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, 3, point, 9a=−3.9
b, equals, minus, 3, point, 8b=−3.8
r, equals, minus, 0, point, 5, 2, 1, 8r=−0.5218 Regression 2
y, equals, a, x, plus, by=ax+b
a, equals, 17, point, 3a=17.3
b, equals, 16, point, 9b=16.9
r, equals, 0, point, 9, 2, 4, 5r=0.9245 Regression 3
y, equals, a, x, plus, by=ax+b
a, equals, minus, 5, point, 1a=−5.1
b, equals, minus, 14, point, 7b=−14.7
r, equals, minus, 0, point, 8, 9, 9, 2r=−0.8992 Regression 4
y, equals, a, x, plus, by=ax+b
a, equals, minus, 13a=−13
b, equals, minus, 2, point, 3b=−2.3
r, equals, minus, 1, point, 0, 1, 3, 7r=−1.0137
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 coefficients \( r \) for each regression.

The closer the value of \( r \) is to 1 or -1, the stronger the linear relationship:

- **Regression 1**: \( r = -0.5218 \) (moderate negative correlation)
- **Regression 2**: \( r = 0.9245 \) (strong positive correlation)
- **Regression 3**: \( r = -0.8992 \) (strong negative correlation)
- **Regression 4**: \( r = -1.0137 \) (This value is not possible for a correlation coefficient, which must be between -1 and 1)

Given this information, **Regression 2** has the highest absolute correlation coefficient value (0.9245), indicating the strongest linear relationship. Therefore, the answer is:

**Regression 2**