Lecture5 Linear Regression

Lecture5 Linear Regression - Linear Regression Lecture 5...

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Linear Regression Lecture 5

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Linear Regression A technique that uses data from two variable to create a straight line, and then use this line to make predictions.
Correlation vs. Regression Correlation = non directional In correlation, we had two variables, arbitrarily defined as X and Y. Regression = directional In regression, X is the predictor (IV) and Y is the outcome (DV). We are inferring that X leads to Y (BUT, this doesn’t mean X causes Y!)

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Linear Relations We assume that there is a linear relation between the two variables (X & Y). Think back to high school algebra: Y = m X + b slope intercept Intercept (m) Slope (b)
Linking Two Variables If we have a scatterplot of two variables that we assume are related in a linear fashion, what’s the best way to draw a line through the data? Variable 1 Variable 2

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Line of Best Fit Least squares method When we draw a line, there will be some error (we aren’t going directly through each point) Error = Y – Ŷ Our goal is to minimize error, so we fit a line such that the sum of the squared deviations from the straight line are minimized
Line of Best Fit Degree people think men should pay for dates 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 dating success (rating) 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 Y – Ŷ Y Ŷ

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The Regression Equation The regression equation predicts values of Y for specific values of X It creates the line that minimizes the error
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Lecture5 Linear Regression - Linear Regression Lecture 5...

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