Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 151STAT 110 – Introduction to Descriptive StatisticsChapter 14Describing Relationships2STAT 110 – Introduction to Descriptive StatisticsPlots and Numerical SummariesMost statistical studies examine data on more than one variable. The steps when trying to talk about two variables at once are the same as what we used earlier in the semester with just one variables:•Plot the data.•Look for overall patterns and deviations from those patterns.•Use numerical summaries.3STAT 110 – Introduction to Descriptive StatisticsScatterplotscatterplot – shows the relationship between two quantitative variables measured on the same individuals•Values of one variable appear on the x-axis. This is typically the one doing the explaining – the explanatory, predictor, or independent variable.• Values of the other variable appear on the y-axis. This is typically the one being explained – called the response or dependent variable.4STAT 110 – Introduction to Descriptive StatisticsScatterplotExampleWhen water flows across farmland, some of the soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow on the amount of soil washed away. Flow is measured in liters/second and the eroded soil is measured in kilograms. flow rate .31 .85 1.26 2.47 3.75 eroded soil .82 1.95 2.18 3.01 6.075STAT 110 – Introduction to Descriptive StatisticsScatterplot• Is there an explanatory variable?• What’s the response variable?• Which variable should be on the x-axis?Flow Rate vs Eroded Soil012345670 1 2 3 4Flow Rate (liters/sec)Eroded Soil (kg)6STAT 110 – Introduction to Descriptive StatisticsInterpreting Scatterplots1. Look for the overall pattern and for striking deviations from the pattern.2. Look for outliers.3. Describe the overall pattern by the form, direction, and strength of the relationship. form – clustered, curved, linear direction – positive or negative strength – determined by how closely the points follow a clear form7STAT 110 – Introduction to Descriptive StatisticsClustered8STAT 110 – Introduction to Descriptive StatisticsCurved9STAT 110 – Introduction to Descriptive StatisticsLinearA Linear Graph-6-4-20246-6 -4 -2 0 2 4 610STAT 110 – Introduction to Descriptive StatisticsAssociationpositively associated – when above-average values and below-average values tend to occur together scatterplot slopes upward as you move from left to rightnegatively associated – when above-average values of one variable tend to accompany below-average values of the other scatterplot slopes downward as you move from left to right11STAT 110 – Introduction to Descriptive StatisticsPositive Association-6-4-20246-6 -4 -2 0 2 4 612STAT 110 – Introduction to Descriptive StatisticsNegative Association-6-4-20246-6 -4 -2 0 2 4 613STAT 110 – Introduction to Descriptive StatisticsCorrelationcorrelation – (r) describes the direction and strength of a straight-line relationship between two quantitative variables• sign indicates negative or positive association• r = 0 no linear association• r = -1 or r = 1 perfect straight line14STAT 110 – Introduction to Descriptive StatisticsCorrelation15STAT 110 – Introduction to Descriptive StatisticsNotes About r•r has no units and won’t change if we change the units of measurement• r ignores the distinction between explanatory and response variables• r is strongly affected by outliers
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