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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.
Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims.
(b) Would you say the
a) moderate and positive
b) low and negative
c) strong and positive
d) strong and negative
e) low and positive
f) moderate and negative
As x increases, does the value of r imply that y should tend to increase or decrease? Explain.
a) Given our value of r, y should tend to decrease as x increases.
b) Given our value of r, y should tend to remain constant as x increases.
c) Given our value of r, y should tend to increase as x increases.
d) Given our value of r, we cannot draw any conclusions for the behavior of y as x increases.
Solution:
The correlation coefficient can be calculated by using the following formula:
Then, the correlation coefficient between X and Y is calculated as follows:
Then,
Thus, the value of the correlation coefficient between X and Y is –0.93. This is negative.
If the correlation value is greater than 0.70, it can be said that the correlation is strong.
Thus, the correlation is strong and negative.
Hence, the correct option is d.
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