chapter12_notes3slides

# chapter12_notes3slides - Notes Introduction to Probability...

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Introduction to Probability and Statistics II Instructor: John Snyder Office: Middlebush 35 Office hours: MW 8am - 9:30am Email: [email protected] 10 27 2015 John Snyder (MU) Stat —— 3500 — 10 27 2015 1 / 78 Multiple Linear Regression and Model Building 1 12.1 - Multiple Regression Models 2 12.2 - The First-Order Model 3 12.3 - Evaluating Overall Model Utility 4 12.4 - Using the Model for Estimation and Prediction 5 12.5 - Interaction Models 6 12.6 - Quadratic and Other Higher Order Models 7 12.7 - Qualitative (Dummy) Variable Models 8 12.8 Models w/ Quantitative and Qualitative Variables 9 12.9 Comparing Nested Models John Snyder (MU) Stat —— 3500 — 10 27 2015 2 / 78 12.1 - Multiple Regression Models Section 1 12.1 - Multiple Regression Models John Snyder (MU) Stat —— 3500 — 10 27 2015 3 / 78 Notes Notes Notes

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12.1 - Multiple Regression Models Introduction In chapter 11, we discussed simple linear regression: Introduced the straight-line regression model relating a response variable y to a predictor variable x .(section 1) Demonstrated how to estimate the parameters of the model using least squares estimation.(section 2) Explored how to test the significance of a relationship between x and y using hypothesis testing(section 4) Showed how to assess the adequacy of the model using R 2 and r .(section 5) Showed how to use the model to estimate E [ y ] and predict y for a given value of x .(section 6) John Snyder (MU) Stat —— 3500 — 10 27 2015 4 / 78 12.1 - Multiple Regression Models Multiple Linear Regression However, in most situations, simple linear regression isn’t very practical. For example, consider building a model to estimate home value. One might consider variables such as: Location. Square footage. Number of bathrooms. You can think of many more! Problems such as this motivate the need to relate multiple predictor variables to one response variable. John Snyder (MU) Stat —— 3500 — 10 27 2015 5 / 78 12.1 - Multiple Regression Models Multiple Linear Regression In this chapter, we will learn multiple regression model . Present several different multiple regression models involving both quantitative and qualitative predictor variables. Demonstrate how these models can describe many different relationships between variables. Assess how well the multiple regression model fits the sample data. John Snyder (MU) Stat —— 3500 — 10 27 2015 6 / 78 Notes Notes Notes
12.1 - Multiple Regression Models Multiple Linear Regression The general form of the multiple regression model is: y = β 0 + β 1 x 1 + β 2 x 2 + . . . + β k x k + ε The value of the coefficient β i determines the contribution of the predictor variable x i . As before, β 0 is the y-intercept and ε is the random error term. John Snyder (MU) Stat —— 3500 — 10 27 2015 7 / 78 12.1 - Multiple Regression Models Multiple Linear Regression The x i variables can be the observed variables themselves or functions of the observed variables.

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