1. Statistics and Probability
CLAST Review Workshop
Statistics and Probability
5. Inferring Relations and Making
Predictions from Statistical Data
(skill III D 1)

2. Overview Trends in data Scatter plots and correlation
Interpolation estimating variation within the observed range
Extrapolation predicting variation beyond the observed range
11/27/2018
Dave Saha

3. Trends in Data Trends may be discerned best from graphs.
Both interpolation and extrapolation are used.
General trends are expected to continue.
Company Profit/Loss
Graphing the profit/loss over time clearly indicates that there is a trend of increasing profit. 30 25
 27  25
Profits (thousands) 20
 22  20 15
 16
 14 10 
’87 ’88 ’89 ’90 ’91 ’92 ’93
11/27/2018
Dave Saha

4. Scatter Plots and Correlation
The relationship, if any, between two variables is called correlation.
A scatter diagram may reveal correlation.
Correlation may vary from –1 to +1.
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The line of regression is the best linear approximation to how the two variables relate.
11/27/2018
Dave Saha

5. WARNING: Strong correlation does not mean causation!                 B     B                          A A
Strong Negative Correlation
as A increases, B decreases
as A decreases, B increases
Strong Positive Correlation
as A increases, B increases
as A decreases, B decreases
WARNING: Strong correlation does not mean causation!
11/27/2018
Dave Saha

6. Weak or No Correlation B B B A A A Weak Negative Correlation                  B  B  B                                                  A A A
Weak Negative Correlation
the enveloping area gets wider
Weak Positive Correlation
the enveloping area gets wider
No Correlation
no apparent relation between A and B
11/27/2018
Dave Saha

7. Interpret Beyond the Data
Interpolation
Relies on reading the graph correctly (skill ID1)
Extrapolation
Requires the assumption that any observed trends will continue
Relies on reading the graph correctly (skill ID1)
The scale(s) of the graph may have to be extended
11/27/2018
Dave Saha