model, which is$$\begin{array}{rcl} \frac{dS}{dt} & = & -\beta IS\\ \frac{dI}{dt} & = & \beta IS-\gamma I\\ \frac{dR}{dt} & = & \gamma I \end{...
I want to determine the six unknown coefficients (uppercase letters) of the model $$x=X_c+(Au+B)\cos(Cv+D),\\y=Y_c+(Au+B)\sin(Cv+D)$$ given a set of data $(x_k,y_k,u_k,v_k)$, by least-squares. As ...