The owners of an online shop use a multiple regression model with three independent variables where y = Shipping Cost ($) x₁ = Product weight (kg) x₂ = Number of items x₃ = Total amount ($) The regression model is y = 8.50 + 12x₁ + 0.1x₂ + 0.05x₃ + 0.08x₂x₃ + e Interpret the value of β₁ for this model. A) The average change in shipping costs associated with an increase in the number of items by 1 when the product weight and the total amount are held fixed. B) The average change in shipping costs associated with a 1-dollar increase in the total amount when the product weight and the number of items are held fixed. C) The difference between the slopes of regression lines depending on the total amount and the number of items. D) The average change in shipping costs associated with a 1-kg increase in product weight when the number of items and the total amount are held fixed. E) The average change in shipping costs when the perceived increase value of the number of items by 1 unit depends on the change of the total amount.

Question

Quizplus · Accepted Answer

β1 (represented here as β₁) in the regression equation corresponds to the coefficient of the product weight variable (x1). This coefficient, 12, indicates how much the dependent variable (shipping cost) is expected to change with a one-unit change in the independent variable (product weight in kg), assuming all other variables in the model are held constant. Therefore, it represents the average change in shipping costs associated with a 1-kg increase in product weight when the number of items and the total amount are held fixed.

The Owners of an Online Shop Use a Multiple Regression