Question

Which of the following regressions represents the strongest linear relationship between x and y?

Regression 1
y = ax + b
a=-19
b=-5.7
T=-0.8422
Regression 2
y = ax + b
= 16.7
b=-9.7
T = 1.0952
a=
Regression 3
y = ax + b
= -16.4
A=I
b= 15.2
T= -0.4126
Regression 4
y = ax + b
a = 10.9
b= -12.8
T = 0.0379

Answer 1

The regression that represents the strongest linear relationship between x and y is the one with the highest absolute value of the T-statistic, which is Regression 2 with a T of 1.0952.

Step-by-step explanation:

To determine which of the given regressions represents the strongest linear relationship between x and y, we need to look at the correlation coefficient, often represented as r or T in statistical context. The correlation coefficient measures the strength and direction of a linear relationship between two variables, with values ranging from -1 to 1. A value of 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and values close to 0 indicate a weak linear relationship.

The given regressions provide the coefficients a and b, but more importantly, a value T for each, which we can interpret as the T-statistic related to the correlation coefficient in the context of linear regression. To assess the strength of the linear relationship, we look for the T with the largest absolute value, as this indicates the strongest evidenced relationship, whether positive or negative.

Here, Regression 2 has the largest absolute value of T (1.0952), suggesting it has the strongest linear relationship between x and y.