Questions tagged [linear-regression]
For questions about linear regressions, an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables.
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Detecting the multicollinearity from model summary [closed]
I am trying my best to understand how to detect multicollinearity from the model summary. In my picture you can see the model. I have no idea how to do it without using any R commands during the exam....
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$R^2$ of regression of residuals when adding an uncorrelated regressor
Suppose we linearly regress $Y$ onto $X_1$, obtaining residuals $\epsilon_1,\ldots,\epsilon_n$. Suppose further that $X_2$ is uncorrelated with $X_1$, and we linearly regress $X_2$ onto $X_1$ (with ...
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Local Linear Fit
What do you call it when you have a set of known $(x,y)$ data points and you estimate a $y$-value for a given $x$-value by performing a linear fit between its two known neighbor $(x,y)$ points?
As an ...
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Continuous piecewise linear (CPWL) function fitting a dataset for which each linear piece contains at least 3 points
Imagine a 2D dataset $(x_i,y_i)_{i=1,...,N}$ and a univariate continuous piecewise linear (CPWL) function composed of $K$ linear pieces $f$ such each point $i$ belongs to the segment $s(i) \in \{1,...,...
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Removing Independent Variable Uncorrelated with All Other Variables in Linear Regression
I've been looking at Wooldrige's Introductory Econometrics and came across the following section related to omitted variables in multiple regression here
The section essentially says that if an ...
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Using complex phases to do linear regression
The following is non-standard but was interested to see if there is value in following this path.
Consider a linear regression problem without intercept, so simply, $y=ax$ and some data is provided $(...
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Applying Block Bootstrap to Simulate Returns and Conduct OLS Regression for Beta Calculation [closed]
I am facing a methodological issue in my Master's thesis and hope someone can provide some guidance. Background: I have a time series of returns for the S&P 500, a variance swap, and a put option ...
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How do nonlinear relationships affect casuality determination
Let's assume that I have only one independent variable and one dependent, and I have a great model with minimal error which deals well with predicting. Let's also assume that I do no know the true ...
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Appropriateness of one observation per unique combination of dummy variables
I am wondering what conclusions you can draw regarding the coefficients of an OLS model when you only have one observation per combination of unique dummy variables.
I have seen someone else do this ...
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Proportion of variance in a linear regression model with a covaring predictor
Given a model:
\begin{align}Y_{i}=Z_{i}*\beta * X_{i} + Z_{i}\tag{Eq. 1}&\end{align}
I am interested in a closed formula for the proportion of variance explained by the predictor variable $X$, ...
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Can anyone see a way to linearize this function for linear regression?
I have the following function:
$$f(x) = \dfrac{a_1}{(x+b_1)^2+c_1} + \dfrac{a_2}{(x+b_2)^2+c_2}.$$
From multiple measurements of $f$ at known $x$ values I would like find the values of $a_1,a_2,b_1,...
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Correlation vs Regression for a simple task
Hello everyone and thank you for taking the time with my issue! I want to apologize in advance if my question would've fit better on stack exchange, but I decided that the question is more related to ...
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Prove $Max(L_1,L_2,L_3)\neq L_2$:$L_i=\frac{S_i^2}{n_i}+\frac{(S-S_i)^2}{n-n_i}$;$S=\sum S_i$;$n=\sum n_i$;$\frac{S_i}{n_i}>\frac{S_{i-1}}{n_{i-1}}$
I will state my question first, and after that, I will write how I arrived to it.
You do not really need to see how I arrived to the question, but I just thought it would be rude not to explain that.
...
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Weighted Least Squares versus ordinary least squares wiki page
If I have a $(X, Y)$ dataset and want to model $y = f(x, \beta)$. In that case for OLS, I would have
$$e(x_i, \beta) = f(x_i, \beta) - y_i$$
Then obviously I would have
$$SSE = \sum_{i}e(x_i, \beta)^2$...
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Use WLS on difference of data to calculate slope, and OLS for intercept
I have a sequence of data observed in the past X days, which I want to assign higher weights to more recent ones so it makes sense to use WLS over OLS.
However, does it makes sense to use WLS to just ...
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