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

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Fitting an ellipse such that the ratio of its radii is in a range

I need to fit an ellipse to a group of points. However, I have an issue and I appreciate if anyone can help me. The issue is that I need to have the fitted ellipse such that the ratio of its radii is ...
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1answer
146 views

Example of a real-world situation where multivariate analysis is applicable.

I have searched a lot of site to understand the situation where multivariate analysis is applicable. But not got any easily understandable example. Would you please give me a real-world example where ...
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22 views

Application of Multivariate Analysis

The following situation is proven valuable where multivariate analysis can be applied. This example is taken from the book Applied Multivariate Statistical Analysis ...
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1answer
33 views

Linear regression with constrained weights

I have a set of $n$ linear combinations, each with $m$ parameters and desired value $b$. I want to find the set of weights $w$ which minimizes the total equations distances (e.g. the sum of distances ...
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16 views

Chi sqaured table for degrees of freedom 616?

In order to check heteroskedasticity, we use the White's test. I tried to follow this method below, however, could not find a table with df=2016 and 95,5% confidence. I don't understand how we get ...
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1answer
27 views

estimate coefficients of $y = \alpha x + \beta y + \gamma z + \epsilon$

I know how to find $m$ and $b$ for $y= mx +b$, which is : $m= \frac{\bar{x}\bar{y}- \bar{xy}}{(\bar{x})^2 - \bar{x^2}}$ and $b= \bar{y} - m\bar{x}$ How can we estimate $\alpha, \beta, \gamma$ and ...
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2answers
38 views

Likelyhood function analysis

I've done some calculations on a large number of data, and created the following graph in excel representing the data: How do I go about analysing this regression in order to find the formula that ...
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1answer
59 views

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
71 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
64 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, ...
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1answer
35 views

Predicting the increase/decrease of number

I have these entries in my database that looks like this: ...
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2answers
60 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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1answer
17 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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1answer
81 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
60 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
288 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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0answers
15 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, ...
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1answer
44 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
38 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
27 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
39 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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1answer
32 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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19 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 ...
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1answer
20 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
33 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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2answers
60 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
42 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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1answer
15 views

Asymptotic var of IV estimator

This post is asked again due to lack of answers first time around. Suppose we have a linear model $y=Q+Rx+error$, where $E(error)=0$, and $z$ is an instrument for $x$ (endogenous) where the ...
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2answers
93 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 ...
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29 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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1answer
121 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
27 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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42 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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13 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
16 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

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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1answer
46 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
14 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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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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18 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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1answer
40 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 ...
2
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1answer
37 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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1answer
40 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
19 views

what is one basic/intermediate regression analysis standard textbook that is math intense

What is one basic/intermediate regression analysis standard textbook that is math intense with proofs/derivations? Also, i need that one to be comprehensive yet the diffculty is suitable for self ...
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1answer
37 views

Matrix form for Weighted Least Squares

If we have the following weighted least-squares regression, with $\hat{\beta} = (X'WX)^{-1}X'WY$ How can we express the squared errors, MSE and the fitted values in matrix form? These are the OLS ...
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1answer
33 views

How to find the deviated form of beta 1 in OLS

How to find the deviated form of beta 1 in OLS Y=β1+β2X+u estimated β1=(ΣX^2ΣY-ΣXΣXY)/(nΣX^2-(ΣX)^2) I do not know how to turn this part (ΣX^2ΣY-ΣXΣXY)into deviated form. I found that estimated ...
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34 views

If we make the lambda very small in ridge regression, why do the beta hats still decrease?

I understand that the betas estimated from minimizing the function (y hat - y)^2 + beta' beta decrease as lambda increase. However, looking at the picture below, why cannot we choose a lambda so ...
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1answer
24 views

Help Linear Regression

It would be really nice if someone could help me out and suggest me with his expert opinion. Going through the table and looking at Part (a) of this question. I believe I should use Scatter plot to ...
2
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1answer
42 views

Standard Error in OLS Regression

Assuming I have the following linear regression set-up: $y_i = \alpha + x_i * \beta + \epsilon_i$ for $i = 1,2,..., n$. When I run the regession, I get a $\beta$ and $\alpha$ estimates, along ...
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1answer
38 views

Multiple Regression with Categorical Predictor Variables of More than Two Levels

I'm planning on running a hierarchical multiple regression in SPSS. In the first step, I would like to enter demographic characteristics, second step continuous predictor variables of interest, and ...