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# Chapter_11 - Chapter 11: Simple Linear Regression Where...

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Chapter 11: Simple Linear Regression

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McClave: Statistics, 11th ed. Chapter 11: Simple Linear Regression 2 Where We’ve Been Presented methods for estimating and testing population parameters for a single sample Extended those methods to allow for a comparison of population parameters for multiple samples
Where We’re Going McClave: Statistics, 11th ed. Chapter 11: Simple Linear Regression 3 Introduce the straight-line linear regression model as a means of relating one quantitative variable to another quantitative variable Introduce the correlation coefficient as a means of relating one quantitative variable to another quantitative variable Assess how well the simple linear regression model fits the sample data Use the simple linear regression model to predict the value of one variable given the value of another variable

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McClave: Statistics, 11th ed. Chapter 11: Simple Linear Regression 4 11.1: Probabilistic Models
McClave: Statistics, 11th ed. Chapter 11: Simple Linear Regression 5 11.1: Probabilistic Models The relationship between home runs and runs in baseball seems at first glance to be deterministic …

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McClave: Statistics, 11th ed. Chapter 11: Simple Linear Regression 6 11.1: Probabilistic Models But if you consider how many runners are on base when the home run is hit, or even how often the batter misses a base and is called out, the rigid model becomes more variable.
McClave: Statistics, 11th ed. Chapter 11: Simple Linear Regression 7 11.1: Probabilistic Models General Form of Probabilistic Models y = Deterministic component + Random error where y is the variable of interest, and the mean value of the random error is assumed to be 0: E ( y ) = Deterministic component.

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McClave: Statistics, 11th ed. Chapter 11: Simple Linear Regression 8 11.1: Probabilistic Models
McClave: Statistics, 11th ed. Chapter 11: Simple Linear Regression 9 11.1: Probabilistic Models The goal of regression analysis is to find the straight line that comes closest to all of the points in the scatter plot simultaneously.

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McClave: Statistics, 11th ed. Chapter 11: Simple Linear Regression 10 11.1: Probabilistic Models A First-Order Probabilistic Model y = 0 + 1 x + where y = dependent variable x = independent variable 0 + 1 x = E ( y ) = deterministic component = random error component 0 = y – intercept 1 = slope of the line
McClave: Statistics, 11th ed. Chapter 11: Simple Linear Regression 11 11.1: Probabilistic Models 0 , the y – intercept, and 1 , the slope of the line, are population parameters, and invariably unknown. Regression analysis is designed to estimate these parameters.

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McClave: Statistics, 11th ed. Chapter 11: Simple Linear Regression 12 11.2: Fitting the Model: The Least Squares Approach Step 1 Hypothesize the deterministic component of the probabilistic model E ( y ) = 0 + 1 x Step 2 Use sample data to estimate the unknown parameters in the model
McClave: Statistics, 11th ed. Chapter 11: Simple Linear Regression 13 11.2: Fitting the Model: The Least Squares Approach Values on the line are the predicted values of total offerings given the average offering.

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## Chapter_11 - Chapter 11: Simple Linear Regression Where...

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