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

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Can the dependent variable in a multivariate linear regression be binary when the independent variables are continuous?

Can the dependent variable in a multivariate linear regression be binary when the independent variables are continuous?
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Realtionship between Statical test and CI, and restriction of the regression model. [on hold]

$1$.What is the relationship between a statistical test, such as the 𝑡-test, and a confidence interval? $2$.The linear regression model is excessively restrictive since it only allows for a ...
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Overfitting: Mean and variance

I have read in a book the next porperty: Lets consider the following true data generating process: $$y=x_1 \beta_1+...+x_p \beta_p + \epsilon = x'true \beta + \epsilon$$ where $E(\epsilon)=0 \ \ \ ...
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Calculating person product moment correlation coefficient on a 3 X 3 table

Usually we are given problems that only involve 2 rows (x and y), but recently saw a problem asking how to compute the correlation coefficient on a table of data that has 3 rows and am not sure how to ...
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26 views

How to fit a set of 3D points to a helical curve?

suppose I have a set of points in $\mathbb{R}^3$, and I want to find an arbitrary helix which best approximates these points. An arbitrary helix in $\mathbb{R}^3$ can be parametrized as ...
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Local quadratic approximation

I wanted to implement some penalized regression parameter estimation algorithm by Fan&Li (http://sites.stat.psu.edu/~rli/research/penlike.pdf, section 3.3), but cannot catch the idea of some ...
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1answer
50 views

How to Fit a Curve to a Given Model with Constraints?

The input are triples $\left\{ x,y,v\right\}$ where $x,y,v \in \mathbb{R} ^{+}$ I need to find function $f(x,y) = v$ by finding parameters of the following model $f(x,y) = a + bx^c + dy^e $ ...
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What would be the standard errors of this transformed regression model, given that I know the standard errors of the original model

Say I have the following regression model: $\ln\left(\dfrac{y_i}{x_{2i}}\right)=\alpha_1+\alpha_2\ln(x_{2i}) + \alpha_3\ln(x_{3i}) +e_i$ where I know the values of the regression coefficients and ...
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25 views

Linear or nonlinear modell

Given those three modells and the assignment to decide whether or not those modells can be transformed into linear modells: (a) $Y_i = \beta_0 + ...
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Does increasing sample size have any effect on omitted variable bias?

Say I have a multiple linear regression model, where two of the variables are positively correlated, and I omit one of these variables from the model. First question - if I increase the sample size, ...
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Coefficient Correlation r of Exponential Functions Regression

I'm writing an exponent regression calculator $Ae^{Bx}$ Sample Data Set (X,Y) is (9, 1) (7, 10) (6,11) (20, 10) (15, 1) A = 5.287 and B = -0.0232. So $F(x) = ...
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What are the causes of overfitting in regression/classification for statistical data?

Say I have some n-dimensional data, and I want to come up with some hypothesis function which generalizes that data for future predictions in the model. "Overfitness" of my hypothesis function is a ...
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19 views

$n$th order Polynomial for $(n+1)$ points

I was reading about Polynomial Fitting and found this sentence: How can one reach this conclusion and prove it?
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14 views

What is the equivalent of $R^2$ ( coefficient of determination in linear regression) for non linear regression?

I have a dataset with two correlating variables. The relation cannot be described as: $y= a+bx$. Therefore I told my math programm to calculate a nonlinear regression line. But unlike in linear ...
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Using optim and fitdistr in R to find parameters

I am using R to fit distributions. I have been given the data and have been asked to find the optimised parameters(for lognormal, weibull, exponential and gamma functions) using: 1) fitdistr and 2) ...
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What does fixed regressor say about our linearity condition?

The linearity condition states that $y_i=(\vec{x}_i)^{T}\vec{\beta}$ for all $i$. Now, if we have fixed regressors, $\{\vec{x}_1,\vec{x}_2,\cdots\}$, our linearity condition only says for those ...
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An example where pearson is wildy different to spearman? [duplicate]

Im looking to spearman and pearson, and from what i understand spearman is better at looking at curves. Can i see an example of a small set of data (10 or less) where this difference is large.
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1answer
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Fit a Quadratic Curve to Data

I have some data and I want to fit a quadratic curve for my data But I don't know that how to it do? My data : $x,y = 100,45;$ $x_1,y_1= 101, 50$; $x_2,y_3=99,35$; $\ldots$ For instance this ...
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An example of when pearson or regression analysis is drastically different to spearman?

Im looking into spearmans rank. I know pearson and regression struggles with curves, but does anyone have any example of when pearson or regression differs with spearman and what this means? Ideally ...
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24 views

Consequences of fitting a regression model with an intercept term when it should be through the origin

Suppose a true model is $Y_i=\beta X_i +e_i$, where $e$ is the random error. Suppose instead we fit the model (using least squares) as $Y_i=\alpha_0+\alpha_1 X_i +v_i$, where $v$ is the random error. ...
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How to Fitting Function to Data

Hi I have some data And I want to fit a polynom these data Firstly I think it should be : $ax^2 +bx+c$ and then $x+x1=-\frac{b}{a}$ ;$x*x1=\frac{c}{a}$ but I can understand that This method ...
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Without homoscedasticity, is OLS still the best estimator (aka BestLinearUnbiasedEstimator…BLUE)?

Consider the Gauss Markov assumptions. Suppose we have a random sample $\lbrace x_n,y_n \rbrace_{n=1}^{N}$. Assume for a simple linear regression model $y_n = \beta_0 + \beta_1 x_n + \varepsilon_n$ we ...
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1answer
26 views

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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How is the $R^2$ value for exponential regression calculated if not by product moment correlation coefficient?

I am analysing some $x$ and $y$ values using Excel by plotting them on a graph and adding a line of best fit then using the equation for the lines of best fit. The exponential line of best fit has a ...
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2answers
33 views

Linear Regression - Predction

With this question I can input data and I can find the linear regression line - but I am totally failing to get the last part - predicting how many hats will be sold in $2017$. How do you do it. ...
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36 views

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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1answer
29 views

Correlation and Linear Regression

I'm tasked with this question but unable to proceed on. Q: Calculate the linear product moment correlation coefficient between x and m for these samples: $$ \Sigma x=205,\\ \Sigma m=1240, \\ \Sigma ...
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1answer
45 views

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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1answer
19 views

Deriving the identity: $\hat{\beta}_1 = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$

For some reason I am having an extremely hard time finding out how the following expression is derived $$ \hat{\beta}_1 = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2} $$ Is ...
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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 ...
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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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3answers
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What is the difference between linear regression on y with x and x with y

I'm plotting the regression line of (GDP$\%$ Change, Poverty Rate$\%$)$\to (x,y)$ in Mathematica What would it mean if I were to switch the axis? (Poverty Rate $\%$, GDP change $%$) ...
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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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3answers
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Question regarding Sum Notation in the least squares formula [closed]

I'm attempting to figure out the difference between Σx^2 and (Σx)^2 in this least squares regression formula http://i.imgur.com/HwxnM28.jpg. Any ideas? I figure there must be a difference.
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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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2answers
36 views

The best fit for variables in a number of equations?

Let's say I have 2 variables $x$ and $y$ and 4 equations. The parameters in capital are known parameters. $$I_1=xA_1+yB_1$$ $$I_2=xA_2+yB_2$$ $$I_3=xA_3+yB_3$$ $$I_4=xA_4+yB_4$$ What's the strategy ...
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Fourier transform used for time series prediction?

For a given time series data set $(t=0,...T)$, we can use Fourier transform to data fitness $$ X(n) = \mu + \sum_{k}\left( A_k cos \frac{2\pi k n}{N} + B_k cos \frac{2\pi k n}{N} \right) +\varepsilon ...
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1answer
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Can a prediction interval be interpreted as a probability?

Suppose I find a 90% prediction interval for some data distribution. This implies that if I sample large enough data from this distribution, then 90% of such data will lie inside the prediction ...
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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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Assigning levels in factorial design.

I am sorry if the question is too basic. Actually while doing some experiment on 2-level factorial design, I assigned +1 to a low level and -1 to high level. I just need the sign of the regression ...
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1answer
22 views

If X and Z are uncorrelated and Z is normal with mean zero and constant variance, why can I assume Z is zero?

I have a data set that I have used to calculate the coefficients for a linear regression. The data set is of the form $\lbrace x_i,y_i\rbrace_{i=1}^{n} $ Let $$Y = \alpha + \beta X + Z$$ where ...
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1answer
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Help with Matrix Regression

The question i have is: Consider two independent random variables $ξ_1$ and $ξ_2$, such that $ξ_1 ∼ N(0,1) $ and $ ξ_2 ∼ N(0,2)$. Let $η_1 =(ξ_1+ξ_2, ξ_2)^{T} ,η_2 =(ξ_1, ξ_1−ξ_2)^{T}$. Find the ...
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Help with Regression question for Revision.

I Have my exam coming up in a few weeks, and am not sure how to go about answering a few questions. One being: For a fixed i = 1,...,n, derive $Cov(\hat{β},Y_{i})$ and $Cov(Y − (\hat{α} − α) − ...
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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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1answer
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Can regressors be considered as random variables?

In the linear regression model $$y = \beta_1 X_1 + \cdots + \beta_p X_p + \varepsilon \, ,$$ can the regressors $\{X_i\}_{i \in \{1, \ldots, p\}}$ be considered as random variables? I know that what ...
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Complexity of Gaussian Process algorithms is $\mathcal{O}(n^3)$

It is often quoted that the complexity of Gaussian Process algorithms is $\mathcal{O}(n^3)$ due to the need to invert an $n \times n$ matrix, where $n$ is the number of data points. But as far as I ...
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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. ...
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1answer
25 views

Formula for finding variables by regression

I'm trying to fit data to the following formula: $$y = a + b x + c/(Sqrt[x]+d)$$ $y=a + b x$ can be fitted easily with linear regression, but I'm lost when it comes to anything more complicated. ...
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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 ~ ...
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Matrix Regression help for exam revision

My regression exam is a month away and i am trying to learn Matrix regression however and struggling with the questions as a whole they are: (a) Consider two independent random variables ξ1 and ξ2, ...