AP3.1NotesWEB.notebook 1 September 13, 2013 Jun 293:28 PM Ch. 2 Test Results chapter 2 test scores mean: 76 median: 81 Jun 293:28 PM 3.1 Scatterplots and Correlation vocab example
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AP3.1NotesWEB.notebook
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September 13, 2013
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Ch. 2 Test Results
chapter 2 test scores
mean: 76median: 81
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3.1 Scatterplots
and Correlation
vocab example
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ObjectivesAfter this section, you should be able to…
• Identify explanatory and response variables in situations where one variable helps explain or influences the other• Make a scatterplot to display the relationship between two quantitative variables• Describe the direction, form, and strength of the overall pattern of a scatterplot• Recognize outliers in a scatterplot
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Why do we study relationships between two
variables?
we already know we can plot data, find numerical summaries, look for overall patterns, describe data
to make predictions, explain phenomena
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Response Variablemeasures the outcome of a study
-may help explain or influence changes in a response
-can help predict changes in the response variable
Explanatory Variable
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Practice ExampleIdentify the explanatory and response variables
amount of rain ; weed growth
resting pulse rate ; amount of daily exercise
percent cloud cover ; chances of percipitation
response explanatory
explanatory response
explanatory response
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What about...Identify the explanatory and response variables
number of fans at the game ; performance of the team
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Scatterplotdisplays relationship between two QUANTITATIVE variables measured on the same individual
eXplanatory variable
resp
onse
var
iabl
eva
riab
le n
ame
variable name
*choose "nice" values*don't have to start at (0,0)
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Scatterplot
fully label graph
including full labels is more important than plottingevery single point exactly accurately
APTIP
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Track and FieldThe table below shows data for 13 students in a statistics class. Each member of the class ran a 40-yard sprint and then did a long jump (with a running start). Make a scatterplot of the relationship between sprint time (in seconds) and long jump (in inches).
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Track and FieldThe table below shows data for 13 students in a statistics class. Each member of the class ran a 40-yard sprint and then did a long jump (with a running start). Make a scatterplot of the relationship between sprint time (in seconds) and long jump (in inches).
Jun 293:28 PM
Track and FieldThe table below shows data for 13 students in a statistics class. Each member of the class ran a 40-yard sprint and then did a long jump (with a running start). Make a scatterplot of the relationship between sprint time (in seconds) and long jump (in inches).
make in calculator!
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Describing Scatterplots
Use D.O.F.S.
Direction: overall positive or negativeOutliers: do there appear to be any?Form: overall linear, non-linear, clustered?Strength: how closely do the points follow the form?
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Track and FieldDescribe the scatterplot
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McDonaldsThe following scatterplot shows the amount of carbs (in grams) and amount of fat(in grams) of beef sandwiches from McDonalds. Describe the relationship between carbs and fat.
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Does a strong association between two variables indicate a cause-and-effect
relationship?
*association does not imply causation
ex/ ice cream sales and drowning deaths
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Homework
3.1 (Day 1) Assignment
`
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Bellwork`
The scatterplot shown displays the interval between consecutive eruptions of Old Faithful against the duration of the previous eruption. Describe the relationship shown in the scatterplot.
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3.1 Scatterplots
and Correlation
vocab example
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ObjectivesAfter this section, you should be able to…
• Know the basic properties of correlation• Calculate and interpret correlation, explaining how it is influenced by outliers
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Similar or Different?
direction?form?
direction?form?
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Correlation (r)
measures the direction and strength of the LINEAR relationship between two quantitative variables
-1 -.5 0 .5 1strong mod. weak mod. strong
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Correlation
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Correlation Characteristics-1 ≤ r ≤ 1
r < 0 means negative association
r > 0 means positive association
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Correlation Competition!
Guess the correlation!
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Can you determine the form of a relationship using only
correlation?
Demo
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Correlation Resistancean outlier will change r
an outlier "in" the pattern will increase strength
an outlier "out" of the pattern will decrease strength
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Correlation Factscorrelation makes no distinction between explanatory and response variables
because r uses standardized values of observations, r will not change when we change units of measurement
r has no unit of measurement
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Ticket Out!
Draw a scatterplot with a WEAK
correlation, give an estimation of what r =
Draw a scatterplot with a STRONG
correlation, give an estimation of what r =
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Homework
3.1 (Day 2) Assignment
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BellworkThe figure below plots the average brain weight in grams versus average body weight in kilograms for 96 species of mammals. There are many small mammals whose points are at the lower left overlap.
(a) The correlation between body weight and brain weight is r = 0.86. Explain what this value means.
(b) What effect would removing the hippo have on the correlation?
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