ch 3 examining relationships
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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…. - PowerPoint PPT PresentationTRANSCRIPT
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….
• 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
Remember …. You already know this….
• Explanatory Variable – attempts to explain the observed outcomes – INDEPENDENT
• Response Variable – measures an outcome of a study– DEPENDENT
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.
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
Drawing Scatterplots
• Scale both axes• Label both axes• Don’t compress plot, make large enough so
plot uses whole grid
3.6 Endangered Manatees
3.6 The Endangered Manatee
Hw : Friday
• 3, 7, 10, 12, 15, 16, 17
3.2 Correlation
• Correlation – measures the direction and strength of the linear relationship between two quantitative variables. Usually written with r.
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)
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
• ************** 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)****************
• 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
Tuesday’s Homework
• 12, 25, 26, 30, 37