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Chap16-Linear-Regressions

# Chap16-Linear-Regressions - 1 Chap 16 Linear Regressions 2...

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1 CHAPTER 16: LINEAR REGRESSIONS Stats & Prob. for Bus. Mgmt (Stat1100) Jochem Chap 16: Linear Regressions box2 Topics of Chapter 16 box5 1. First-Order Linear Model square6 1.1 Least Squares Method (LSM) square6 1.2 Conditions for using LSM 2 box5 2. Assessing the Model square6 2.1 Standard Error of Estimate square6 2.2 Coefficient of Determination (R 2 ) square6 2.3 Testing the slope coefficient square6 2.4 Testing the assumptions box5 3. Correlation vs. Causation Chap 16: Linear Regressions box2 1. First-Order Linear Model box5 Deterministic versus probabilistic models: square6 Deterministic models are “identities”: square6 Net Income = Gross Income – Tax Profits = Revenue – Costs 3 square6 square6 Future Value = Present Value * (1+interest rate)^periods square6 Probabilistic models have “wiggle room”: square6 Income = f (education, work experience, age, …) square6 Prob. of Hangover = f (alcohol consumption, weight, food,…) square6 House price = f (lot size, bedrooms, house size, …) Some things do not follow an exact formula; there are many other factors that we cannot exactly pin down. Chap 16: Linear Regressions box2 1. First-Order Linear Model box5 Example house prices: square6 Suppose we’d like to predict house prices. square6 Suppose that from experience/intuition we know that for ea. square foot in house size, the house price increases by \$100. 4 square6 We may conclude the following: y = \$100,000 + \$100*x where y = house price x = house size in square feet This would be a deterministic model for each house size, there is exactly one price. House prices however fluctuate and do also include other observable and unobservable characteristics.

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Chap 16: Linear Regressions box2 1. First-Order Linear Model box5 Example house prices: square6 Suppose we’d like to predict house prices. square6 Suppose that from experience/intuition we know that for ea. square foot in house size, the house price increases by \$100. 5 square6 We may conclude the following: y = \$100,000 + \$100*x + ε where y = house price x = house size in square feet We can add an term called “epsilon” or “error” hat usurps this variation. Chap 16: Linear Regressions box2 1. First-Order Linear Model box5 Example house prices: square6 Suppose we’d like to predict house prices. square6 Suppose that from experience/intuition we know that for ea. square foot in house size, the house price increases by \$100. 6 square6 We may conclude the following: y = \$100,000 + \$100*x + ε where y = house price x = house size in square feet Such a model is called a first-order linear model or simply a linear regression model . Linear, as we assume that the house size has a linear relationship to the house price. First-order as in our model there are only first-order terms (i.e., no squared, or cubic terms) impacting the price. Chap 16: Linear Regressions box2 1. First-Order Linear Model box5 In generic terms: where 7 square6 y = dependent variable square6 x = independent variable square6 = intercept square6 = slope of the line square6 = error variable/term (“epsilon”) Why do we say here “slope of the line”?
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