Question

Which of the following regressions represents the strongest positive linear relationship between x and y?
Regression 1
y, equals, a, x, plus, by=ax+b
a, equals, 19, point, 3a=19.3
b, equals, 0b=0
r, equals, 1, point, 0, 8, 8, 2r=1.0882 Regression 2
y, equals, a, x, plus, by=ax+b
a, equals, minus, 16, point, 9a=−16.9
b, equals, 1, point, 6b=1.6
r, equals, minus, 0, point, 8, 3, 4, 3r=−0.8343 Regression 3
y, equals, a, x, plus, by=ax+b
a, equals, 13, point, 2a=13.2
b, equals, minus, 15, point, 5b=−15.5
r, equals, 0, point, 0, 6, 9, 4r=0.0694 Regression 4
y, equals, a, x, plus, by=ax+b
a, equals, 7a=7
b, equals, 12, point, 1b=12.1
r, equals, 0, point, 7, 8, 2, 3r=0.7823
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 positive linear relationship between \( x \) and \( y \), we need to look at the correlation coefficient \( r \) for each regression:

- **Regression 1**: \( r = 1.0882 \)
- **Regression 2**: \( r = -0.8343 \)
- **Regression 3**: \( r = 0.0694 \)
- **Regression 4**: \( r = 0.7823 \)

Correlation coefficients \( r \) can range from -1 to 1.
- Values close to 1 indicate a strong positive linear relationship.
- Values close to -1 indicate a strong negative linear relationship.
- Values near 0 indicate little to no linear relationship.

In this case:
- **Regression 1** has an \( r \) greater than 1, which is not possible for a correlation coefficient and suggests a typographical error regarding its validity.
- **Regression 2**'s \( r \) is negative, indicating a negative relationship.
- **Regression 3** and **Regression 4** have positive coefficients, with **Regression 4** having the higher \( r \) value.

Thus, among the valid correlation coefficients, **Regression 4** (with \( r = 0.7823 \)) represents the strongest positive linear relationship.

**Answer: Regression 4**