Question

A simple linear regression model and is represented as y = β0 + β1x1 + ɛ,; What do β0and β1 (the Greek letters read as betas) represent? (They must be shown in the correct order!)

1. Intercept, slope
2. Dependent, independent
3. Slope, intercept
4. Slope, dependent

Answer 1

In the simple linear regression equation y = β0 + β1x1 + ε, β0 represents the y-intercept, and β1 represents the slope of the regression line.

Step-by-step explanation:

In a simple linear regression model represented by the equation y = β0 + β1x1 + ε, the Greek letters β0 (beta-zero) and β1 (beta-one) represent specific components of the linear equation. The β0 represents the y-intercept of the regression line, which is the value of y when the independent variable x1 is zero. On the other hand, β1 represents the slope of the regression line, indicating the expected change in the dependent variable y for a one-unit increase in the independent variable x1.

Therefore, the correct interpretation of β0 and β1 in the given order is:

1. Intercept (β0)
2. Slope (β1)