The correlation of sample X with itself is ...

Question

BlackTom AI · Accepted Answer

The provided data shows an incomplete multiple-choice setup: there are no answer options listed to analyze, only an answer field with ["1"] and an empty answer_options array. This means we cannot evaluate which option matches the claimed correct answer, so we must rely on general domain knowledge to address the core concept.

First, consider the question itself: 'The correlation of sample X with itself is ...' In statistics, the correlation of any variable with itself is at its maximum possible value. For Pearson correlation, which measures linear association between two variables, correlating a vector with itself yields r = 1, provided there is variation in the data.

Important nuance: if the sample X has zero variance (i.e., all observed values are identical), the standard Pearson correlation becomes undefined because it involves dividing by the standard deviation of X, which would be zero. In practice, many software packages return NaN or raise an error in this degenerate case, rather than assigning a numeric value like 1.

Assuming a typical situation where sample X has variability (not a constant vector), the correlation of X with itself is 1. If the question intends to address the degenerate case of zero variance, the appropriate answer would indicate that the correlation is undefined or not computable.

Given the absence of answer options, we cannot point to a specific choice or explain why other options are incorrect. However, the central concept remains: for a non-constant sample, the self-correlation is 1; for a constant sample, the correlation is undefined due to zero variance.

If you have the actual list of answer choices, I can map each option to this reasoning and explain precisely why each would be correct or incorrect in context.

ERMCPS5350_003_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 12. Quiz for Class 12

The correlation of sample X with itself is ...

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类似问题

Of the following, the correlation coefficient that indicates the weakest relationship between the two variables being measured is ______________.

The correlation in between mobile usage and exam score of a person found to be -2.2. What is your inference from the above statement.

The correlation between temperature in ◦F and age in weeks was r = −0.70. If we converted the temperature to ◦C and age to months, what would the 29 correlation be?

Their correlation coefficients will be the same, since the correlation coefficient is unitless.

r = −0.85

r = −0.03

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