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 =
4
3
x − 4
(1 point)
2.66
−0.99
0.90
1.00
GeoGebra). For your r-value, use the first two decimal places.
y =
4
3
x − 4
(1 point)
2.66
−0.99
0.90
1.00
Answers
GPT-4o mini
To find the correlation coefficient \( r \) for the given linear equation \( y = \frac{4}{3}x - 4 \), we need to understand that this equation describes a linear relationship. The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables.
For any perfect linear relationship, the value of \( r \) will be either 1 (for a positive slope) or -1 (for a negative slope). Since the slope of the equation \( \frac{4}{3} \) is positive, we can expect the value of \( r \) to be close to 1.
Since this is a direct equation of a line, and you can observe that it's linear with a perfect correlation, the correlation coefficient (r-value) is \( 1.00 \).
Thus, the correct answer is:
**1.00**
For any perfect linear relationship, the value of \( r \) will be either 1 (for a positive slope) or -1 (for a negative slope). Since the slope of the equation \( \frac{4}{3} \) is positive, we can expect the value of \( r \) to be close to 1.
Since this is a direct equation of a line, and you can observe that it's linear with a perfect correlation, the correlation coefficient (r-value) is \( 1.00 \).
Thus, the correct answer is:
**1.00**