Question

In simple linear regression, the number of unknown constants are :

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

In simple linear regression, we fit the equation $Y = a + bX$. The two constants are $a$ and $b$. In multiple linear regression with $k$ independent variables, there are $k+1$ constants.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Simple linear regression is a statistical method that models the relationship between a single independent variable ($X$) and a dependent variable ($Y$) using a straight line.
Key Formula or Approach:
The population simple linear regression model is expressed as: \[ Y = \beta_0 + \beta_1 X + \epsilon \] Where: - $\beta_0$ is the intercept parameter (constant).
- $\beta_1$ is the slope parameter (constant).
- $\epsilon$ is the random error term.

Step 2: Detailed Explanation:
To construct the regression line from sample data, we estimate two unknown constants:
1. The intercept ($\hat{\beta}_0$ or $a$): representing the expected value of $Y$ when $X = 0$.
2. The slope ($\hat{\beta}_1$ or $b$): representing the change in $Y$ for a one-unit change in $X$.
Because there are exactly two parameters defining the linear relationship, there are 2 unknown constants.

Step 3: Final Answer:
The number of unknown constants is 2, corresponding to Option (B).