Math Problem Statement

The consumption function captures one of the key relationships in economics. It expresses consumption as a function of disposal income, where disposal income is income after taxes. The attached file "Regression Dataset" shows data on average US annual consumption (in $) and disposable income (in $) for the years 2000 to 2016.

  1. Find the sample linear regression equation for the model

  2. In this model, the slope coefficient is the marginal propensity to consume.

Interpret its meaning

  1. What is the predicted consumption if disposal income is $33,000?

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Economics
Marginal Propensity to Consume
Statistics

Formulas

Linear Regression Equation: Y = a + bX
Slope: b = Σ[(X - X̄)(Y - Ȳ)] / Σ(X - X̄)^2
Marginal Propensity to Consume (MPC): MPC = ΔC / ΔY

Theorems

Ordinary Least Squares (OLS) Estimation

Suitable Grade Level

Undergraduate Economics/Statistics

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