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=43x−4 (1 point) Responses −0.99 negative 0.99 2.66 2.66 1.00 1.00 0.90
Answers
GPT-4o mini
To find the correlation coefficient \( r \) for the linear equation \( y = 43x - 4 \), we observe that this is a simple linear regression equation where the slope is 43. For a perfect linear relationship (which this is, since it can be expressed as \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), the correlation coefficient \( r \) will be 1.
This is because:
- The correlation coefficient can range from -1 to 1.
- An \( r \) value of 1 indicates a perfect positive linear relationship.
- Since the slope of the line is positive (43), the \( r \) value is also positive.
Thus, for the equation \( y = 43x - 4 \), the correct correlation coefficient rounded to two decimal places is:
**1.00**
This is because:
- The correlation coefficient can range from -1 to 1.
- An \( r \) value of 1 indicates a perfect positive linear relationship.
- Since the slope of the line is positive (43), the \( r \) value is also positive.
Thus, for the equation \( y = 43x - 4 \), the correct correlation coefficient rounded to two decimal places is:
**1.00**