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**Unformatted text preview: **1 CHAPTER 16: LINEAR REGRESSIONS Stats & Prob. for Bus. Mgmt (Stat1100) Jochem Chap 16: Linear Regressions b Topics of Chapter 16 b 1. First-Order Linear Model s 1.1 Least Squares Method (LSM) s 1.2 Conditions for using LSM 2 b 2. Assessing the Model s 2.1 Standard Error of Estimate s 2.2 Coefficient of Determination (R 2 ) s 2.3 Testing the slope coefficient s 2.4 Testing the assumptions b 3. Correlation vs. Causation Chap 16: Linear Regressions b 1. First-Order Linear Model b Deterministic versus probabilistic models: s Deterministic models are identities: s Net Income = Gross Income Tax 3 s Profits = Revenue Costs s Future Value = Present Value * (1+interest rate)^periods s Probabilistic models have wiggle room: s Income = f (education, work experience, age, ) s Prob. of Hangover = f (alcohol consumption, weight, food,) s 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 b 1. First-Order Linear Model b Example house prices: s Suppose wed like to predict house prices. s Suppose that from experience/intuition we know that for ea. 4 square foot in house size, the house price increases by $100. s 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. Chap 16: Linear Regressions b 1. First-Order Linear Model b Example house prices: s Suppose wed like to predict house prices. s Suppose that from experience/intuition we know that for ea. 5 square foot in house size, the house price increases by $100. s We may conclude the following: y = $100,000 + $100*x + 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 b 1. First-Order Linear Model b Example house prices: s Suppose wed like to predict house prices. s Suppose that from experience/intuition we know that for ea. 6 square foot in house size, the house price increases by $100. s We may conclude the following: y = $100,000 + $100*x + 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 b 1. First-Order Linear Model b In generic terms: where 7 s y = dependent variable s x = independent variable s = intercept s = slope of the line s = error variable/term (epsilon) Why do we say here slope of the line?...

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