Which of the following best describes the difference between the interpretation of the correlation coefficient and the beta coefficient for a regression equation expressing the relationship between variables X and Y? A) The beta coefficient represents the linear relationship between X and Y, whereas the correlation coefficient represents the percent variability in Y explained by X B) The beta coefficient represents the difference between observed and expected values of Y, whereas the correlation coefficient represents the linear relationship between X and Y. C) The beta coefficient predicts increases or decreases in Y with increases or decreases in X, whereas the correlation coefficient provides a unit-free measure of the strength of the relationship. D) The correlation coefficient predicts increases or decreases in Y with increases or decreases in X, whereas the beta coefficient provides a unit-free measure of the strength of the relationship.
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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Which of the following best describes the difference between the interpretation of the
correlation coefficient and the beta coefficient for a regression equation expressing the relationship between variables X and Y?
A) The beta coefficient represents the linear relationship between X and Y, whereas the correlation coefficient represents the percent variability in Y explained by X
B) The beta coefficient represents the difference between observed and expected values of Y, whereas the correlation coefficient represents the linear relationship between X and Y.
C) The beta coefficient predicts increases or decreases in Y with increases or decreases in X, whereas the correlation coefficient provides a unit-free measure of the strength of the relationship.
D) The correlation coefficient predicts increases or decreases in Y with increases or decreases in X, whereas the beta coefficient provides a unit-free measure of the strength of the relationship.
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