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Ch 3 Examining Relationships

Ch 3 Examining Relationships. When there is more than just one…. Ask What individuals? What variables? How are the measured? All quantitative? Or at least one categorical? Simply Explore? Or think a variable explains or causes changes?. SCATTERPLOTs….

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Ch 3 Examining Relationships

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  1. Ch 3 Examining Relationships

  2. When there is more than just one… • Ask • What individuals? • What variables? How are the measured? • All quantitative? Or at least one categorical? • Simply Explore? • Or think a variable explains or causes changes?

  3. SCATTERPLOTs…. • Most effective way to show relation between 2 quantitative variables measured on the same individuals • The values of one variable (explanatory) appear on the horizontal axis and the other variable (response) on the vertical axis • Each point represents one individual

  4. Remember …. You already know this…. • Explanatory Variable – attempts to explain the observed outcomes • INDEPENDENT • Response Variable – measures an outcome of a study • DEPENDENT

  5. Problem 3.1 • The amount of time a student spends studying for a statistics exam and the grade on the exam. • The weight and height of a person • The amount of yearly rainfall and the yield of a crop • A student’s grades in statistics and in French • The occupational class of a father and of a son.

  6. Interpreting a Scatterplot • Look for overall pattern and distribution • Describe by • FORM – clusters, linear, curved, etc. • DIRECTION – positive, negative, none • STRENGTH – strong, medium, weak, etc. • OUTLIERS – falls outside overall pattern

  7. Drawing Scatterplots • Scale both axes • Label both axes • Don’t compress plot, make large enough so plot uses whole grid

  8. 3.6 Endangered Manatees

  9. 3.6 The Endangered Manatee

  10. Hw : Friday • 3, 7, 10, 12, 15, 16, 17

  11. 3.2 Correlation

  12. Correlation – measures the direction and strength of the linear relationship between two quantitative variables. Usually written with r.

  13. Facts to know about correlation… • Makes no distinction between explanatory and response variables. (it doesn’t matter which variable you call x or y in the formula) • Requires that both variables be quantitative • R uses standardized values of the observations, so r does not change if the units of measurement are changed. (correlation itself has NO unit of measurement it is JUST a number)

  14. Continued…. • Positive r means positive association, negative r means negative association • r is always a number between -1 and 1, r near zero means VERY weak. Strength of r increases as value moves closer to either -1 or 1. rare cases of r=1, or r =-1 only occur when there is perfectly linear relationship • ONLY measures linear relationship, does not measure curved relationships • NOT resistant: r is STRONGLY affected by a few outliers

  15. ************** Remember that Correlation is not a complete description of two –variable data. EVEN when the data is linear. You should give the means and standard deviations of both x and y as well. (Means and standard deviations because these are used in the formula for r)****************

  16. Finding correlation in your calculator…. • MAKE sure your Diagnostics are ON! • Enter both data sets into L1 and L2 • Stat – Calc – 8.LinReg(a + bx) • LinReg(a+bx) L1, L2, Y1

  17. Tuesday’s Homework • 12, 25, 26, 30, 37

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