Question

Consider the regression model Yᵢ=β₀​+β₁​Xᵢ+uᵢ

a Derive the formula for the slope parameter in a simple linear regression model in deviation form.
b. Show that the intercept parameter in a simple linear regression model in deviation form is equal to zero.

Answer 1

The formula for the slope parameter in a simple linear regression model in deviation form can be derived by calculating the covariance between the deviations of Y and X divided by the variance of X. The intercept parameter in a simple linear regression model in deviation form is equal to zero.

Step-by-step explanation:

In a simple linear regression model in deviation form, the formula for the slope parameter (β₁) can be derived by calculating the covariance between the deviations of Y (Yᵢ) and X (Xᵢ) divided by the variance of X.

This can be represented as:

β₁ = Cov(Xᵢ, Yᵢ) / Var(Xᵢ)

For the intercept parameter (β₀) in a simple linear regression model in deviation form, it is equal to zero.

This means that when the deviations of Y (Yᵢ) and X (Xᵢ) are calculated and centered around their respective means, the regression line will pass through the point (0,0) on the scatterplot.