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, 4, point, 5a=4.5
b, equals, 2, point, 2b=2.2
r, equals, 0, point, 8, 6, 7, 3r=0.8673 Regression 2
y, equals, a, x, plus, by=ax+b
a, equals, 14a=14
b, equals, minus, 1, point, 2b=−1.2
r, equals, 0, point, 5, 8, 9, 8r=0.5898 Regression 3
y, equals, a, x, plus, by=ax+b
a, equals, 3, point, 5a=3.5
b, equals, 18, point, 9b=18.9
r, equals, 0, point, 8, 6, 5r=0.865 Regression 4
y, equals, a, x, plus, by=ax+b
a, equals, 9, point, 7a=9.7
b, equals, 12, point, 5b=12.5
r, equals, 1, point, 0, 7, 2, 4r=1.0724
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 should focus on the \( r \) value, which is the correlation coefficient. The closer the \( r \) value is to 1 (or -1), the stronger the linear relationship.

Here are the \( r \) values for each regression:

- **Regression 1**: \( r = 0.8673 \)
- **Regression 2**: \( r = 0.5898 \)
- **Regression 3**: \( r = 0.865 \)
- **Regression 4**: \( r = 1.0724 \)

However, a correlation coefficient must be between -1 and 1. Since Regression 4 has an \( r \) value of 1.0724, it is not a valid correlation coefficient.

Now, comparing the valid \( r \) values:

- Regression 1: \( r = 0.8673 \)
- Regression 2: \( r = 0.5898 \)
- Regression 3: \( r = 0.865 \)

The strongest linear relationship based on the largest valid \( r \) value is:

**Regression 1** with \( r = 0.8673 \).

Therefore, the answer is:

**Regression 1**.