Understanding the Equation Y' - a + bX

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.

In the equation Y' - a + bX, Y' represents the predicted value of the dependent variable Y.

Option D: Predicted value of Y, given a specific X value, is the correct answer.

When we have a linear regression model, the equation Y' - a + bX represents the estimated or predicted value of the dependent variable Y. Here's a breakdown of the equation:

• Y' represents the predicted value of Y, which is what we are trying to estimate based on the given equation.
• 'a' is the intercept or the constant term in the equation, which represents the value of Y when X is equal to zero.
• 'b' is the slope or coefficient of X in the equation, which represents the change in Y for a unit change in X.

So, the equation Y' - a + bX allows us to estimate the value of Y given a specific value of X, using the intercept 'a' and the slope 'b'. Therefore, option D is the correct answer.

Let's go through the other answer choices to understand why they are not correct:

• Option A: Slope of the line (represented by 'b') is incorrect because it represents the change in Y for a unit change in X, not the predicted value of Y.
• Option B: Value of Y when X=0 (represented by 'a') is incorrect because it only represents the intercept of the line and does not give the predicted value of Y.
• Option C: None of these answers is incorrect because one of the answer choices (option D) is indeed correct.
• Option E: Y-intercept (represented by 'a') is incorrect because it only represents the value of Y when X is equal to zero, not the predicted value of Y.

Therefore, the correct answer is option D: Predicted value of Y, given a specific X value.