# Questions tagged [mathematical-statistics]

Mathematical theory of statistics, concerned with formal definitions and general results.

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### Linear regression model excel

Suppose you fit the regression model E(Y) = b0 + b1X1 + b2X2. Further, suppose that the p-value associated with coefficient b2 is 0.312. What does this tell us?
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### Deriving the basis functions for natural cubic spline

Im looking through Section 5.2.1 of Elements of statistical learning, and am confused by this section I understand that, from this answer , the definition of $d_k(X)$ is important in order to derive ...
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### Statistic to take account of sensitivity of temperature values

I have a unique problem. I am looking to quantify the difference between two temperature value of different components. I am looking at three statistic to see that difference Absolute mean difference ...
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### Asymptotic Distribution of the Wald Test Statistic

I am trying to understand the asymptotic distribution of the Wald test statistic, specifically under the alternative hypothesis which I've found little reference to. For clarity, the binary ...
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### Linear transformation *not* to use to scale mean and SD

I'm working through the Exercises in Regression and Other Stories. Exercise 3.6 on Linear transformations asks you to provide a formula to rescale a variable with mean = 35 and SD = 10 to have mean = ...
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I have been trying to understand the concept behind factorial design and its importance in connection to linear regression. I will be glad if somebody can give a clear and tone down explanation in ...
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### Is there a commonly-accepted/used notion of parametric statistical model equivalence?

To fix notation, let a set of possible data $X$ and a set of admissible parameter values $\Theta$ be given. Let $\mathscr P(X)$ be the set of probability distributions on $X$. A parametric ...
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### Intuition behind unequal class interval histograms

In a histogram with unequal class interval, say for example, the data: ...
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### Independence of groups within a single predictor variable

Say I have two variables: 'Sale Price' of a house, and 'Overall Quality' which is an ordinal variable with values between 1 and 10 (1=lowest quality, 10=highest quality). I want to perform an F test ...
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### Confidence intervals/ellipses when variables are correlated

I was looking to create a confidence ellipse for my X and Y variable in order to identify potential outliers. I'm new to this area so my understanding and use of this method may be wrong (please ...
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### References for use of symplectic geometry in statistics?

I have heard that many problems in Mathematical Statistics can be stated and solved in terms of Symplectic Geometry. Unfortunately this was a pretty vague statement and I am interested in something ...
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### How to calculate the variance and expected value of a random variable with density function f(x) in R

was wondering how to calculate the expected value and variance of some function f(x). For the Expected value $\mu,$ I integrated x*f(x) and I'm confident that is correct, but I'm confused about how to ...
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### Adjusting OverAll Time Performance using sectional Times

Assume I have two runners, Runner_1 is the average runner and Runner_2 is Usain Bolt. We let the two runners compete in 3 different races on a 100m distance. We assume that the benchmark time for 50m ...
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### Which statement for statistical test is accurate, regarding significance?

Statistical tests between 2 mean shows us whether the difference between sample means is significant given the inherent sample variance. Statistical tests between 2 mean shows us whether the ...
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### What are the units of entropy of a normal distribution?

I have a random process that follows a normal distribution. It's parameters are mean = 35 units, std.dev. = 8 units. I've seen from the wiki entry for the normal distribution that there is a formula ...
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### Bayesian vs Frequentist Prediction Methods and Frequencey Garantees

After reading Larry Wassermans blog on the difference between Bayesian and Frequentist inference I started to appreciate that frequency guarantees can be desirable regardless of the inference method ...
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