Using data from 100 hospitals, a correlation of r = 0.78 is found between the si
ID: 3024026 • Letter: U
Question
Using data from 100 hospitals, a correlation of r = 0.78 is found between the size of a hospital (measured in number of beds) and the average length of patient stays (measured in days). Which of the following is true?
There is a pretty strong positive linear correlation between number of beds and length of hospital stay.
Increasing hospital size must be the cause of longer patient stays.
“Severity of illness” is a possible lurking variable that is behind this relationship.
Suppose the correlation between two variables (x, y) in a data set is determined to be r = 0.63, What must be true about the slope, b, of the least-squares line estimated for the same set of data?
The slope b is always equal to the square of the correlation r.
The slope will have the opposite sign as the correlation.
The slope will also be a value between 1 and 1.
The slope will have the same sign as the correlation.
Please explain so I understand how to do it! Thank you!
Explanation / Answer
Using data from 100 hospitals, a correlation of r = 0.78 is found between the size of a hospital (measured in number of beds) and the average length of patient stays (measured in days). Which of the following is true?
Correlation does not indicate causation because there could be a lurking variable that is responsible for association between variables. Therefore, correct option is:
“Severity of illness” is a possible lurking variable that is behind this relationship.
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Suppose the correlation between two variables (x, y) in a data set is determined to be r = 0.63, What must be true about the slope, b, of the least-squares line estimated for the same set of data?
Slope and correlation have same sign.Therefore, correct option is:
The slope will have the same sign as the correlation.
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