# Tagged Questions

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### Difference between identity and diagonal covariance matrices

thanks in advance for the help. Suppose I am training a linear model. What are the conceptual differences between using a diagonal covariance matrix and the identity? It is clear to me that the ...
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### Calculating Pearson correllation

I'm doing some Pearson Correlation for the first time and could use a little help. What I have is a grid of film ratings for different users and I need to calculate the correlation between each user ...
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### The meaning of correlation coefficient and p-value

I found the following quote in a study, but I'm not sure exactly what it means: Using linear regression, the immunization schedules of these 34 nations were examined and a correlation ...
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### Determine Patterns

I have some weather data that I would like to analyze. I have about a millions rows of data, and each row has about 100 attribute values. Each attribute value represents some measurement (i.e., ...
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### Regression with Mean, Standard Deviation, Range and Correlation

A research team collected data on students in a statistics course. Their dependent variable was the student’s score on the final examination, which ranged from 200 to 800 points. The observed average ...
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### Sample Size for Correlation Testing

A research team wishes to test the null hypothesis: $H_0, r=0$ at $\alpha = 0.025$ against the alternative: $H_1, r>0$ using Fisher’s transformation of the Pearson product moment correlation ...
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### Work out if the relationship between 2 datasets is constant

I have 2 one-dimensional datasets, let's call them a and b. I want to know the correlation between ...
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### What test should I use to statistically compare two intraclass correlation coefficients (ICC)?

I need to compare two generalizability (G) coefficients for data that are from two separate populations. G coefficients are a type of intraclass correlation coefficient (ICC). The literature on ...
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### Correlation Statistic with a neutral score

I'm trying to develop a correlation statistic to compare lines/random variables (represented as a series of points). I want the correlation value to convey little information if one the lines is a ...
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### Difference between Kendall tau distance and Kendall tau rank correlation coefficient

What is the difference between Kendall tau distance and Kendall tau rank correlation coefficient? Which one I should use to calculate how similar two arbitrary permutations of ranks are? Suppose, we ...
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### Expectation and convolution question.

I am learning in an image processing course, and the professor did the following: As part of a derivation, has this: What I do not understand, is how he was able to remove $r(i,j)$ to the ...
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### factor analysis for given data

suppose that we have following data i have done covariance matrix and eigenvalue decomposition ...
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### Multiple correlation

My question is very elementary. I need to implement a software that computes the multiple correlation of a set of datas that I have. In order to do that, I need would like to find the generic formula ...
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### Interval of non-uniformly distributed set of numbers adjusted that it properly excludes extremes

Let's say I have an interval of numbers from 1 to 9 with the following frequency of distribution: numbers 1, 2 and 3 about 20 occurrences number 6 has 2 occurrences and number 9 has only ...
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### calculate direct and indirect path coefficients

suppose we have following data wth mean and standard derivation corresponding ...
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### Multiple regression and hypothesis test $H_0$:$\beta_2=0$

Multiple regression model $H_0$:$\beta_2=0$, $H_1$:$\beta_2 \neq 0$ where $\beta_2$ is the vector of elements ($\beta_2, \beta_3, \dots, \beta_k$) and $\beta$ is slope of regression line. Why it is ...
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### Redundancies in covariance matrix

We know that covariance matrix is symmetrical. I have a vague intuition that there may be some other redundancies beyond that. For example, if A is correlated to B and B is correlated to C then A and ...
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### A question about Pearson correlation coefficient

Suppose that we have two vectors $x=(x_1,\ldots,x_n),y=(y_1,\ldots,y_n)$ is the following correct about their Pearson correlation coefficient? $\operatorname{corr}(x,y)=\operatorname{corr}(x+a,y+b)$ ...
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### Curve Fitting and Multiple Experiments

Say I do an an experiment 5 times, each of which gives you a list of data points. Do I fit a curve to each one separately and then average the parameters and their uncertainties? Or do I take the ...
I'm trying to work out an expression for a correlation of the weighted sums of two r.v.'s with a third r.v. To be precise, I have a trivariate normal distribution: $$\{X,Y,Z\}\approx ... 1answer 262 views ### Proving Y = aX + b given correlation coefficient |\rho(X, Y)| = 1 With correlation coefficient defined as:$$\rho(X, Y) = \frac{\text{Cov}(X, Y)}{\sqrt{\text{Var}(X)}\sqrt{\text{Var}(Y)}}$$can you help me prove$$|\rho(X, Y)| = 1 \implies Y = aX + b
I have 500 observed data of variable $x$ and corresponding $y$. The functional model is where Is it possible to find suitable constants $A , B$ ,$\alpha , \beta$ so that the observed ...