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