# Questions tagged [regression]

This tag is for questions on (linear or nonlinear) regression, which is a way of describing how one variable, the outcome, is numerically related to predictor variables. The dependent variable is also referred to as $~Y~$, dependent or response and is plotted on the vertical axis (ordinate) of a graph.

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### Linear regression plot does not look linear, does it mean I can do better?

so i am using the fetch_california_housing() dataset from scikit-learn and did some simple linear regression with this. Here is a screenshot of the dataset characteristics. I plotted the predicted ...
21 views

### Line of Best-Fit Between Two Polymetric Curves

I have been using basic regression in excel to find the correlation between two variables. I have since been able to produce two curves in an attempt to model the variable against each other. Two ...
37 views

### Function fitting curve

I have $(x_1,y_1),\dots (n_n,y_n)$ experimental data. I know that the function for fitting data is $$y=21-A\left(1-\text{exp}\left(-(B+Cx)^D\right)\right)$$ Of course, I can not use Linear Regression. ...
1 vote
28 views

### How to correct the output when using LPM (Linear Probability Method)?

I have a .csv with 10 inputs and 1 output. The "problem" is that the output is binary ("0" or "1"). I am using multiple linear regression to predict the output. From ...
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### Mean value of linear regression with another regression

A survey is given to adults in each family. $a$ is the age of the adult,and $b$ is the age of the oldest child - these are recorded. The ages of the oldest child are summarized in the following box ...
36 views

### Best regression model for points that follow a sigmoidal pattern

I have the following list of points : I'm trying to find the best regression model to fit these points. The logistic regression is not close enough to the points : I guess I need something closer to ...
1 vote
29 views

### Simplification - Power of diagonal matrix and circulant matrix [closed]

I am solving a matrix equation for the elements of the diagonal matrix $D$. Therefore, I must find vector real vector $e$, where $D = diag(e)$. Vector $x$ and $y$ are given and are complex vectors. V ...
28 views

### Find parameters of a gaussian transformation

I have a system of equations where the relationship between input and output is derived from a pixel lattice: \begin{equation} x_i(k+1) = \sum_j \alpha e^{ \frac{\left(dr_{ji}^2 + dc_{ji}^2 \right)}{2 ...
37 views

### Do Gaussian Processes not generalize well out of the training range?

I'm a beginner of the Gaussian Processes (GPs). I would like to know the generalizability of GPs. I trained a GP using training data generated by an objective function (the range $-5<x<5$, 10 ...
11 views

### How to calculate sample standard deviation of the intercepts that are obtained from all possible combinations (having $n \ge 3$ points)?

Starting with an example: Having the points $P_1(1,29),P_2(2,50),P_3(4,88)$. Then there are $4$ possible ways to choose points to find the "best" line (using ordinary least-squares). The $4$ ...
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1 vote
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### Loss function for regression - vanishing cross term

[From PRML Bishop, p:48] I do not understand how the cross term vanishes in the integration. I have tried writing this out, but it does not really make sense to me. The same operation happens in "...
25 views

### Regression calculation of initial individual weight considering variations in weighing dates and missing data

I need to determine the initial individual weight of each animal as accurately as possible, taking into account the following challenges: The animals may be weighed on different days. There may be ...
1 vote
14 views

### Solution of RBF constraint least squares

I have to design a matrix A that solves a linear system: $𝑦=𝐴𝑥$, where x is a known complex vector and y is a known complex vector. The requirement is that A is an RBF kernel, i.e., it has the ...
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### $$ Does good $R^2$ necessarily tells us that the experiment went right? $$ Is not extrapolation dangerous when used for a far point?

In an experiment, the relation between $x$ and $y$ is linear. $x_\text{actual} = \alpha_x x_\text{observed} + \beta_x + \gamma_x$. [Here, $\alpha$ is the slope, $\beta$ is the intercept, and $\gamma$ ...
17 views

### High values of r^2 and residual sum of squares

The table below shows the average time T it takes for a computer to sort n items n (items) 5 10 50 100 500 1000 T (microseconds) 17.4 28.2 157.6 305.5 ...
23 views

### A parametric model for inverse of quadratic equation

I have data $\left\{ q_i, p_i \right\}_{i = 1}^{N}$ from a model $p_i = a q_i^2 + b q_i + c$: I know data is always in the positive quadrant as $q_i \geq 0, \, p_i \geq 0$ and I also know $a > 0$ (...
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### How can I calculate p-values, t-statistics, and Standard Error for multiple regression by hand?

I'm attempting to calculate p-values and t-statistics for multiple regression, but all the resources I've been finding on the topic have confusing or inconsistent information. The best resource I've ...
17 views

### Need help with regression exercises

I'd an exam recently and I got 2 exercises from regression part of an exam I couldn't have solved. Can you help me. I will provide both exercises and my attempts to solving them. Exercises: Based on ...
24 views

### When does averaging affect a linear regression?

Given the following: data $(x_{data},y_{data})$, where x values may be measured multiple times. For example, $$x_{data} = ( 1, 2, 2, 3,3,3, 4 )$$ $$y_{data}=(8,10,9,1,2,1.5,−7)$$ And a fitting ...
36 views

### Comparison of regression coefficients between simple and multiple linear regression models

Let's say we want to predict weight ($y$) of a person based on age ($x_1$) using linear regression. Assume a simple linear regression $y = m*x_1 + c_1$ Now we want to include height ($x_2$) of a ...
74 views

### How do I fit "diamond" ellipsis curve?

I have bunch of x,y data that at first seem to be fittable with a logarithmic function. My current plot looks like this: As you can see, the logarithmic fit using ...
1 vote
66 views

### How is the regression coefficient derived?

Searched quite a bit in the forum but cant find this. In Wikipedia the derivation of the regression coefficient for simple linear regression is skipped and points to a book that isn't freely available....
66 views

### Geometry of linear regression

In this image, a linear regression fit is made to the data points $X\in \mathbb R^{N\times 2}$. As you can see, the fitted values $\hat y$ is inside a plane/hyperplane. However, in linear regression, ...