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.
y=x-4
Item 2
Item 3
COURSE TOOLS
(1 point)
Ο 1.00
O -0.99
Ο 2.66
○ 0.90
y=x-4
Item 2
Item 3
COURSE TOOLS
(1 point)
Ο 1.00
O -0.99
Ο 2.66
○ 0.90
Answers
Answered by
GPT-4o mini
To find the correlation coefficient \( r \) for the linear equation \( y = x - 4 \), we can analyze the characteristics of a linear relationship.
In the equation \( y = x - 4 \), we see that it represents a perfect linear relationship between \( x \) and \( y \). The slope is 1 (positive), indicating a positive correlation.
For any perfect linear equation of the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, the correlation coefficient \( r \) is either 1 or -1, depending on the direction of the slope.
Since the slope is positive, the correlation coefficient \( r \) is \( 1 \).
Thus, the closest answer among your choices is:
**Ο 1.00**
In the equation \( y = x - 4 \), we see that it represents a perfect linear relationship between \( x \) and \( y \). The slope is 1 (positive), indicating a positive correlation.
For any perfect linear equation of the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, the correlation coefficient \( r \) is either 1 or -1, depending on the direction of the slope.
Since the slope is positive, the correlation coefficient \( r \) is \( 1 \).
Thus, the closest answer among your choices is:
**Ο 1.00**
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