Aidyn Crosby

2022-09-29

What is the main difference between correlation and causation? (Answer the question in a short paragraph (roughly 3-5 sentences). If necessary, explain the concept and/or give examples)

cegukwt

Beginner2022-09-30Added 10 answers

Associated variables:

Two variables are associated or related if the value of one variable gives you information about the value of the other variable.

Correlation:

Correlation analysis is used to measure the strength of the association between variables. In other words it can be said that correlation describes the linear associations between quantitative variables.

Required assumptions for correlation:

Unlike association, both the two variables should be quantitative to calculate correlation.

There should be linearly related to calculate correlation coefficient.

The scatterplot should not contain outliers to calculate correlation.Cause-and-effect:

The cause-and-effect occurs between two groups if the one group makes the changes in another group.

Causation:

If one event is the result of the occurrence of other event then the variables of the two events are said to be under causation. In other words, it can be said that there exist causal relationship between the two variables.

The correlation between the two variables does not infer that the change in one variable is the cause of the change in other variables.

Also, correlation does not imply causation.

A study states that there is a high correlation between ‘divorce rate in Maine’ and ‘per capita consumption of margarine’.

But this does not imply that the event ‘per capita consumption of margarine’ is the consequence of the event ‘divorce rate in Maine’ because correlation does not imply causation.

Two variables are associated or related if the value of one variable gives you information about the value of the other variable.

Correlation:

Correlation analysis is used to measure the strength of the association between variables. In other words it can be said that correlation describes the linear associations between quantitative variables.

Required assumptions for correlation:

Unlike association, both the two variables should be quantitative to calculate correlation.

There should be linearly related to calculate correlation coefficient.

The scatterplot should not contain outliers to calculate correlation.Cause-and-effect:

The cause-and-effect occurs between two groups if the one group makes the changes in another group.

Causation:

If one event is the result of the occurrence of other event then the variables of the two events are said to be under causation. In other words, it can be said that there exist causal relationship between the two variables.

The correlation between the two variables does not infer that the change in one variable is the cause of the change in other variables.

Also, correlation does not imply causation.

A study states that there is a high correlation between ‘divorce rate in Maine’ and ‘per capita consumption of margarine’.

But this does not imply that the event ‘per capita consumption of margarine’ is the consequence of the event ‘divorce rate in Maine’ because correlation does not imply causation.

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

Which characteristic of a data set makes a linear regression model unreasonable?

Find the meaning of 'Sxx' and 'Sxy' in simple linear regression

In the least-squares regression line, the desired sum of the errors (residuals) should be

a) zero

b) positive

c) 1

d) negative

e) maximizedCan the original function be derived from its ${k}^{th}$ order Taylor polynomial?

Should the independent (or dependent) variables in a linear regression model be normal or just the residual?

What is the relationship between the correlation of two variables and their covariance?

What kind of technique is to be adopted if I have to find an equation or model for say, $D$ depends on $C$, $C$ changes for a set of $B$, which changes for different $A$.

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?

Can you determine the correlation coefficient from the coefficient of determination?

How can one find the root of sesquilinear form with positive definite matrix?

From numerical simulation and regression analysis I discovered that the root-mean-square amplitude of white noise with bandwidth $\mathrm{\Delta}\phantom{\rule{negativethinmathspace}{0ex}}f$ is proportional to $\sqrt{\phantom{\rule{negativethinmathspace}{0ex}}\mathrm{\Delta}\phantom{\rule{negativethinmathspace}{0ex}}f}$. How can this be derived mathematically ?

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 $(.4268,.5914)$.