The Value of 20 in Least Squares Equation

D

The regression is written as Y' = a + bX. The letter "a" is the Y intercept and b is the slope of the line. Y' is the predicted value of Y given a specific value of X.

Here b = 20.

The given equation, Y' = 10 + 20X, represents a linear regression model estimated using the method of least squares. In this equation, Y' represents the predicted value of the dependent variable (Y), and X represents the independent variable.

The coefficient in front of X, which is 20 in this case, indicates the slope of the regression line. Specifically, it represents the change in the predicted value of Y (Y') for each unit increase in X. Therefore, the correct interpretation of the value 20 in this equation is:

D. For each unit increased in X, Y increases by 20

This means that for every one-unit increase in the independent variable X, the predicted value of the dependent variable Y increases by 20 units. It implies a linear relationship between X and Y, where an increase in X is associated with a proportional increase in Y, with a slope of 20.

The Y-intercept, which is the constant term in the equation (10 in this case), represents the value of Y when X is equal to zero. However, it is not related to the value of 20 in the equation.

Therefore, the correct answer is D. For each unit increased in X, Y increases by 20.