Briefly explain what it means by "High correlation does not imply causality." Give an example of two variables that are strongly correlated but no conclusion can be made for "a change of one causes a change of the other".

Briefly explain what it means by "High correlation does not imply causality." Give an example of two variables that are strongly correlated but no conclusion can be made for "a change of one causes a change of the other".

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

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Briefly explain what it means by "High correlation does not imply causality."
Give an example of two variables that are strongly correlated but no conclusion can be made for "a change of
one causes a change of the other".

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2a. Give examples of two variables that have a strong positive linear correlation and two variables that havestrong negative linear correlation.2b. Explain in your own words why the linear correlation coefficient should not be used when its absolutevalue is too low or close to zero. Give an example.2c. In the passage below identify the explanatory variable and the response variable. Explain why youanswered this way.A nutritionist wants to determine if the amounts of water consumed each day by persons of the same weight and on the same diet can be used to predict individual weight loss.
Does a high value of r2 allow us to conclude that two variables are causally related? Explain. - A high value of r2 can only allow us to conclude that two variables are causally related in linear relationships, but not in nonlinear relationships. - Yes. Regression or correlation analysis always allows us to conclude that two variables are causally related. - A high value of r2 can only allow us to conclude that two variables are causally related in nonlinear relationships, but not in linear relationships. - No. Regression or correlation analysis can never allow us to conclude that two variables are causally related. - Yes. Since r2 is the percentage of the total sum of squares that can be explained by using the estimated regression equation, a high value of r2 allows us to conclude that two variables are causally related.
If we find that there is a linear correlation between the concentration of carbon dioxide in our atmosphere and the global temperature, does that indicate that changes in the concentration of carbon dioxide cause changes in the global temperature? Choose the correct answer below. A. No. The presence of a linear correlation between two variables does not imply that one of the variables is the cause of the other variable. B. Yes. The presence of a linear correlation between two variables implies that one of the variables is the cause of the other variable.
Give a plausible example of a three-variable research problem in which partial correlation would be a useful analysis. Define X1, X2, and Y. Make sure that you indicate which of your three variables is the "controlled for" variable ( X2). What results might you expect to obtain for this partial correlation, and how would you interpret your results (e.g., spurious correlation, mediation, moderation, and so on)?
Which of the following statements about correlation are true? Check all that apply. If the correlation between two variables is 0, there is no clear linear relationship between the two variables. Correlation measures and describes the behavior of a single variable. A correlation of 1 indicates that there is little or no linear relationship between the two variables. If the correlation between two variables is –1, it indicates a perfect negative linear relationship between the two variables. A negative correlation means that two variables tend to change in opposite directions. The correlation indicates the strength and the direction of the linear relationship between two variables. If the correlation between two variables is close to 1, there is a positive linear relationship between the two variables.
In general, a zero correlation means as the values of one variable increase, there is a tendency for the values of the other variable also to increase. as the values of one variable increase, there is a tendency for the values of the other variableto decrease. as the values of one variable increase, there is no tendency for the values of the other variable to change in any consistent, predictable fashion. as the values of one variable decrease, there is a tendency for the values of the other variable also to decrease.
Help please!
A zero correlation bewteen X and Y is least likely to occur if?
A scientist, who wants to study the effects of precipitation on rice crops, sets up an experiment with 4 groups of rice crops. Rice crop harvest vs. precipitation level Group B Group A 0 150 Group C Precipitation (cm/annually) Harvest (pounds/acre) 0 60 Which statement best describes the relationship between the dependent and independent variables in this study? 20 O The amount of precipitation is dependent on the amount of rice harvest. O The amount of rice harvest is positively correlated with the increase in precipitation. The amount of rice harvest is not affected by the amount of precipitation. The amount of rice harvest is negatively correlated with the increase in precipitation. 200 Group D 40 300
A phrase often repeated in this class is "correlation is not causation". Which of the following best describes what this phrase means? Correlation is not causation means that just because two values appear to be related on a graph doesn't mean that one necessarily causes the other. Correlation is not causation means that when we see values that move together (e.g. ice cream sales and murder rates), we can assume that one must be causing the other. Correlation is not causation means that if values move in opposite directions (e.g. average temperature goes down and grades go up), we can assume that one must influence to the other. O Correlation is not causation means that when values are shown to be related in a graph, this is proof that they are not causal.
The coefficient of correlation will be zero if if the relationship between two variables x and y is non-linear. if there is no linear relationship between two variables. if the covariance between two variables x and y is 1. None of the above.
What does a correlation coefficient of 2 indicate? There is a weak relationship between the two quantitative variables. It indicates a calculation error, as the correlation coefficient cannot be 2. There is a strong relationship between the two quantitative variables. It indicates a non-linear relationship between the two quantitative variables. There is no linear relationship between the two quantitative variables.