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part19 - Public Health 6450 Fall 2011 Lynn Eberly and Andy...

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Public Health 6450 Fall 2011 Lynn Eberly and Andy Mugglin Division of Biostatistics School of Public Health University of Minnesota [email protected] Part 19

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Review Introduction to Simple Linear Regression Detailed Example Where are we going? Previously: Describing Relationships Between Quantitative Variables (Ch. 2) Scatterplots Correlation Current topics: Introduction to Simple Linear Regression (Ch. 2) Estimating the regression line Residuals Cautions about regression Next topics: Details on Simple Linear Regression (Ch. 10) Eberly and Mugglin PubH 6450 Fall 2011 Part 19 2 / 44
Review Introduction to Simple Linear Regression Detailed Example What kinds of questions do we use regression to answer? The Regression Line Deviations From the Line What is regression for? Regression analysis is used to quantify the linear relationship between two quantitative variables. In this way, it is like correlation, but regression goes farther: It allows us to draw the line that best describes the linear relationship between X and Y . It allows us to predict the value of the outcome Y for a specified value of X . It allows us to quantify how much of a change in the value of Y is seen with a specified change in the value of X . Eberly and Mugglin PubH 6450 Fall 2011 Part 19 3 / 44

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Review Introduction to Simple Linear Regression Detailed Example What kinds of questions do we use regression to answer? The Regression Line Deviations From the Line Wine and Heart Disease Is higher wine consumption associated with lower rates of heart disease? How much lower are heart disease rates for each extra liter per person per year? Eberly and Mugglin PubH 6450 Fall 2011 Part 19 4 / 44
Review Introduction to Simple Linear Regression Detailed Example What kinds of questions do we use regression to answer? The Regression Line Deviations From the Line Wine and Heart Disease (cont’d) How much lower are heart disease rates for each extra liter per person per year? 2 4 6 8 100 150 200 250 300 Alcohol from wine (liters per person year) Heart disease deaths (per 100,000 person year) What is X ? What is Y ? Form: Linear or not? Direction: Positive or negative? Precision: Points lie close to the line or not? Strength: The line is steep or shallow? Can we answer this question of interest with a correlation? Eberly and Mugglin PubH 6450 Fall 2011 Part 19 5 / 44

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Review Introduction to Simple Linear Regression Detailed Example What kinds of questions do we use regression to answer? The Regression Line Deviations From the Line Population Living on Farms How fast did the number of people living on farms in the US decrease? Year 1935 1940 1945 1950 1955 1960 Population 32.1 30.5 24.4 23.0 19.1 15.6 1965 1970 1975 1980 1985 1990 15.9 12.4 9.7 8.9 7.2 3.9 All numbers are in millions. The US Census stopped counting the number of people living on farms in 1993.
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