# Tagged Questions

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### Bayesian linear regression cost function

I am studying classification using linear regression . Now, I want to map it in Bayesian regression. Let talk about binary classification using linear regression again. Assume that I have a set ...
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### How to represent the parameters in logistic function

I want to find the parameters in logistic function. I read the guide at here. It very clear to explain. But it did not has final solution that I need. Now, we will consider a basis logistic function ...
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### Model selection in regression: Estimated parameters seem to be “non-significant”

I have conducted an experiment which manipulated three factors (Factor 1: 3 levels, Factor 2: 2 levels, Factor 3: 2 levels). The response variable is binomially distributed (1 = correct or 0 = not ...
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### Variance- covariance matrix

Consider $H$ denotes hat matrix and $e$ denotes residual. In the book Applied regression Analysis by Draper/Smith, it is written that : $\mathbb V(e_i)$ is given ...
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### Dummy recoding for more than two categorical variables

Say I am doing a study with 3 different types of fruit and I want to make a regression depending on the type that tries to predict the amount sold. I know that I could make 2 dummy variables: orange ...
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### Optimizing Independent Variables to Maximize Dependent Variable

I looked around online and couldn't find anything that was answering my question so I thought I would take to the stack! I'm interested in knowing if there is a statistical or mathematical way of ...
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### Linear regression as $\dim(\beta) \rightarrow \infty$

Consider the linear regression, $$Y_i = X_i\beta + U_i \qquad E[X_i'U_i]=0$$ where $X_i=(1,W_{i},W_{i}^2,..\ldots,W_i^K)$ and $\beta \in \mathbb{R}^{K+1}$. The joint distribution of $(X_i,Y_i)$ is ...
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### Derivative of an exponentially weighted moving average

It has been a while since my university math courses, so let me apologize right off the bat... I'm using GSL to perform non-linear regression analysis and am mostly happy with the outcome, however, ...
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### Update a regression on the fly?

Say I have 100 people each with a height, weight, and age. I make a regression that predicts age based on height and weight. Now, I would like to update that model when I meet someone new. I don't ...
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### R squared (Proportion of variance explained) in terms of conditional variance?

My question concerns a comparison between 2 models in terms of proportion of variance explained. Let $y_{t+1}$ denotes the variable I want to explain or predict and $\mathcal{F}_t$ the information ...
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### Unconditional sampling distribution of regression coefficients

I am trying to find the (unconditional) sampling distribution of a regression coefficient in a simple linear regression. The linear regression $Y = \beta_0 + X\beta_1 + \epsilon$ is conducted for $N$ ...
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### Testing if $X_1$ has an influence of $Y$

Consider you have the suspicion that $Y$ is influenced by two attributes $X_1$ and $X_2$: $$Y=\theta_0+\theta_1X_1+\theta_2X_2+\theta_3 X_1X_2+U$$ The following data are given. Test ...
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### When residual standard error is equal to standard deviation of dependent variable in linear regression?

I wonder when residual standard error is equal to standard deviation of dependent variable in linear regression? Could someone provide some information on this topic and explanation?
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### Is the sum of predicted y values equal to the sum of actual y values?

Say I have a set of points Y and I want to accuratly predict the values of Y by using three variables X1,X2,X3. Hence my equation is Y=intercept + C1*X1 + C2*X2 + C3*X3 After performing linear ...
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### Conditional Expectation, Orthogonality, and Correlation

I know that if $\epsilon$ and $x$ are independent, then $E[\epsilon|x]=E[\epsilon]$ and Cov$(\epsilon,x)=0$. However, $E[\epsilon|x]=E[\epsilon]=0$ implies Cov$(\epsilon,x)=0$ iff $\epsilon$ and $x$ ...
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### Trigonometric regression

What methods are performed for regression with trigonometric functions? E.g. : Sequence: $$-1, 0, 1, -1, 0, 1, \text{.....}$$ Regression: ...
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### Why Linear Regression

First i will like to say that i am not a statistician nor am i good in the field. I have been collecting data for over a period of e.g 100 days and each day has a varying amount of data that i can ...
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### Strong vs weak relationship in this correlation

I produced this plot and regression line in R and I thought my results were quite odd. Is the relationship of the correlation determined by how steep the regression line is? So in this case it isn't ...
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### Find sample size underlying these regression results.

I have been trying to work out the answer to this question and have been having no luck, so hopefully you can help. The questions asks you to find sample size from two regression results as below: ...
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### Does more data give you a better forecast?

Say I have a large set of data. Each data point corresponds to a particular day in the year, so for 1 year I will have 365 points. Say I have collected this sort of data for 5 years. Now, I want to ...
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### stats project - good model, what to do with it?

I've recently been working on a stats project for school. I have been comparing a country's 'quality of life index' with 'moral' opinions survey to see if there are relations. Here's some example ...
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### Help larry water his tomato plants with math

I have a bit of a real world problem that I believe Math can help me solve. I think it might be easiest to phrase in a manor similar to that of high school textbook. Larry has a device that can ...
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### Variance of Estimated Coefficients in Logistic Regression

I have a logistic regression model with a binary variable as the response and a categorical variable with 3 categories as a predictor. The fitted model is: logit(P(Y=1)) = intercept -0.19*C2 + ...
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### Calculating R-squared with duplicate data

I have the following question regarding the proper usage of R-squared value. Say I have an equation, that predicts energy consumption for the month of a building. One of the input variables accounts ...
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### Determine whether ARMA(p,q) is stationary and/or invertible?

Determine whether an ARMA(p,q) process is stationary and invertible such that $y_t = \sum_{i=1}^{p} \phi_i y_{t-i} + \sum_{i=1}^{p} \theta_{i} \epsilon_{t-i}$ with the restriction that ...
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### multicollinearity with intervals

You have multicollinearity when you have 2 variables (X1,X2) that have a relationship, X1=a+X2 where a is constant. My question is: is there still a multicollinearity issue if a is not constant, ...
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### Intuition and the math behind normalization

What exactly is the purpose of normalization. From what I read, it is to adjust two different sets of values so you can compare them, but I don't understand why, nor the math behind it. Could anyone ...
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### Proofs on regression analysis

How can I prove: 1) estimating population variance $\hat\sigma^2={1 \over n-2}[S_{YY}-{S^2_{XY} \over S_{XX}}]$. 2)expected value of error mean square=$E(EMS)=\sigma^2$ To prove (2): I showed that ...
### What is ${\rm cov}(e_i, \hat y_i)$ in simple linear regression?
The model is $y_i = \beta_0 + \beta_1x_i + \epsilon_i$ What is ${\rm cov}(e_i, \hat y_i)$? What is ${\rm cov}(\epsilon_i, \hat \beta_1)$? What is ${\rm cov}(e_i, \epsilon_i)$? For 1, I am writing ...