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
a = 16.7
b =
T =
-9.7
1.0952
Regression 3
y = ax + b
a = -16.4
b= 15.2
T= -0.4126
Regression 4
y = ax + b
a = 10.9
b= -12.8
= 0.0379
T=
.

Answer 1

Regression 2, with a T value of 1.0952, represents the strongest linear relationship between x and y among the given options because it has the highest absolute T value.

Step-by-step explanation:

To determine which regression represents the strongest linear relationship between x and y, you need to look at the value of T (the t-statistic) in each regression. In the context of linear regression, a higher absolute value of the t-statistic indicates a stronger relationship between the independent variable (x) and the dependent variable (y). A positive t-statistic suggests a positive association, while a negative t-statistic indicates a negative association. However, the strength is determined by the absolute value.

Here are the T values for the given regressions:

• Regression 1: T = -0.8422
• Regression 2: T = 1.0952
• Regression 3: T = -0.4126
• Regression 4: T = 0.0379

Given these values, Regression 2 has the highest absolute value of T at 1.0952, indicating the strongest linear relationship between x and y among the four options provided.