Regression Line and Regression Coefficient

The regression line represents the linear relationship between two variables, X and Y. It is a line that best fits the data points and is used to predict the value of Y for a given value of X. The equation of a regression line is represented as Y = a + bX, where 'a' is the intercept and 'b' is the slope or regression coefficient.

Regression Line: Y = a + bX = 5

Given that the regression line is equal to 5, we can assume that the equation of the regression line is Y = a + bX = 5. This means that for any given value of X, the predicted value of Y will be equal to 5.

Regression Coefficient: b

The regression coefficient, 'b', represents the slope of the regression line. It indicates the change in the value of Y for a one-unit change in X. In this case, we need to determine the value of the regression coefficient given that the regression line is equal to 5.

Calculation of Regression Coefficient

To find the regression coefficient, we can compare the given equation of the regression line with the standard regression line equation Y = a + bX.

Comparing the two equations, we can see that the intercept 'a' is not given. However, we can determine the slope 'b' by comparing the coefficients of X.

In the given equation, the coefficient of X is equal to 1, while in the standard equation it is represented as 'b'.

Therefore, the regression coefficient 'b' is equal to 1.

Interpretation

The regression coefficient of 1 indicates that for every one-unit increase in X, the predicted value of Y will increase by 1. Since the regression line is equal to 5, it means that the predicted value of Y will always be 5, regardless of the value of X.

This implies that there is a perfect positive linear relationship between X and Y, where the value of Y is always 5 times the value of X.