Scatterplots Association and Correlation

Scatterplots Association and Correlation - Transcript

Chapter 7
Scatterplots Association and Correlation

You can observe a lot by watching Yogi Berra


Scatterplots
Most common and effective display of data Observe patterns trends relationships and outlying values Observe the relationship between two quantitative variables Ask whether there is an association between the two variables


Scatterplots


Look at the direction of the points




Look at the form


Positive Negative





Look at how much scatter the plot has Look for any outliers


Linear Non linear

Points that stand away from the overall pattern

Scatterplots TI Tips

Roles for Variables


Explanatory Variable




Response Variable


Predictor variable x axis y axis



Roles that we choose are based upon how we think about the variables The variables may or may not explain anything or respond to anything

Correlation Conditions


Correlation




Quantitative Variable Condition


Measures the strength of the linear association between two quantitative variables Know the variables units and what they measure Know that the correlation is linear Report the correlation with and without the outlier s

Strength Enough Condition


Outlier Condition


Finding the Correlation


Always check the conditions first

Correlation Properties
Sign gives the direction of the association Between 1 and 1 Treats x and y symmetrically No units Not affected by change in units scale or center Measures strength of linear association Sensitive to outliers


Strengthening Scatterplots



When a scatterplot shows a non linear form that consistently increases or decreases we can straighten the form by re expressing one or both variables

What Can Go Wrong


Don t say Correlation when you mean Association


Association


Vague term Describes relationship between two variables



Correlation


Precise term Describes the linear relationship between quantitative variables

What Can Go Wrong


Check the Conditions




Don t confuse Correlation with Causation


Don t correlate categorical variables Be sure the association is linear



Watch out for Lurking variables


Don t try to explain correlation by saying that the predictor variable has caused the response variable to change Hidden variable simultaneously affecting both variables

Let s Try Lunch Pg 133 13


Variables






Conditions


Calories average number of calories a child consumed during lunch Time average number of minutes a child spent at the table when lunch was served Quantitative both calories and time are quantitative Straight enough scatterplot looks linear Outlier There are a few stray points but the none are very far from the rest of the points

Lunchtime

Lunchtime
The correlation coefficient is Interpretation



r 0 65

The scatterplot shows a negative direction with lower calories going with higher times The plot is generally straight with a moderate amount of scatter The correlation coefficient of 0 65 indicates a linear association A few cases stand out with lower times related to higher calorie intake as well as a few with higher times related to lower calorie intake