Final answer:
The formula for the slope parameter in a simple linear regression model in deviation form is ((Yi - Ȳ) - β0 - ui) / (Xi - Ẋ).
Step-by-step explanation:
In a simple linear regression model in deviation form, the formula for the slope parameter is represented as β1. To derive this formula, we can start with the equation Yi = β0 + β1Xi + ui. In deviation form, we replace Yi with (Yi - Ȳ) and Xi with (Xi - Ẋ), where Ȳ represents the mean of Y values and Ẋ represents the mean of X values. Thus, the deviation form of the regression model equation becomes (Yi - Ȳ) = β0 + β1(Xi - Ẋ) + ui. Now, we can perform some algebraic manipulations to isolate β1:
(Yi - Ȳ) = β0 + β1(Xi - Ẋ) + ui
Yi - Ȳ = β0 + β1Xi - β1Ẋ + ui
β1Xi - β1Ẋ = Yi - Ȳ - β0 - ui
β1(Xi - Ẋ) = (Yi - Ȳ) - β0 - ui
β1 = ((Yi - Ȳ) - β0 - ui) / (Xi - Ẋ)
Therefore, the formula for the slope parameter (β1) in a simple linear regression model in deviation form can be derived as ((Yi - Ȳ) - β0 - ui) / (Xi - Ẋ).