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.

Regression is a statistical measurement used in finance, investing and other disciplines that attempts to determine the strength of the relationship between one dependent variable (usually denoted by $~Y~$) and a series of other changing variables (known as independent variables).

Types of Regression –

  • Linear regression
  • Logistic regression
  • Polynomial regression
  • Stepwise regression
  • Stepwise regression
  • Ridge regression
  • Lasso regression
  • ElasticNet regression

The two basic types of regression are linear regression and multiple linear regression.

The general form of each type of regression is:

  • Linear regression: $~Y = a + b~X + u~$
  • Multiple regression: $~Y = a + b_1~X_1 + b_2~X_2 + b_3~X_3 + ... + b_t~X_t + u~$

Where:

  • $Y =~$ the variable that you are trying to predict (dependent variable).
  • $X =~$ the variable that you are using to predict Y (independent variable).
  • $a =~$ the intercept.
  • $b =~$ the slope.
  • $u =~$ the regression residual.

There are multiple benefits of using regression analysis. They are as follows:

$1.~$ It indicates the significant relationships between dependent variable and independent variable.

$2.~$ It indicates the strength of impact of multiple independent variables on a dependent variable.

Reference:

https://en.wikipedia.org/wiki/Regression_analysis

This tag often goes along with the tag.

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what's the bias of y = $a(x+\epsilon) + b$ linear regression

It is an interview question, I simplify the question as dim = 1, it is better if the solution is about multiple dimension. We know that the assumption of OLS is $$y = ax+b+\epsilon,\quad \epsilon\sim N(0,\sigma^2).$$ And its estimation is unbiased.…
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Programmatic Cubic Regression

All, Thanks in advance for your help. There're a lot of "low hanging fruit" problems at work I need to tackle as a tech-level employee. One of them is curve-fitting 6 data points to a cubic curve, and the other regression questions don't address it…
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Is there a formula for non-linear regression equations?

I'm trying to code a regression calculator, because I like setting stupid challenges for myself that have been done before. I know what the formula for linear regression is already (I think): $a= \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{n(\sum…
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Conditional mean of distribution?

In a simple linear regression the predicted y values are also the “conditional means” at each x value. For each x value, there is a distribution of y values in the population. How exactly do we know each y value on the regression line is the mean of…
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Exponential Function Regression

I need to find the exponential function y = c0e^(c1*x) using fit in Mathematica for the data points {1850, 1.3}, {1900, 1.6}, {1950, 3.0}, {1980, 4.4}, {2000, 6.0}}.
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Regression coefficient DiD

Following the discussion on: https://www.publichealth.columbia.edu/research/population-health-methods/difference-difference-estimation If we specify the regression equation to estimate the DiD as: $$Y= β_0 + β_1*[Time] + β_3*[Time*Intervention] +…
ceins
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What is the difference between a Statistical Model and Mathematical Model?

I was studying regression and came across the terms statistical and mathematical models. Can anyone please elaborate how a statistical model is different from a mathematical model?
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Interpretation of regression formula returned by computer software

I have a dataset consisting of 744 records. Data exploring software generated an equation I don't know how to interpret in simple words. I really appreciate if you could help me about this matter. This dataset consists of two variables x and y…
inzzz
  • 101
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Multiple regression problems (restricted regression, dummy variables)

Q1. Model 1: $Y=X_1\beta_1+\varepsilon$ Model 2: $Y=X_1\beta_1+X_2\beta_2+\varepsilon$ (a) Suppose that Model 1 is true. If we estimates OLS estrimator $b_1$ for $\beta_1$ in Model 2, what will happen to the size and power properties of the…
postman
  • 181
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Support vector machine regression

Linear SVM Regression: Primal Formula: Suppose we have a set of training data where xn is a multivariate set of N observations with observed response values yn. To find the linear function f(x)=x′β+b, and ensure that it is as flat as possible. What…
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linear regression on calculator

I have the equation T(t)=T_0 e^kt . and some coordinates (t,T). t: (10,20,30,40,50,60). (T: 45,40,37,33,27,24) I transform it to y = ae^bx = lna+bx. I then change the coordinates to the form (x, lny) and use the stat function of my calc to plot in…
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Matrix regression proof that $\hat \beta = (X' X)^{-1} X' Y = {\hat \beta_0 \choose \hat \beta_1}$

Matrix regression proof that $\hat \beta = (X' X)^{-1} X' Y = {\hat \beta_0 \choose \hat \beta_1} $ where $\beta$ is the least square estimator of $\hat\beta$ of $\beta$ attempt So I know ${\hat \beta_0 \choose \hat \beta_1} = {\overline{Y} - \hat…
bob
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Regression to find formulas from dataset (from an RPG game - Warspear Online)

I'm looking for a formulas from an RPG game, to simplify the designation of the elements I used full names instead conventional letters. How the system in game was designed? Are there any dependencies here? Here is the code that you can paste into…
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Fitting a function to a sequence of datapoints (quadratic)

I'm looking for a formula for the next term in a sequence (example from an RPG game). $\begin{matrix} n & f(n)\\\hline 1 & 29 \\ 2 & 33 \\ 3 & 37 \\ 4 & 41 \\ 5 & 46 \\ 6 & 50 \\ 7 & 55 \\ 8 & 60 \\ 9 & 65 \\ 10 & 70 \\ 11 & 75 \\ 12 & 81 \\ 13 & 86…
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Joint Linear Regression hypothesis test

Suppose I have the following joint model: $$ y_{f_i} = \beta_1 + \beta_2 t_i + \beta_3 s_i +\epsilon_i $$ $$ y_{m_i} = \beta_4 + \beta_5t_i + \beta_6 s_i +\epsilon_i $$ where $y_{f_i}$ corresponds to the female portion of the response variable, and…
mrnovice
  • 5,773