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

learn more… | top users | synonyms

0
votes
0answers
28 views

advantage and disadvantage of using SVD to solve least square problems

I usually just use $AA^T$ or QR decomposition of A to solve least square problems. But SVD seems to be the popular way to solve the problem. what is the advantage and disadvantage of SVD? thanks!
2
votes
1answer
13 views

Problem with verifying variance of residual

I am supposed to show the following: $$Var(e_{ij}) = \sigma^{2}\left(1-\frac{1}{n_i}\right)$$ Where the follwing is known: $$y_{ij} = \mu + \alpha_{i} + \varepsilon_{ij}$$ $$e_{ij} = y_{ij} - ...
0
votes
1answer
27 views

Linear regression custom fit function, calculate A and B using system of linear equations

Good afternoon! As a part of solved examples from previous year examination, there is a following bi-dimensional table of frequencies: ...
1
vote
1answer
26 views

Linear Regression quadratic terms

I have a hard time understanding the term 'linear regression'. For what I know, linear means polynomial of degree 1. But then, I found that in one of my lectures, the lecturers are saying that this ...
-1
votes
1answer
25 views

Using least squares regression for line of best fit

Use the least square approximation to find the closest line (the line of "Best Fit") to the points: $$(-6,-1), \quad (-2,2), \quad (1,1), \quad (7,6)$$ I'm attempting to use the least squares ...
0
votes
1answer
70 views

What's the most efficient way to fit a surface to three or more points?

Say I have a function of the form $s=b-mp+at$, where $p$ and $t$ are the independent variables, and I have 3 or more points of the form $(p,t,s)$. I want to find the best values for $b$, $m$, and $a$ ...
0
votes
1answer
50 views

How to find Parameters in nonlinear Regression Model?

I have a nonlinear Regression Model with eleven observations of $x,y$. How do I find the parameters $a,b,c,d$ of the model: $ y=f(x)=a + b \sin cx e^{dx}$ by using the function: $$\Phi(a, b, c, ...
0
votes
0answers
23 views

Correlation/Regression for Continuous and Discrete data

I want to correlate a data where one axis is continuous (ranging from 0 to 1), other axis is discrete. Discrete axis scale is 1 to 5 (1 is for Strongly Disagree and 5 is for Strongly agree). How ...
0
votes
0answers
37 views

Mathematical equivalent to curve fit between polynomials

I am adapting a calculation done in an Excel workbook to code. Right now, we are predicting a variable based on three other variables, say $x,y,z$. We are creating six functions of $x$ and $y$ at ...
0
votes
0answers
18 views

Linear regression with rounded down dependable variable.

I have a problem where I need to find the underlying linear relationship between an independent variable and it's dependent variable. However, I know that the dependent variable is being rounded down ...
0
votes
1answer
22 views

Does scatterplot matrix “work” with quadratic variables?

basically I want to plot a scatterplot matrix using a few variables. For simplicity lets say my model is: $$z=\alpha_0 + \alpha_1w+\alpha_2x+\alpha_3y+\alpha_4y^2 + \epsilon$$ When I plot the matrix, ...
1
vote
1answer
73 views

Why do the components of an equivalent kernel sum to 1?

Let $\textbf{x} = (x_1, \dots, x_n)^T \in \mathbb{R}^n$ and $k \in \mathbb{N}$. We define $$ X := \begin{pmatrix} 1 & x_1 & \cdots & x_1^k \\ \vdots & \vdots & & ...
1
vote
0answers
16 views

Approximation technique when data is missing?

I am doing some statistical studies and I would appreciate some guidance to some approximation techniques when not all data is available. I have a model that takes certain input parameters (discrete, ...
0
votes
0answers
33 views

Statistical Multiple Linear Regression Log Transformation

If for example we have a multiple linear regression as follows: $$hydrcarb=x_1+x_2tanktemp+x_3disptemp+x_4tankpres+x_5disppres+x_6tankpres^2+x_7dispres^2$$ And I am trying to do a backward ...
0
votes
2answers
38 views

How we can linearize this equation?

I have an equation that it seems to be a non-linear equation. I want to compute the parameters a1 till a4.I want to simply do a linear regression to find the parameters, which is much easier than a ...
0
votes
1answer
35 views

X - axis of a linearized polynomial.

The other day in my Physics class we had some sample data that we wanted to linearize. The graph resembled a root curve. So to linearize it, we took the square root of all the x data and replotted ...
0
votes
1answer
24 views

Regression project in octave/matlab

I'm trying to establish a polynomial model to adjust the variation of the dollar throughout the year. Suppose hypothetically that I have the following data ...
0
votes
0answers
26 views

The correlation between alpha and beta

Consider the following 2-variable linear regression where error $e_i$'s are independently and identically distributed with mean 0 and variance 1; $$ y_i=\alpha + \beta (x_i - \bar {x}) + e_i$$ where ...
1
vote
0answers
33 views

Does gradient descent and normal equation give the same answer?

I tried to optimize for a linear regression model using both approaches and they gave me two completely different answers. My sample data set was: df <- data.frame(c(1,5,6),c(3,5,6),c(4,6,8)) ...
0
votes
0answers
10 views

Is it always possible to find a logistic regression model that yields zero training error on any dataset?

I am leaning towards no. A logit regression model is just one function, and there is no way its coefficients can accurately predict an entire dataset, outliers and all. Is this the correct intuition?
0
votes
1answer
31 views

Maximum and minimum penalty in lasso regression family

I am trying to adjust penalty, lambda, in group lasso regression, but I have no idea about it. Just to clarify, group lasso regression is a kind of multiple linear regression which use penalties on ...
1
vote
1answer
39 views

finding column vectors - linear transformations

$L:\mathbb{R}^3\rightarrow \mathbb{R}^2$ with bases $\mathcal{S}=\left\{\left(-1,1,0\right),\left(0,1,1\right),\left(1,0,0\right)\right\} \: \text{for} \:\mathbb{R}^3 \:\text{and} \\ ...
0
votes
1answer
35 views

Show ARIMA(1,1) with mean $\mu$ is an ARMA process

I am trying to show that an ARIMA(1,1) process with mean $\mu$ is an ARMA process, as well as to show if it causal and/or invertible. The set up is: Let $X_t$ be a causal and invertible ARMA(1,1) ...
0
votes
0answers
34 views

OLS: Estimation with negative coefficients

I have probably an easy problem, however I'm not really sure how to do it: Basically, I would like to estimate a linear regression with OLS. So far so easy. However, the model that I would like to ...
0
votes
0answers
33 views

Intuitive understanding about LSE

Let y= X$\beta$ + $\epsilon$ where y is $n \times 1$ vector, X is $n \times p+1$ matrix, $\beta$ is $p+1 \times 1$ vector, $\epsilon$ ~ $N(0, \sigma^2I_{n}$) now, let $y_{i}$ = $\hat{y_{i}}$ for some ...
0
votes
1answer
43 views

Math notation clarification

I'm working on learning more about logistic regression and I came across an equation with some confusing notation that I've never seen before: $$ \frac{\delta}{\delta \theta_{y'}^{(j)}} l(\theta) = ...
0
votes
0answers
24 views

minimum orders in linear regression to get a perfect fit

The problem is that, $(X_i, Y_i), i = 1,\ldots, n$ is an i.i.d. bivariate sample. Show that it is possible to fit a polynomial model using least square such that the fitted values are equal to the ...
1
vote
1answer
51 views

Significance level for a hypothesis test for a linear regression

Consider linear regression model $Y_i=a+b\cdot x_i+\epsilon_i$, $i=1,2,3,4,5$, where $a,b\in\mathbb{R}$ are unknown and $x_1=x_2=1,x_3=3,x_4=x_5=5$, $\epsilon_i$ are iid, normally distributed with ...
1
vote
1answer
22 views

contour plot in multiple linear regression

I have recently saw some examples about contour plots and multiple linear regression, for what I know a countour plot is obtained for having a graphical view of how the weights in a linear regression ...
3
votes
1answer
329 views

Find x,y & z (xyz+xyz=zyx)

I saw this problem the other day at work and found it pretty interesting: $$xyz + xyz = zyx$$ Find $x, y, z$ and the base(s) which this is true. Note that $x,y,z$ are simply digits concatenated, ...
0
votes
0answers
25 views

Question about ridge estimator

I have tried to show that ridge estimator is the solution to following problem min $(\beta- \hat{\beta})^t$$X^t X$$(\beta- \hat{\beta})$ subject to $\beta^t \beta =< d^2$ and $\beta$ is a $p$ x 1 ...
1
vote
1answer
38 views

Comparison of parameter: two different populations

I was wondering what the best way is to check for the equality of two parameters for a regression with no constant including possibly a confidence interval and p-value. $$H_0:\beta_1=\beta_2\ \vert\ ...
0
votes
0answers
32 views

two way ANOVA and linear regression model.

I know that Analysis of variance model can be written as a linear regression model using indicator regressors. For, one way ANOVA, I can write down the regression model. But for two way ANOVA ...
0
votes
1answer
47 views

Power form of regression equation which is not centered at x=0?

For a given set of data, the power form of the regression equation is given by $$y=b\cdot x^{m}$$ where $$m=\frac{n(\sum \mathrm{ln}(x_i)\mathrm{ln}(y_i))-(\sum \mathrm{ln}(x_i))(\sum ...
0
votes
1answer
19 views

standard error for the parameters of a linear regression model

Given a linear model $\mathbf{y} = \beta \mathbf{X} + \epsilon$, it is well known that the estimate for $\beta$ that gives the minimum residual sum of squares (RSS) is given by $\hat{\beta} = ...
0
votes
1answer
27 views

How to report significant digits in coefficient of determination?

Say that I fit some data with some model, for instance a linear function $y = mx+b$. What is the proper way to report the fitted coefficients and the goodness of fit? Specifically, if I do the fit in ...
1
vote
1answer
17 views

Interpreting linear regression.

I'm not very versed in statistics or anything so I'm in the dark for this. For my biology (Grade 12) class I've been looking at journals and papers and I've seen a lot of graphs expressed in the form ...
1
vote
0answers
41 views

Odd Ratio and Logistic Regression

Windy and Play Tennis = 9 Windy and Not Playing Tennis = 8 Not Windy and Play Tennis = 14 Not Windy and Not Playing Tennis = 8 I performed logistic regression in Weka and got odd ratio as 0.3448 for ...
0
votes
0answers
52 views

Chi Square Formula and Degrees of Freedom Questions

I have a population sample with 200 points of data and 3 degrees of freedom so am I supposed to do a chi square formula with all 200 points of data? I believe that is what I'm supposed to do but I'm ...
2
votes
1answer
55 views

Is it possible to have two lines of best fit?

Could you rig a data set to have two lines of equally good (and best) fit? Or is it impossible?
1
vote
0answers
48 views

Increase the probability of correct prediction using multiple regression

First off let me begin by saying that I'm brand new to statistics and I would appreciate it if you could dumb down any answers for my problem. I am trying to create a general prediction of how much a ...
0
votes
0answers
15 views

How do I get the proper p-value of a time series average of regression coefficients?

I have run cross-sectional regression on the returns of 50 companies on 16 regressors, for 128 days. The regression output looks something like this: ...
0
votes
2answers
45 views

How to find more than two coefficient for single variable nonlinear equation?

I don't have good knowledge on mathematics, but now I faced one problem with maths. That is, I have a data set which contains only one independent and one dependent variable. Now I have a equation ...
0
votes
0answers
25 views

Logistic regression - How to interpret a graph?

Can somebody help me to understand these two graphs. I don't know how to interpret them correctly. Thanks!
1
vote
0answers
38 views

Linear regression of time series data - moving linear regression

Situation A suitable analogy for my real-world problem would be a shop - customers arrive, spend a random amount of time in the shop and leave. The arrival behaviour of customers follows a Poisson ...
0
votes
0answers
10 views

Difference Between Three Similar Error Reducing Algorithms

I found a Least Square Error Recognition algorithm that finds the least mean square error from a 2-d matrix element by element. Logistic regression from this site, on the other hand, seeks to ...
0
votes
0answers
22 views

L1 regression statistics

Consider fitting the below dataset using L1 regression: x: 8.3 8.3 12.1 12.1 17.0 17.0 17.0 24.3 24.3 24.3 33.6 y: 224 312 362 521 640 539 728 945 738 759 663 Why do the regression estimates ...
0
votes
0answers
968 views

How do I find Sxx in a Simple linear regression model?

In a Simple linear regression model, I have only Sxy and Syy data with me. How shall I derive Sxx, linking Sxy and Syy based on first principles? I know the formulas separately. I want to find Sxx, ...
0
votes
0answers
33 views

Classical Regression Model: Combining linearity and strict exogeneity

I am studying the Classical Regression Model for random samples. Hence consider the random sample $(y_i,\mathbf{x_i})$ Where: ...
0
votes
0answers
19 views

How to derive F statistic for general linear hypothesis

I want to derive the F statistic for general linear hypothesis $H_0$ : T$\beta$ = c vs $H_1$ : T$\beta$ $\not =$ c where T is $p * q$ matrix with rank q I have tried to express $SS_{Res} (RM)$ - ...