04-06-2011 Linear Regression

# 04-06-2011 Linear Regression - • •1 Lecture 20 April 6...

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Unformatted text preview: •4/6/2011 •1 Lecture 20: April 6, 2011 • Material for today in Chapter 12: • Introduction to simple regression: bottom p.494-middle p.504 • Next class: middle p. 504-bottom p. 515 The following slide is a summary of last class. •4/6/2011 •2 Interpretation of r = .747 • A moderately strong • and • positive • linear association • between • household income • and • food expenditures Back To The Original Data: Let’s Do A Plot • X Y • 30 10 • 45 16 • 50 17 • 55 20 • 70 17 Back To The Original Data: Axes and Units • X Y • 30 10 • 45 16 • 50 17 • 55 20 • 70 17 •4/6/2011 •3 Back To The Original Data: Plot the 2 Means • X Y • 30 10 • 45 16 • 50 17 • 55 20 • 70 17 Back To The Original Data: Axis for Each Mean • X Y • 30 10 • 45 16 • 50 17 • 55 20 • 70 17 Back To The Original Data: Plot the Five Pairs • X Y • 30 10 • 45 16 • 50 17 • 55 20 • 70 17 •4/6/2011 •4 Back To The Original Data: Regions I - IV • X Y • 30 10 • 45 16 • 50 17 • 55 20 • 70 17 Limitations of Linear Correlation • It measures the degree to which variables are linearly associated . • It says nothing about – Causality – Functional relationships • Example: Crop yield (on the vertical axis) vs. fertilizer application rate (on the horizontal axis) – This relationship is parabolic, i.e., an upside-down U. – The correlation coefficient would be close to zero. – To see this, make use of the regions in the previous slide and note what happens when you » calculate the products within each region, and then » sum over all of the products.» sum over all of the products....
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## This note was uploaded on 10/13/2011 for the course FINOPMGT 250 taught by Professor Kouzehkanani during the Spring '08 term at UMass (Amherst).

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04-06-2011 Linear Regression - • •1 Lecture 20 April 6...

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