Based on the absolute values of the correlation coefficients, Regression 2 has the strongest linear relationship between x and y, with |r| = 0.9245.
The strength of the linear relationship between two variables, x and y, can be assessed by the correlation coefficient (r) in each regression equation. The correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
Regression 1: |r| = 0.5218
Regression 2: |r| = 0.9245
Regression 3: |r| = 0.8992
Regression 4: |r| = 1.0137
Based on the absolute values of the correlation coefficients, Regression 2 has the strongest linear relationship between x and y, with |r| = 0.9245. The closer the absolute value of the correlation coefficient is to 1, the stronger the linear relationship.
Which of the following regressions represents the strongest linear relationship between x and y?
a 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
b 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
c 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
d 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