Question

Which of the following regressions represents the strongest linear relationship between x and y?
Regression 1
y, equals, a, x, plus, by=ax+b
a, equals, minus, 14, point, 3a=−14.3
b, equals, 11, point, 9b=11.9
r, equals, minus, 0, point, 0, 8, 4, 6r=−0.0846 Regression 2
y, equals, a, x, plus, by=ax+b
a, equals, 6, point, 1a=6.1
b, equals, minus, 1, point, 6b=−1.6
r, equals, 0, point, 7, 6, 7, 1r=0.7671 Regression 3
y, equals, a, x, plus, by=ax+b
a, equals, minus, 16, point, 1a=−16.1
b, equals, minus, 17, point, 3b=−17.3
r, equals, minus, 1, point, 1, 0, 0, 2r=−1.1002 Regression 4
y, equals, a, x, plus, by=ax+b
a, equals, 16, point, 5a=16.5
b, equals, minus, 3, point, 3b=−3.3
r, equals, 0, point, 2, 0, 8, 1r=0.2081
Answer
Multiple Choice Answers
Regression , 1Regression 1
Regression , 2Regression 2
Regression , 3Regression 3
Regression , 4Regression 4

Answer 1

To determine which regression represents the strongest linear relationship between \( x \) and \( y \), we need to look at the correlation coefficient \( r \) for each regression:

1. **Regression 1**: \( r = -0.0846 \)
2. **Regression 2**: \( r = 0.7671 \)
3. **Regression 3**: \( r = -1.1002 \) (Note: This value is invalid for a correlation coefficient, which must be between -1 and 1)
4. **Regression 4**: \( r = 0.2081 \)

The correlation coefficient \( r \) indicates the strength and direction of a linear relationship:
- A coefficient close to 1 indicates a strong positive linear relationship.
- A coefficient close to -1 indicates a strong negative linear relationship.
- A coefficient around 0 indicates little to no linear relationship.

Among the valid values, Regression 2 has the highest absolute value for \( r \) (0.7671), indicating a strong positive linear relationship.

Thus, the answer is **Regression 2**.