Leonel Schwartz

2022-10-02

Please, give examples of two variables that have a perfect positive linear correlation and two variables that have a perfect negative linear correlation.

seppegettde

Beginner2022-10-03Added 7 answers

Perfect positive linear correlation:

Correlation coefficient value is +1 then the two variables have perfect positive correlation.

Perfect negative linear correlation:

Correlation coefficient value is -1 then the two variables have perfect negative correlation.

Example of perfect positive linear correlation is: income and expenditure, heights and weights of a group of persons.

Example of perfect negative linear correlation: price and demand of a commodity, the volume and pressure of a perfect gas.

Correlation coefficient value is +1 then the two variables have perfect positive correlation.

Perfect negative linear correlation:

Correlation coefficient value is -1 then the two variables have perfect negative correlation.

Example of perfect positive linear correlation is: income and expenditure, heights and weights of a group of persons.

Example of perfect negative linear correlation: price and demand of a commodity, the volume and pressure of a perfect gas.

Which of the following statements is not correct for the relation R defined by aRb, if and only if b lives within one kilometre from a?

A) R is reflexive

B) R is symmetric

C) R is not anti-symmetric

D) None of the aboveA line segment is a part of a line as well as a ray. True or False

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a) zero

b) positive

c) 1

d) negative

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Correlation bound

Let x and y be two random variables such that:

Corr(x,y) = b, where Corr(x,y) represents correlation between x and y, b is a scalar number in range of [-1, 1]. Let y' be an estimation of y. An example could be y'=y+(rand(0,1)-0.5)*.1, rand(0,1) gives random number between 0, 1. I am adding some noise to the data.

My questions are:

Is there a way where I can bound the correlation between x, y' i.e. Corr(x,y')?I mentioned y' in light of random perturbation, I would like to know what if I don't have that information, where I only know that y' is a estimation of y. Are there any literature that cover it?What is the benefit of OU vs regression for modeling data, say data in the form of ($x,y$) pairs?

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In a Simple Linear Regression analysis, independent variable is weekly income and dependent variable is weekly consumption expenditure. Here $95$% confidence interval of regression coefficient, ${\beta}_{1}$ is $(.4268,.5914)$.