How correlation coefficient is Independent of Units of

Coradossi7xod 2022-03-27 Answered
How correlation coefficient is Independent of Units of Measurement?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Answered 2022-03-28 Author has 16 answers
Correlation a measure which indicates the “go-togetherness” of two data sets. It can be denoted as r. The value of correlation coefficient lies between –1 and +1. The positive 1 indicates that the two data sets are perfect and both are in same direction. The negative 1 indicates that the two data sets are perfect and both are in opposite direction. It will be zero when there is no relationship between the two data sets.
Correlation coefficient - r:
The Karl Pearson’s product-moment correlation coefficient or simply, the Pearson’s correlation coefficient is a measure of the strength of a linear association between two variables and is denoted by r or rxy.
The coefficient of correlation rxy between two variables x and y for the bivariate data set (xi,yi) for i=1,2,3…N is given below:
The Pearson’s product-moment correlation does not take into consideration whether a variable has been classified as a dependent or independent variable. It treats all variables equally. A change of scale and origin does not affect the value of r. Indeed, the calculations of Pearson’s correlation coefficient were designed in such that the units of measurement do not affect the calculation. This allows the correlation coefficient to be comparable and not influenced by the units of the variables used.
From the above said points, it is clear that, rxy=ryx. In the formula for r, if we exchange the symbols x and y, then the result is same. This is because the formula is not dependent on the symbols.
It measures the degree of linear relationship between the variables. When we construct the correlation coefficient, the units of measurements that are used, cancel out. Thus, the correlation coefficient is independent of units of measurement.

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-07-10
Suppose that λ 1 ( A ) λ 2 ( A ) λ n ( A ) are (real) eigenvalues of a Hermitian matrix A and denote the empirical measure by L A := 1 n i = 1 n δ λ i ( A ) . Let F A to be distribution function related to the (counting) measure L A . We have the following integration by parts formula
g d L A g d L B = ( F A F B ) d g ,
in which g   : R R is a bounded function with bounded total variation. I am curious whether the integration by parts in this case is connected to Abel's summation by parts, and if so, can anyone explicitly present the connection?
asked 2022-05-24
Let ( X n ) n 0 be a sequence of random variables and τ , t stopping times with respect to the sequence ( X n ) n 0
{ τ + t = n } = { τ + t = n } { t n } = k = 0 n { τ + t = n } { t = k } = k = 0 n { τ = n k } { t = k } .
As { τ = n k } F n k F n and { t = k } F k F n for any k n, this implies that { τ + t = n } F n , and so τ + t is a stopping time.
Now, my question is, let assume that I am considering τ t I know that in general, τ t is not a stopping time. However, if I were to consider my birthday this year (a stopping time), which is a deterministic stopping time. At any time, I know exactly when my birthday occurs. Also, I know two days before my birthday i.e, τ 2. What kind of a formulated counterexample will show that τ 2 is indeed a stopping time in this setting.
asked 2022-03-23
Four student measured the same volume of a glass of water. They all made three trials and summarized their results in the given table. Suppose the accepted volume of the glass of water is 4.20 mL. Analyze the table below and answer the following questions.
5. Who has a precise but not accurate measurement? Why?
6. Who has an accurate but not precise measurement? Why?
7. Who has an accurate and precise measurement? Why?
 Volume of Water in the Glass (mL)   Trial  Andrew  William  Diane  Lianne 16.907.604.324.2425.017.624.304.2638.807.654.294.25 
asked 2022-05-20
Guiding question:Should measure theory be learned before functional analysis or should it be the other way around?
Perhaps there is no largely agreed upon answer to this so I'll ask:
More specific question: What connections are there between the two subjects that might make a person choose to study one before the next?
All feedback is appreciated.
asked 2022-05-14
We want to prove the following implication :
A F S A { S T } F T
Since A F S , we have A F and A { S t } F t .
We will then show that
A { S T } F T
Meaning :
A { S T } { T t } F t
We have :
A { S T } { T t } = A { S t } { T t } { S t T t }
The ''chosen'' set { S t T t }, according to the book, guarantees that the stopping time S will be less or equal to T, and at the same time, the chosen set is in fact F t -measurable, which helps a lot in the proof
It's not very clear to me where it did come from.
I understand that
{ S T } { S t } { T t } , t R +
but the exact choice of { S t T t } is still not obvious.
asked 2022-04-21
In a study, the data you collect is wage per hour. What is the level of measurement?
a. ratio
b. nominal
c. ordinal
4. interval
asked 2022-06-17
State the number of possible triangles that can be formed using the given measurements, then sketch and solve the triangles, if possible.
m A = 48 , c = 29 , a = 4

New questions