Question

In simple linear regression $Y = \beta_0 + \beta_1 X + \epsilon$, $\beta_0$ and $\beta_1$ are known as

• A. slope and intercept of the regression line
• B. intercept and slope of the regression line
• C. first order slope and first order intercept of the regression line
• D. mean and variance of $X$

Hint:

Always associate $\beta_0$ with the intercept (constant term) and $\beta_1$ with the coefficient of the independent variable $X$ (the slope).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In simple linear regression, we model the relationship between a dependent variable $Y$ and an independent variable $X$ using a straight-line equation.

Step 2: Detailed Explanation:
The standard simple linear regression model is given by:
\[ Y = \beta_0 + \beta_1 X + \epsilon \]
Let us define the parameters:
- $\beta_0$ represents the $Y$-intercept, which is the expected value of $Y$ when $X = 0$.
- $\beta_1$ represents the slope of the regression line, which measures the expected change in $Y$ for a one-unit change in $X$.
- $\epsilon$ is the random error term.
Thus, $\beta_0$ and $\beta_1$ are the intercept and slope of the regression line, respectively.

Step 3: Final Answer
The correct option is (B).