04-06-2011 Linear Regression

04-06-2011 Linear Regression - 4/6/2011 1 Lecture 20: April...

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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: Lets 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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04-06-2011 Linear Regression - 4/6/2011 1 Lecture 20: April...

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