introduction to linear regression
DESCRIPTION
Introduction to Linear Regression. Conceptual Data Analysis Series. Episode Objectives. What is linear regression? When would I use linear regression? How is a regression line calculated?. Correlation. Correlation. Correlation. Regression. Regression. Application. Application. - PowerPoint PPT PresentationTRANSCRIPT
Introduction to Linear
Regression
Conceptual Data Analysis Series
Episode Objectives
What is linear regression?
When would I use linear regression?
How is a regression line calculated?
Correlation
rX X Y Y
X X Y Y
( )( )
( ) ( )2 2
Correlation
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Regression
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Regression
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SAT Score Senior High School Year
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Application
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SAT Score Senior High School Year
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SAT Score Senior High School Year
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Regression Lines
Y = mX + b
Y’ = bX + a
Regression Lines
Y = mX + b
Y’ =
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Regression Lines
Y = mX + b
Y’ = 2X + 0
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Regression Lines
Y = mX + b
Y’ = 2X + 0
Y’ = 2(5) + 0 = 10
Regression Lines
Y = mX + b
Y’ = 2X + 0
Y’ = 2(5) + 0 = 10
Y’ = 2(6.2) + 0 = 12.4
Regression Lines
Y = mX + b
Y’ = 1.9791x + 0.1773
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Residuals
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residual
residual
Calculating the Equation
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20f(x) = 1.97909090909091 x + 0.177272727272728R² = 0.977995897613682
X
Y'
Review
Regression is an extension of correlation
Regression permits us to can predict values of Y based on X, and vice versa
Causal statements still requires good experimental research design