Assume the least squares equation is Y' = 10 + 20X. What does the value of 10 in the equation indicate?
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A. B. C. D.C
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 a=10.
In the given least squares equation, Y' = 10 + 20X, the value of 10 represents the Y-intercept of the regression line. The Y-intercept is the value of Y when X is equal to zero.
To understand this concept further, let's break down the equation:
In the equation Y' = 10 + 20X, the constant term 10 represents the Y-intercept. It is the value of Y when X is zero. In other words, when the independent variable X has no effect or is not present, the predicted value of Y is equal to 10.
To illustrate this, let's consider a simple example:
Suppose we have a regression model that predicts the salary of individuals based on their years of experience. The equation for this model is Salary = 10 + 20 * Years of Experience. Here, the constant term 10 is the Y-intercept.
If we set the years of experience (X) to zero, we find that the predicted salary (Y') is equal to 10. This means that a person with zero years of experience is predicted to have a salary of 10 in this model. However, it's important to note that the interpretation may not always be meaningful in every context, as X can represent different variables in different situations.
In summary, the value of 10 in the equation Y' = 10 + 20X represents the Y-intercept, which is the value of the dependent variable Y when the independent variable X is equal to zero. Therefore, the correct answer is option C: Y-intercept.