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FOUNDATIONAL CONCEPTS Model Specification: What is SLR? y = β₀ + β₁x + ε Response vs. predictor variable What does the line represent? (conditional mean) Slope interpretation. Intercept interpretation.
Typology: Lecture notes
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School of Industrial and Systems Engineering
Learning Objectives:
A company, which sells medical supplies to hospitals, clinics, and doctor's offices, had considered the effectiveness of a new advertising program. Management wants to know if the advertisement is related to sales. This company intends to increase the sales with an effective advertising program.
The data are recorded for 41 countries, including both developed and developing countries. The data include the following columns. Country Inflation.difference Exchange.rate.change Developed Australia - 1. 2351 - 3. 1870 1 Austria 1. 5508 1. 4781 1 Belgium 1. 0371 0. 0395 1 Canada 0. 0461 - 1. 6416 1 Chile - 18. 4126 - 20. 6329 0
Ø In 2000 Bush and Gore were the main candidates for President in the U.S. Buchanan, a strongly conservative candidate, was also on the ballot. In the state of Florida , Bush and Gore essentially tied, hence the counts were examined carefully county by county. Ø Palm Beach County exhibited strange results. Even though the people in this county are not conservative, many votes were cast for Buchanan. Examination of the voting ballot revealed that it was easy to mistakenly vote for Buchanan (a conservative candidate) when intending to vote for Gore. We will thus predict whether those who voted for Buchanan were indeed going for a conservative candidate.
The regression framework is characterized by the following:
RESPONSE VARIABLE versus PREDICTING VARIABLE? Response Variable: It is a Random Variable. It varies with changes in the predictor/s along with other random changes. Predicting Variable: It is a Fixed Variable. It does not change with the response, but it is set fixed before the response is measured.
A regression analysis is used for:
1. Prediction of the response variable; 2. Modelling the relationship between the response variable and the explanatory variables; or 3. Testing hypotheses of association relationships. Linear Regression: The basis of what we will be talking about most of this course is the linear model. Virtually all other methods for studying dependence among variables are variations on the idea of linear regression. “All models are wrong, but some are useful. “ George Box “Embrace your data, not your models .” John Tukey
Simple linear regression Y = # 0 + # 1 X + ε Multiple linear regression Y = # 0 + # 1 X 1 + # 2 X 2 + ε Polynomial Regression Y = # 0 + # 1 X +# 2 X^2 + ε .
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Whether a linear or polynomial model in X, we can estimate the relationship using linear regression.
Simple linear regression Y = # 0 + # 1 X + ε Multiple linear regression Y = # 0 + # 1 X 1 + # 2 X 2 + ε Polynomial Regression Y = # 0 + # 1 X +# 2 X^2 + ε
