1
vote
0answers
11 views

Number of significant linear predictors if predictors are not independent?

I would like to determine which of a set of candidate predictors $\{x_1, x_2,\ldots, x_n\}$ are significantly relevant to the linear prediction of $y$. Typically, one can compare a full model ...
0
votes
0answers
8 views

What is the minimum number of data points required to use ARIMA(p,d,q)? [migrated]

I'm using the $\mathrm{ARIMA}$$(p,d,q)$ model to predict future time series data in R (see also R's ARIMA documentation). Q: What is the minimum the number of data points we must have in the time ...
0
votes
1answer
12 views

Multiplying a binary predictor variable with another predictor variable.

Is it completely valid, to have an equation with a certain amount of variables, where two of the variables multiply each other? For example, I want to have an equation $Y = B_0 + B_1X_1 + B_2X_2 ...
2
votes
0answers
92 views

Is it compulsory to make transformation to the econometric model in order to have only diagonal elements on variance-covariance matrix of errors?

I need some sharped and advanced advices for the following issue ... Model and its assumptions I'm working on the methodology of a two-way error component model. Here is the model: $y_{jis} = ...
0
votes
1answer
31 views

Does improving a model's accuracy directly improve the forecast?

Say I have a years worth of data on donut sales, and I use linear regression with variables such as daily occupancy, daily weather etc. because there is a good correlation between each variable and ...
1
vote
1answer
35 views

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 ...
0
votes
1answer
32 views

Cross-Validation

Does anyone understand the paragraph below? The paragraph comes from Cross-valiation explanation at wikipedia. "It can be shown under mild assumptions that the expected value of the MSE for the ...
1
vote
0answers
37 views

Determining how accurate an ellipse fit is

So I have an image of bacteria particles which are often shaped very irregularly with many grooves. Im trying to fit ellipses onto these particles so I can get a better, more smooth analysis of the ...
1
vote
2answers
137 views

Computing $\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Theta)dS$

I'm trying to evaluate the following integral, which I know must be zero, $$\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Gamma)dS$$ Where, $$\langle ...
1
vote
1answer
60 views

Maths concept for salient point in graph data

I have collected data concerning the total post counts of users in an online forum (see graphic). What I am hoping to do is compare the language of 'first posts' with the language of 'later posts'. ...
1
vote
2answers
292 views

There are 5 servers. Each server has 1% downtime. What's the probability that at at least three servers are down?

There are 5 servers. Each server has $1$% downtime. What's the probability that at at least three servers are down? My reasoning is the following: A) There is $(1-0.01)^5$ probability that $5$ from ...
2
votes
2answers
60 views

How can I find a function that accurately matches a x,y scatter plot

I have a complicated piecewise function(see below), that I use in a spreadsheet to determine what a subcontractor get paid on a particular job. For example if a job is worth $$270 dollars the ...
0
votes
1answer
23 views

Apartment re-rental rate follow a Beta or Gamma distribution?

I'm attempting to approximate the variance within how quickly a given housing unit could be re-rented once the previous tenants vacate. Assuming notice is given, it is much more likely that it will be ...
0
votes
1answer
44 views

Probability & Forecasts

I am doing a forecast on turnover and would like to know how i can work out the probability that the next sales figure will be over a certain amount given that we have all the data from previous ...
1
vote
1answer
52 views

How does one model independent trials in statistics.

In my probability class, we covered the proof of the following result, known as the "strong law of large numbers": Theorem. Let $(\Omega,\mathscr F,P)$ be a probability space, $\{X_n\}_{n\in\mathbb ...
1
vote
2answers
141 views

How to derive thresholds from a pooled sample of values

Question: The context of this question is actually finance, however the question itself is a statistical issue. Suppose I have the following expression: $$\rho = \frac{2\bar{x}}{(s^*_x)^2}+1 \ \ ...
0
votes
0answers
22 views

propability of largest samples of repeated random divisions

I have a bunch of numbers $A_1=\{a_{1,1},\dots,a_{n,1}\in\mathbb R^+\}=\{1,\dots,1\}$, that get multiplied by independent uniformly $[0,1]$ distributed samples, e.g. $a_{i,2}=X_ia_{i,2}$. This process ...
1
vote
0answers
25 views

Prediction model from input/output observations

I want to make a prediction model for the following transformation $f:\mathbb{N}^N \rightarrow \mathbb{R}^M$ $N$ is around 20 and vectors $\mathbf{v} \in \mathbb{N}^N$ are sparse with $\sum_{i=1}^N ...
0
votes
2answers
66 views

Modeling dependency between two variables

I want to model the dependence between two variables. Now there are a few ways to do this, for example writing one variable as a function of the other or using correlation. I have also looked into ...
0
votes
0answers
63 views

Financial mathematic with Feynman-Kac

I have a really big task in financial mathematics and a small part of it (to set up the problem), I need to write a PIDE (the Feynman-kac) where we estimate options with jumps. It is derived from the ...
0
votes
0answers
91 views

Understanding degrees of freedom in a standard linear model

So I'm taking a class in applied regression analysis right now, and it is being taught with no theory whatsoever. I am TOTALLY lost on the concept of degrees of freedom. All I've been told / can find ...
1
vote
1answer
121 views

Mathematical model building with dependent and independent variables

I have been working with data and building models on data. I have developed models in regression using cubic and power series. It works fine for variables with one dependent and one independent ...
1
vote
1answer
79 views

How to Prove by definition, the given process is a Markov Process?

Define the process Xt by X0 = 1, and for t = 1, 2, . . . Xt = { uXt-1, with probability p, { vXt-1, with probability 1-p where 0 < v < 1 ...
0
votes
1answer
144 views

Operations research - linear programming help appreciated.

George Weasley, the owner of Weasleys' Wizard Wheezes, recently found that his Skiving Snackboxes have become extremely popular amongst the students at Hogwarts School of Witchcraft and Wizardry, and ...
0
votes
1answer
37 views

Predicting time t given time t-n

..Hi, Everyone! I'm having a bit of trouble with a statistics/forecasting problem and I could use some help. I have temperature measurements for each hour of each day for the past 10 years. Given the ...
0
votes
1answer
78 views

Statistics on three variables/factors

I have what is probably a simple problem. I'm trying to say something about sells of candy bars. I got data of sells for a population of children. There are three parameters (factors) to this data: ...
0
votes
1answer
31 views

Model selection with different error distributions

I have three different models for a given set of data. Each of the models has a different error distribution. These error distributions are known. How can I decide what is the best model?
2
votes
0answers
71 views

Boltzmann machines - motivation for the energy function

I've been studying Boltzmann machines lately and was wondering if anyone could give me a "high-level" explanation or motivation for the energy function used: $$E = -\sum_{i<j} w_{ij} \, s_i \, s_j ...
2
votes
2answers
96 views

Linear Models - Regression Analysis

As a student learning Applied Regression Analysis, I come from a background with very little information about this topic. I understand that given $y = \beta_0 + \beta_1x_1 + \epsilon$ $E(y\mid x) = ...
4
votes
1answer
40 views

Regression model for a shearing process

30 Widgets are randomly assigned to a shearing process. There are 3 such processes, each getting 10 widgets. The lengths of each widget are recorded before undergoing the shearing. The amount that ...
1
vote
0answers
90 views

Best way to statistically compare two polynomial models?

I'm working on modeling and comparing data sets, and I need a good way to see if there is a significant difference between the data from the 2 models. An example of the models are here. I initially ...
3
votes
1answer
63 views

Inverse of itinerary function

Let $S^{-1}:\Sigma \to \Lambda$ be inverse of itinerary function. I showed that $S$ is continuous and bijective. How to show that $S^{-1}$ is continuous?
-3
votes
1answer
255 views

In general, is it easier to solve problems that have random variables, or problems that are basically the same that don't [closed]

This question is asked because I don't understand how random variables will affect various math problems, and knowledgeable mathematicians would. By easier, we mean less steps If we make our own ...
0
votes
1answer
19 views

Smoother Generalized Mixed Linear Models

I wondered if anyone could help me figure out what a smoother was in regard to Generalized Mixed Linear Models or point me in direction of some relevant litterature. Regards!
2
votes
2answers
440 views

Binary Logistic Regression Model Processing

Thanks for showing interest and wanting to help out. My aim is to develop a model that - as accurately as possible - predicts how entities in a population will either cooperate or defect, as a % of ...
2
votes
0answers
72 views

Measuring Model Bias

If given the choice between two statistical models (for argument's sake, let's say Model 1 is $y = \beta_0 + \beta_1 x_1 + \epsilon$ and Model 2 is $y = \beta_0 + \beta_1 x^2_1 + \epsilon$), is there ...
0
votes
1answer
27 views

Is there a statistic model that selects attributes in each state?

Every state has its own sub-attributes, for example, state S{ATTR1, ATTR2, ATTR3}. We can train the model use data with states filled with all three attributes. When we want to predict, we just want ...
1
vote
2answers
82 views

Multiple regression with model $Y = (1 + c_1X_1)(1 + c_2X_2)\ldots(1 + c_nX_n)$

I'm currently working with data contained in $Y, X_1, X_2, \ldots, X_n$ and wish to fit it to the model: $Y = (1 + c_1X_1)(1 + c_2X_2)\ldots(1 + c_nX_n)$ where the $c_i$ are coefficients to be ...
0
votes
0answers
146 views

Figuring out MEMS gyroscope measurement's standard deviation from data sheet

Is it possible to figure out standard deviation of Invensense ISZ500 / IDG500 MEMS gyroscope angular velocities measurement $\mu$ from datasheet? I'm guessing, if at all, the necessary data are ...
2
votes
1answer
138 views

Mathematical idea behind tax bracket

This may be a lame question. The tax bracket is a way to calculate the tax based on the taxable income. For example Imagine that there are three tax brackets: 10%, 20%, and 30%. The 10% rate ...
1
vote
1answer
76 views

Detecting lines and circles in x/y datasets

I'm trying to do some simple gesture recognition. Circles, I'm assuming, will simply be a set of points which are all within some specified distance range from center. Lines on the other hand, I'm not ...
4
votes
0answers
463 views

How did Target figure out a teen girl was pregnant before her father did?

First of all I do not have a mathematics degree only a B.S. in finance so please take that into account when writing an answer. Generally what type of mathematics is involved here? And specifically ...
0
votes
1answer
68 views

Building a model based on sample [closed]

So I have a several samples of data, and I have to come of with some model, that is described by this data. Is there any general approach to this problem? $$ \begin{array}{lll} 0.433873 & ...
2
votes
2answers
133 views

Choosing set of best estimators for linear least squares

I have a measured experimental dataset which is well approximated by the sum of several basis functions in linear combinations. Linear least squares of course gives me the optimal weight for each ...
0
votes
1answer
497 views

How do I fit a model with piecewise linear regression

I have a set of points in 3D (x,y,z). I ordered these points from the lowest to highest. So, I want to used linear regression to fit a line through these ordered points and then to find out a break ...
3
votes
1answer
688 views

Understanding the Pareto distribution as applied to wealth

The Pareto distribution is used to say, given a particular person X, what is the pdf of his wealth. I would like to explore the reciprocal question: Given the total amount of wealth in a population, ...