# Tagged Questions

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

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### How to make a covariance matrix from multiple observations of different objects?

I have $N$ objects. From each object, I sample $M$ values $(x,y)$ like so: ...
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### Weighted Linear Regression

I am performing linear regression analysis on a time-series of data. Data contains some missing values, My question is, if I impute the missing values using mean of all the values and I want to ...
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### Minimize the sum of distances between a sample and two “centers”

Suppose we have a set of readings $\{X_{i}\}$, each of which is a real number. What I want is to find 2 numbers, $a$ and $b$, such that minimize the sum of distances between each $X_{i}$ and ...
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### coefficient of determination: absence of cross products [closed]

With regard to the coefficient of determination, why is the total variation equal to the sum of the explained variation and the unexplained variation and there are no cross-products?
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### Question on optimization algorithm to train peculiar regression

I've been in my operations research course, and we have been working on optimization in particular problems within regression. We hypothesize that for variables $h,s,d,t,$ there is this set ...
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### Linear Regression without X? :

(Have been working in matrix algebra) Given model: $y_i = a + e_i$ ( $y_i= α+ϵ_i$ ) That is $y$ subset $i$ and error term subset $i$ Where the expected value of each error term for each entry ...
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### Curve fitting on non-linear ODE data

Background The graph below was generated by a set non-linear ODEs. For those of you who might want to know: It shows the maximum distance achieved by a cylinder when fired at a specified initial ...
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### How to use leave-one-out cross-validation scheme to compute the accuracy of a linear model fit

Using the least squares estimation I calculated the model fit for a dataset where: $$p = \beta_{0} + \beta_{1} * t$$ How could I use leave one out cross-validation(CV) scheme to compute accuracy ...
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### Estimating elasticity of y with respect to x in a log-log specification

The question My rudimentary workings so far is that; log(y_i/x_i) = log(y_i)-log(x_i) Factorise, so, log(y_i/x_i) = log(y_i) + upsilon_i - log(gamma_i + 1) Thus, elasticity of y to x is always >1 ...
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### Logistic Regression Varimp Always Different From Other Models; Text Analytics R

I've been running logistic regression, neural networks, naive bayes, and SVM models on my tweets dataset. I'm doing a sentiment analysis, where R is predicting whether a text is positive, neutral, or ...
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### Hat matrix and leverages in classical multiple regression

What is Hat matrix and leverages in classical multiple regression? What are their roles? And Why do use them? Please explain them or give satisfactory book/ article references to understand them. ...
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### Multiple Calculations of Dummy Variable effects?

If I am using dummy variables to fit a regression model, I know that I am comparing each variable to whatever the baseline that I decide is. So let's say that I have a dummy variable with 5 levels in ...
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### Codification of matrix $X$ in $Y=XB+\epsilon$

The variables for the data below is age, group (treatment 1,2,3), Y response variable. \begin{bmatrix}60&1&5.5\\57&2&4.5\\59&3&8.1\\68&1&0.6\\67&2&1.9\\...
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### what's the difference between the following two main functions

what's the difference between the following two main functions? Let's say if I have a response Y and predictor X and Z and Z is a factor, what's the difference between these two functions 1). Y ~ X+Z+...
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### Likelihood of an autoregressive model

I have the following autoregressive model: $Y_I=\lambda_t + \alpha_t(Y_t-\lambda_{t-1}) + \epsilon_t$ where $\lambda_t=\beta_1+\beta_2cos(\pi t/6)+\beta_3sin(\pi t/6)$ and $\epsilon$ has a ...
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### How to compute Simple Linear Regression equation not using Least Squares Estimators?

I know how to compute the Simple Linear Regression (SLR) equation using Least Squares Estimators, $b_0$ and $b_1$. But I was given the following table:  \begin{array}{c|lcr} & \text{mean} &...
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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? ...