RelationshipBetween2QuantitativeVariables

RelationshipBetween2QuantitativeVariables - A. 3 C. 7 6 2 5...

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Unformatted text preview: A. 3 C. 7 6 2 5 4 3 0 Y cur ved Y po s 1 -1 2 1 0 -2 -1 -2 -3 -3 -2 -1 0 X 1 2 3 -3 -4 -3 -2 -1 B. 3 1 2 3 1 2 3 D. 8 7 2 6 5 1 4 0 Y clumped Y ne g 0 X -1 -2 3 2 1 0 -1 -2 -3 -3 -3 -2 -1 0 X 1 2 3 -4 -5 -3 -2 -1 0 X A.: linear and positive C.: non-linear, convex B.: linear and negative D.: clustered and positive In real data the types of association can be more tentative, messy, and mixed. Examples: (PlacesRated.JMP, CarModels2003-4.JMP) E. 25000 G. T h e_A r t s 20000 15000 10000 5000 Housing Cost 20000 15000 0 0 1000 2000 3000 4 000 5000 6000 Hlt hC-Environ 10000 F. 5000 100 200 300 4 00 500 600 700 800 900 Climat e-Terrain 70 H. 50 4 50 40 4 00 30 350 20 10 2.0 3.0 4 .0 5.0 Weight (000 lbs) 6.0 D ispla cement CI MPG Highwa y 60 300 250 200 150 100 50 E.: linear, positive 0 40 50 60 Height 70 80 F.: non-linear, negative (weakly curved; ignore top left outlier) G.: non-linear, pos., clustered H.: non-linear or clustered? (Height<60: no assoc.; Height>60: pos. assoc.?) Ra ndom Weight 2 WEIGHT 200 100 100 70 HEIGHT 80 60 Ra ndom Weight 3 60 Ra ndom Weight 1 200 200 100 70 HEIGHT 80 60 70 HEIGHT 80 200 100 60 70 HEIGHT 80 To reproduce the above experiment, do the following: 1) Open PennStudentsRandom.JMP 2) Graph > Overlay Plot > ‘HEIGHT’ →X, ‘Random WEIGHT’ →Y, > OK 3) Right-click on ‘Random Weight’ in spreadsheet > Formula > Apply. Click repeatedly on Apply: every time, a new shuffle of the values in ‘Random Weight’ is generated and shown in the overlay plot. [This does not work with Fit Y by X.] Measuring the Strength of Linear Association: The Correlation Coefficient of two Variables Correlation in Practice Correlation measures linear dependence. Yet, if we calculate the correlation of variables x and y that are non-linearly associated, the correlation will also see a degree of linear association. Four datasets with the same correlation value 0.81: ...
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RelationshipBetween2QuantitativeVariables - A. 3 C. 7 6 2 5...

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