Question
Find the correlation coefficient of the following linear equation using technology (such as GeoGebra). For your r-value, use the first two decimal places, if necessary.
y=5x+27
(1 point)
Responses
−1
negative 1
1
1
0
0
10
10
y=5x+27
(1 point)
Responses
−1
negative 1
1
1
0
0
10
10
Answers
GPT-4o mini
To find the correlation coefficient for the linear equation \(y = 5x + 27\), we recognize that the equation describes a perfect linear relationship between \(x\) and \(y\).
In this case, the correlation coefficient (\(r\)) for a perfect linear relationship is either \(1\) or \(-1\), depending on the direction of the relationship. Here, since the slope (5) is positive, the correlation coefficient is \(1\).
So, the value of the correlation coefficient for the equation \(y = 5x + 27\) is:
**1**
In this case, the correlation coefficient (\(r\)) for a perfect linear relationship is either \(1\) or \(-1\), depending on the direction of the relationship. Here, since the slope (5) is positive, the correlation coefficient is \(1\).
So, the value of the correlation coefficient for the equation \(y = 5x + 27\) is:
**1**