Question

Which of the following regressions represents the strongest negative linear relationship between x and y?
Regression 1
y, equals, a, x, plus, by=ax+b
a, equals, 15, point, 9a=15.9
b, equals, minus, 14, point, 7b=−14.7
r, equals, 0, point, 7, 8, 3, 9r=0.7839 Regression 2
y, equals, a, x, plus, by=ax+b
a, equals, 3a=3
b, equals, 5, point, 5b=5.5
r, equals, 0, point, 5, 4, 2, 1r=0.5421 Regression 3
y, equals, a, x, plus, by=ax+b
a, equals, minus, 9a=−9
b, equals, 4b=4
r, equals, minus, 0, point, 4, 9, 7, 3r=−0.4973 Regression 4
y, equals, a, x, plus, by=ax+b
a, equals, minus, 6, point, 4a=−6.4
b, equals, 6, point, 4b=6.4
r, equals, minus, 0, point, 7, 1, 2, 3r=−0.7123
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 negative linear relationship, we need to focus on the correlation coefficient (r) values. The correlation coefficient indicates the strength and direction of a linear relationship between two variables.

Here are the provided regressions and their correlation coefficients:

1. **Regression 1**
- r = 0.7839 (positive relationship)

2. **Regression 2**
- r = 0.5421 (positive relationship)

3. **Regression 3**
- r = -0.4973 (negative relationship)

4. **Regression 4**
- r = -0.7123 (negative relationship)

Among the regressions, the one with the strongest negative relationship is Regression 4, as it has the lowest value of r (r = -0.7123) compared to Regression 3 (r = -0.4973).

Thus, the answer is:

**Regression 4**