12c_Ch15_Regression

12c_Ch15_Regression - You should. . . Regression understand...

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Regression You should. . . • understand how to make predictions based on a: – Scatterplot – regression line – Least squares regression line • understand proportion of variance accounted for — in terms of regression • Once we establish a relationship between two variables, it is often useful to make predictions that go beyond the available data. • Given a correlation between two variables, can we predict values on one variable given values on the other variable? Example • Can we predict salary from height?
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Height and Salary Height (in.) Salary (thousands) X Y --------------- ------------------------- 77 47.1 73 46.2 70 42.8 69 45.4 67 42.1 66 34.1 63 33.1 Regression • Two "rough" approaches to prediction: scatterplot regression line Prediction Using a Scatterplot Height and Salary • If a person is 74 inches tall, what will her/his salary be? • We know that: • a 73 inch person makes $46,200 • a 77 inch person makes $47,100 • Note: There is no 74 inch person in our data
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Scatterplot for Height and Salary 60 65 70 75 80 30 35 40 45 50 Salary (thousands) Height (inches) 60 65 70 75 80 30 35 40 45 50 Salary (thousands) Scatterplot for Height and Salary 60 65 70 75 80 30 35 40 45 50 Salary (thousands) 73” person 77” person Scatterplot for Height and Salary 60 65 70 75 80 30 35 40 45 50 Salary (thousands) 73” person 77” person 74”? Scatterplot for Height and Salary
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60 65 70 75 80 30 35 40 45 50 Salary (thousands) Height (inches) Scatterplot for Height and Salary 60 65 70 75 80 30 35 40 45 50 Salary (thousands) Scatterplot for Height and Salary 60 65 70 75 80 30 35 40 45 50 Salary (thousands) Scatterplot for Height and Salary 60 65 70 75 80 30 35 40 45 50 Salary (thousands) $46,200 $47,100 We predict that a person 74 inches tall will make between $46,200 and $47,100 (approximately)
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We predict that a person 74 inches tall will make between $46,200 and $47,100 (approximately) 60 65 70 75 80 30 35 40 45 50 Salary (thousands) Height (inches) $46,200 $47,100 77” 73” 74” Prediction Using a regression line “Fit by eye” Regression line • A regression line is a line that “best fits” the points in a scatterplot Fit a regression line by eye 60 65 70 75 80 30 35 40 45 50 Salary (thousands)
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Fit a regression line by eye 60 65 70 75 80 30 35 40 45 50 Salary (thousands) Height (inches) What do we predict a 74 inch person will make? 60 65 70 75 80 30 35 40 45 50 Salary (thousands) What do we predict a 74 inch person will make? 60 65 70 75 80 30 35 40 45 50 Salary (thousands) 74” What do we predict a 74 inch person will make? 60 65 70 75 80 30 35 40 45 50 Salary (thousands) 74”
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What do we predict a 74 inch person will make? 60 65 70 75 80 30 35 40 45 50 Salary (thousands) Height (inches) 74” Using a regression line fit by eye, we predict that a person 74 inches tall will make approximately $47,000 60 65 70 75 80 30 35 40 45 50 Salary (thousands) 74” $47,000 But what exactly is a regression line ? • A line that comes closest to "best" describing the linear relationship between two variables • We could fit the regression line by eye, but it would be difficult -- if not impossible -- to find the truly best line Least Squares regression line • Mathematical solution • Equation for a straight line that best describes the linear relationship between two variables
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Least Squares regression line
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This note was uploaded on 08/22/2011 for the course PSY 207 taught by Professor Pfordesher during the Fall '07 term at SUNY Buffalo.

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12c_Ch15_Regression - You should. . . Regression understand...

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