Mathematics score,x and physics score, y, are related by the regression equation Y= 1.2X + 1.5.

Question

What is the value of the regression coefficient?

Answer 1

In the context of regression analysis, the regression coefficient for the independent variable \(X\) (in this case, the mathematics score) is the coefficient of \(X\) in the regression equation.

Given the regression equation:

\[ Y = 1.2X + 1.5 \]

The coefficient of \(X\) is \(1.2\).

Thus, the value of the regression coefficient is 1.2.

Answer 2

Can you elaborate more

Answer 3

Certainly! Let's delve deeper into the concept of regression and what a regression coefficient represents.

What is Regression?

Regression analysis is a statistical technique used to examine the relationship between two or more variables. In simple linear regression, we typically have one dependent variable \(Y\) (in this case, the physics score) and one independent variable \(X\) (in this case, the mathematics score).

The Regression Equation

The general form of a simple linear regression equation is:

\[ Y = bX + a \]

Where:

• \(Y\) is the dependent variable.
• \(X\) is the independent variable.
• \(b\) is the regression coefficient (also known as the slope of the regression line).
• \(a\) is the y-intercept of the regression line.

In your provided equation:

\[ Y = 1.2X + 1.5 \]

Understanding the Coefficients

1. Regression Coefficient (Slope): The coefficient of \(X\) (which is \(1.2\) in this case) indicates the change in the dependent variable \(Y\) for a one-unit change in the independent variable \(X\). So:

   • If the mathematics score \(X\) increases by 1 point, the physics score \(Y\) is expected to increase by \(1.2\) points.
   • In practical terms, this means there is a positive relationship between mathematics and physics scores. Higher scores in mathematics are associated with higher scores in physics.

2. Y-Intercept: The constant term \(1.5\) is the value of \(Y\) when \(X\) is zero. In this context, it would imply that if a student had a mathematics score of 0, their expected physics score would be \(1.5\).

Conclusion

In summary, the regression coefficient \(1.2\) indicates a positive relationship where every increase of 1 unit in the mathematics score results in an increase of 1.2 units in the physics score. Understanding this relationship can help in predicting outcomes and analyzing educational performance across related subjects.