# 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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### Are stationarity and low autocorrelation the prerequisite of regression model?

As said in the title, are stationarity and low autocorrelation the prerequisite of general / linear regression model ? That is, if a time series is non-stationary or large autocorrelation, would it be ...
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### How can I calculate the derivative of J(Θ) which contains sigmoid function in linear regression?

I am taking a machine learning course and since my math is extrementy rusty I am not sure how to go about solving this exercise. Given the derivative of the sigmoid function with respect to Θj I need ...
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### prove that $(\hat{\beta}-\beta)'(X'X)^{-1}(\hat{\beta}-\beta)$ and SSE are independent

We have $$(\hat{\beta}-\beta)'(X'X)^{-1}(\hat{\beta}-\beta)$$ and SSE $=\sum_{i=1}^{n}(\hat{y_{i}}-y_{i})^{2}=\sum_{i=1}^{n}y_{i}^{2}-\hat{\beta'}X'y$ and I have to prove that these 2 quantities are ...
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### Why do two different approaches using matrix algebra yield different results?

I am solving a problem involving linear regression and I am finding that two different approaches to the matrix algebra is yielding different results. In the second approach, I am merely simplifying ...
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### What is the estimate coefficient when design matrix is singular, when using the Moore-Penrose generalized inverse matrix?

The OLS estimators is But if $Y$ is a $50 \times 1$ matrix, and the design matrix $X$ is $50 \times 16$. The design matrix $X^T X$ is singular, then what will the estimate coefficient function be, ...
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### Fitting a simple polynomial to different possibilites

I have a few sets of numbers. For example, let's say my sets are - 1,5,8,12,25 2,14,36,45,47 5,9,17,55,80 29,37,64,93,102 48,69,77,86,167 Given these sets, I want to fit a ...
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### How to prove sum of errors follow a chi square with $n-2$ degree of freedom in simple linear regression

In simple linear regression, the model is \begin{equation} Y_i = \beta_0 + \beta_1 X_i + \varepsilon_i \end{equation} where $\varepsilon_i$ are i.i.d., and \begin{equation} \varepsilon_i \sim N(0, \...
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### Show that $X^T X = \sum_{i=1}^n \mathbf{x}_i \mathbf{x}_i^T$

Referring to this post: https://stats.stackexchange.com/questions/164223/proof-of-loocv-formula The line which says $\sum_{t=1}^TX_t'X_t=X'X$ is the result I'm trying to interpret. Or in perhaps ...
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### Consistency of OLS estimation

My question is about consistency of OLS parameter estimate for a linear regression model $y_t = x_t' b + \epsilon_t$ ($t = 1,2, \ldots, T)$. Here $x_t$ and $b$ are $1\times k$ vectors (there are $k$ ...
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### Finding Conditional Expected Value and Conditional Variance

Very stuck with this problem. Not meant to make any more assumptions than laid outin the question. I have a regression model: $\ln(𝑠𝑎𝑣_𝑖)$ = $𝛽_0 + 𝛽_1\cdot \ln (𝑖𝑛𝑐_i) + 𝑢_i$ (where sav ...
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### struggling to understand R output for linear regression with categorical variables

If i where to fit some random linear regression model like fit<-lm(Height~factor(Location)+Daily.calcium.intake+Fathers.daily.prtintake,data=some data set ) as a random example where Location ...
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### Probit vs Linear Probability Model for binary independent variable

I am new to binary regression models. From my understanding, the probit is better than the LPR because it allows for varying marginal effects and constraint Y_hat to be within 0 & 1. However, if ...