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

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1answer
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How to apply non-linear regression to Logistic (sigmoid) curve

I've been looking at a useful way to represent Doppler shift from a satellite passing over a ground station. I've calculated the Doppler shift frequency values at 1-second interval for the duration of ...
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2answers
45 views

Maple: How do I type “solve” with an arrow under?

I am trying to learn using Maple 18 (Mac). I have defined a function with a list of X and Y values. f := x->LinReg(X, Y, x) Now I would like to output the unknown "x" value that correlates with ...
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1answer
31 views

Rates of convergence of an OLS estimator

I have a linear regression model $$ y_t=x_t\beta+e_t,\quad t=1,\ldots,N. $$ Here $x_t$ is non-random and given by $(1,\delta_t t)$ where $\delta_t$ is 1 for odd $t$ and $0$ otherwise. Moreover, ...
2
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1answer
30 views

Predicting the increase/decrease of number

I have these entries in my database that looks like this: ...
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1answer
11 views

Develop relation between dependent and independent Using Tobit model

Depenent variable (Y): Range (0 to 10) (Not less than 0 and not more than 10) (range which i collected from field survey) Independent Variables: X1 - Time (in sec) X2 - Distance (in meter) X3 - ...
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2answers
54 views

Using inverse of matrix A as approximate inverse of matrix that is very close to A

Say we have two matrices, $A$ and $A'$ so that $A\approx A'$, and we have the inverse of $A$, $B$, where $AB=I$, and the inverse of $A'$ where $A'B'=I$. If we have some guarantee about how big any ...
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0answers
15 views

Linear regression, analyze of correlation, remove a variable [on hold]

I have done a linear regression on a excel file in function of the variable A then I did an analyze of correlation. My teacher said that after that I can remove a variable but how to chose it ? My ...
3
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1answer
449 views

Fitting a sine function to data

I have a sequence of $n$ points $(x_i,y_i)$, for $i=1,\dots,n$. I would like to find the function, of the form $y=V\sin(x+\phi)$, which best fits the points. Which numerical method could I use? I have ...
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0answers
25 views

statistical analysis [on hold]

Two independent random samples of annual starting salaries for individuals with masters and bachelors degrees in business were taken and the results are shown below ...
2
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1answer
24 views

Analytic solution for matrix factorization using alternating least squares

The standard form for ridge regression aims to minimize the following cost function. $$ \min\ \ \sum_i(y_i-x_i^T\beta)^2 + \lambda\sum_j\beta^2_j $$ As described here, it's possible to differentiate ...
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0answers
40 views

standard deviation and adjusted R-squared for simultaneous regressions

I am conducting a study that requires two steps of statistical estimation. First, I run a regular OLS regression, from which I gather three outputs that I need: coefficient values standard ...
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1answer
42 views

MATLAB curve fitting - least squares method - wrong “fit” using high degrees

Anyone here that could help me with the following problem? The following code calculates the best polynomial fit to a given data-set, that is; a polynomial of a specified degree. Unfortunately, ...
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1answer
31 views

How to fit a function to experimental data? [closed]

I have an experimental data say $y=[1,2,3,4,5]$ for given $x$ values and I have a set of equations model fit as $$\sum (y -ax +cx)=0 \text{ and } \ \sum (y+ax - cx)=0$$ How to solve this for $a$ ...
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0answers
11 views

Multivariate regression with nonindependent variables

I'm trying to run a multivariate regression in which not all variables are independent, and an not sure if this is possible. The reason is as follows: Let's say we have a large number of contracts, ...
0
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1answer
39 views

adjusted R squared with multiple dependent varialbles

A question about regression in statistics. What is the formula for adjusted R squared if there are multiple dependent variables
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1answer
31 views

Recalculate R^2 deleting 1 point

Is there a way to recalculate $R^2$ of a regression that I delete a point (for example an outlier point)? The idea is to get the $R^2$ without a point but without recalculating all the regression. ...
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1answer
26 views

How to proof that least square estimator $\hat{B}$ doesnt exist when $x$ is linearly dependent?

For the linear regression model $Y=xB+e$, prove that if the columns of $X$ are linearly dependent, the least square estimator $\hat{B}$ does not exist I know that since $\hat{B}$ is an unbiased ...
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0answers
12 views

questions about distribution of multivariate normal

I'm looking at this past exam question, For A) Cbhat~N(CU,C(summation)C') B)I have very faint idea of what to do, I tried finding some theroems about distribution but couldn't find any that ...
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1answer
28 views

Question on regression

So I've been given this formula For regression $R^2=1 - \sum \frac{{(y_i - \hat{y}_i)}^2}{(y_1-\bar{y})^2}$ Now an obvious question that has come to me is why $R^2$ stays the same in certain ...
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1answer
26 views

Linear regression involving angles in a triangle.

In a survey experiment, three independent measurements $29.5^{\circ}$, $30.5^{\circ}$, $120.5^{\circ}$ are obtained from the three angles $\alpha,\beta,\gamma$ of a triangle. Formulate the ...
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0answers
17 views

Trying to find similarity between collection of points

This is a kind of weird problem, and I'm not sure what the best Stack Exchange to post this on is, but I assume Mathematics could help the most. I have many sets of points in 3D space (xyz ...
0
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1answer
15 views

how binary quantile regression divides the dependent variable into quantiles

I am not very clear with binary quantile regression. As if it was ordinary quantile regression, it would divide the dependent variable's value by its ascending value into quantiles. But I cannot ...
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1answer
299 views

Multiple linear regression with interaction

I'm doing a multiple linear regression with interacting variables. I'll give you an example: $y$=value, $x_1$=material, $x_2$=weight, $x_3$=color $x_1$ and $x_2$ are interacting variables but $x_3$ ...
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2answers
52 views

Parameter optimization using a regression model.

I am working on an optimization problem. I build a regression model to understand the behavior of a system which depends on two variables which are functions of another two variables. My regression ...
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1answer
21 views

Proof of Correlation Coefficients

Good evening, I have a problem with an exercise: Let $X$ and $Y$ be two real square integrable random variables with var$X>0$, var$Y>0$. The correlation Corr$(X,Y)$ quantifices how far $X$ and ...
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3answers
2k views

Correlation Coefficient and Determination Coefficient

I'm really new to linear regression and am trying to teach myself. In my textbook there's a problem that asks why R^2 in the regression of Y on X = the sample correlation between X and Y the whole ...
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1answer
4k views

Computational complexity of least square regression operation

In a least square regression algorithm, I have to do the following operations to compute regression coefficients: Matrix multiplication, complexity: $O(C^2N)$ Matrix inversion, complexity: ...
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2answers
36 views

Assumption of a Random error term in a regression

In one of my recent statistics courses, our teacher introduced the linear regression model. The typical $y=\alpha + \beta X + \epsilon$, where $\epsilon$ is a "random" error term. The teacher then ...
1
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1answer
83 views

Incorrect angle detected between two planes

I want to calculate the angle between 2 planes, Reference plane and Plane1. When I feed the X,Y,Z co-ordinates of pointCloud to the function plane_fit.m (by Kevin Mattheus Moerman), I get the output ...
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0answers
468 views

What is the Moore-Penrose pseudoinverse for scaled linear regression?

The matrix equation for linear regression is: $$ \vec{y} = X\vec{\beta}+\vec{\epsilon} $$ The Least Square Error solution of this forms the normal equations: $$ ({\bf{X}}^T \bf{X}) \vec{\beta}= ...
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0answers
382 views

Moore–Penrose pseudoinverse reference

Given the eigendecompositions $AA^{\top}=Q \Lambda Q^{\top}$ and $A^{\top}A=P \Lambda P^{\top}$, where $\Lambda$ is a diagonal matrix (of eigenvalues) and $P$ and $Q$ are unitary eigenvectors matrices ...
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0answers
8 views

How to interpret Standard Residual Deviation?

have fitted regression lines for 200 data sets where each data set contains 40 data points.As a result of that now I have 200 Standard Residual Deviation values and need to interpret that results. How ...
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0answers
25 views

Using Mean vs Median for Rapidly Changing Data

I am writing a report on global GDP per capita trends. As many of you know, were large shifts in the growth rates of these figures before and after the Great Recession. There has been some analysis on ...
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6answers
957 views

Why get the sum of squares instead of the sum of absolute values?

I'm self-studying machine learning and getting into the basics of linear regression models. From what I understand so far, a good regression model minimizes the sum of the squared differences between ...
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0answers
18 views

Algebraic expression of a regression matrix

Let's say I'm doing a multivariate regression between a set of input $n$-dimension vectors (noted by the matrix $X=\{X_1,X_2,...X_m\}$) and a transformed version (noted by the matrix ...
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0answers
38 views

Hypothesis testing - Beta coefficient

Apologies if this is trivial, just linke me somewhere. I'm currently taking statistics 101, I can't wrap my head around the hypothesis testing of coefficients. As follows, the t-test reads $$T=\frac ...
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11 views

MSE in case of log-transformed dependent variable

Let's consider the following log-linear model: $log(Y_i) = \alpha + X_i\beta + \epsilon_i$ for i = 1, ..., N The fitted value is: $\widehat{log(Y)} = \hat{\alpha} + X\hat{\beta}$ Assuming ...
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0answers
14 views

Curve fitting using a graph extracted from an article, is it possible?

I want to curve fit a graph from an article which I can only extract from the pdf file as a screenshot. Therefore, I do not have the coordinates of the data points explicitly, yet I know that the ...
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0answers
15 views

How to compute confidence bound in linear regression

In a simple linear regression problem, let $A$ be an $m\times n$ matrix of samples, $A=[x^T_1; x^T_2; ...;x^T_m]$, $w$ is the $n\times 1$ parameter vector, and $b$ is $m\times 1$ response vector. The ...
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1answer
42 views

Optimization Problem (Linear Algebra)

I am not trying to cheat or anything, so any reference to online literature or MOOCs, that teach this stuff, will be highly appreciated. The problem is to prove that the following optimization ...
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0answers
10 views

Regression question (details inside). Measuring the incremental impact on the dependent variable of one category over other categories

Formulate a regression equation you would use to test for the differences in ROE between firms that used tier 1 investment banks as their advisors and those that used tier 2 or tier 3 banks (note: ...
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0answers
41 views

$E(\bar{Y})=\bar{Y}$? [Linear Regression]

A book, I am reading, derives the covariance between $b_0$ and $b_1$ as follows: By definition, $$Cov(b_0,b_1)=E[(b_0-Eb_0)(b_1-Eb_1)]$$ $$=E[(b_0-\beta_0)(b_1-\beta_1)]$$ ...
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0answers
13 views

Statistics linear modelling in R

Suppose I have a date set of the form: Test Subject/Sex/No. of mistakes made in the morning/ No. of mistakes made in the afternoon A / M / 2 / 5 B / F / 1 / 4 C / M / 3 / 5 D / F / 1 / 5 Suppose ...
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0answers
12 views

Cannot figure out autocavariance

The moving average model of order q has the form $$Y_t =β_0 +e_t +b_1e_{t−1} +b_2e_{t−2} +...+b_qe_{t−q}$$ where $e_t$ is a serially uncorrelated random variable with mean $0$ and variance $σ^2_e$. ...
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0answers
15 views

Time series regression

What if I have a stationary independent variable and 2 non-stationary dependent variables, and I want to run a regression on them, what model is the most appropriate?
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24 views

Deriving single linear regression parameters in terms of multiple linear regression parameters

Suppose the true population model is ln(wage) = B0 + B1(education) + B2(experience) + v (v is error term) Suppose the model is estimated as ln(wage) = B3 + B4(education) + u How do I calculate ...
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1answer
38 views

Is there such a thing as a combination of linear and non-linear regression in one form?

Let's say I have a dataset D with many variables. I can get a multiple linear regression from that in the form ...
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1answer
38 views

Size of sample and correlation coefficient

$X$ and $Y$'s correlation coefficient is $r=0.5$. What is the size of sample when the correlation is significant at $\alpha=0.05$ with two sided test? Is there a more "formal" way to solve this ...
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1answer
33 views

How to take the derivative of Matrices

I was browsing the derivation of the Least Squares estimates and stumbled about this problem. It said that: $$E = (Y + XB)^2$$ $$\frac{dE}{dB} = -X^TY + X^TXB$$ It is to my understanding that the ...
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0answers
18 views

Derive the F-statistic for this model

Problem: Consider the model $y=\beta+\varepsilon$, where $\varepsilon\sim N_4(0,\sigma^2I)$, and $\sum_{i=1}^4\beta_i=0$. Derive the F-statistic for testing $H_0:\beta_1=\beta_2$. I tried to write the ...