Question

The following questions all refer to the population regression model and/or the sample regression model from a bivariate regression model where the population regression model is: Y = α + βX + ε and the sample regression model is: Ŷ = a + bx. Which of the following is the sample y-intercept?

a) a

b) b

c) α

d) β

Answer 1

In the context of bivariate regression models, the sample y-intercept is represented by 'a' in the equation Ŷ = a + bx. It is where the regression line crosses the y-axis.

Step-by-step explanation:

The question here is related to the components of the regression model used in statistical analysis. The specific query is to identify the sample y-intercept in the provided regression equations. In the population regression model Y = α + βX + ε, α represents the population y-intercept while in the sample regression model Ŷ = a + bx, a represents the sample y-intercept. Thus, the correct answer to the question of which of the options represents the sample y-intercept in the regression model is a.

The y-intercept is where the regression line crosses the y-axis, which is the estimated average value of Y when X is 0. It can have meaningful interpretation or could be nonsensical depending on the context of the data being analyzed.