Tagged Questions

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

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What is the difference in how $\mathrm{R}^2$ and $\mathrm{R}$ values are interpreted?

In statistics, there is the $\mathrm{R}$ value for the product moment correlation coefficient and the $\mathrm{R}^2$ value for the coefficient of determination. In both cases they are described as a ...
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Automatic curve fitting to find order of an algorithm?

I'm a newbies in mathematics. I'm looking for an automatic best curve fitting function to find the order of an algorithm. I would like to know if it does exists a math library function that would ...
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Plotting data with error bars with gaussian distributed error

I want to fit a straight line model of the form $y_i = a+ b\ x_i$ to the list of $(x, y)$ pairs given below. How can I plot the data with error bars in both coordinates? ...
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Retrieve inputs for second pass (cross section) regression from Time series linear regression

I will explain my question through simple example best demonstrating the issue. Basically I work with Matlab, so if there is already implemented lib functions for this - That's can be the answer. And ...
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Prove information matrix equality for binary Logit model

I need to prove the information matrix equality for a binary logit model. I know that in general the information matrix equality means the following: "The Information Matrix Equality (IME), which is ...
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Calculated product of two projection matrices

how do i show that $$P_MP_m=P_mP_M=P_m$$ where $$P_M=X_M(X'_MX_M)^{-1}X'_M$$ $$P_M=X_m(X'_mX_m)^{-1}X'_m$$ and $X_m$ is embedded into the larger matrix with the same number of columns $X_M$.
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Parameterizing conditional expectations in terms of regression coefficients (gaussian case)

Consider three jointly normally distributed random variables $X,Y$ and $Z$. I know that in the Gaussian case $$E[Z\mid X, Y]=\beta_{ZX;Y}X +\beta_{ZY;X} Y$$ where $\beta_{ZX;Y}$ notes the ...
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using simple regression to capture a “normal range” for a dependent variable against a factor?

The question reads as follows My JMP output of the simple regression of the data is as follows: Is this all I need? The question phrasing is somewhat throwing me for a loop. Is there something ...
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How to interpret parameter in proportional hazard model?

How can I show that $b$ in this proportional hazard model $y=1-x^{e^{bz}}$ is the percent change in $y$ with a unit change in $z$? For brevity, I have neglected to show the functional form of $x$, ...
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How to interpret b in $y=x^{e^{bz}}$ in nonlinear regression?

What is the correct way to interpret b in this nonlinear equation $y=x^{e^{bz}}$? I've estimated the model and b seems to be the percent change in y with a unit change in z, but I am unsure how to ...