stats questions we are often asked what is r and r 2 ? when can i use r and r 2 ?
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Stats Questions We Are Often Asked What is r and R 2 ? When can I use r and R 2 ?. r – little r – what is it?. r is the correlation coefficient between y and x r measures the strength of a linear relationship r is a multiple of the slope. *. *. *. *. *. *. *. *. - PowerPoint PPT PresentationTRANSCRIPT
DEPARTMENT OF STATISTICS
Stats Questions We Are Often Asked
What is r and R 2 ?
When can I use r and R 2 ?
DEPARTMENT OF STATISTICSr – little r – what is it?
r is the correlation coefficient between y and x
r measures the strength of a linear relationship
r is a multiple of the slope
DEPARTMENT OF STATISTICSr – when can it be used?
Only use r if the scatter plot is linear
Don’t use r if the scatter plot is non-linear!
x
y
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** *r = 0.99
DEPARTMENT OF STATISTICSr – what does it tell you?
How close the points in the scatter plot come to lying on the line
r = 0.99
x
y
**** ** ** ** * **** ** ** *r = 0.57
x
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DEPARTMENT OF STATISTICSR 2 – big R 2 – what is it?
R 2 is the coefficient of determination
Measures how close the points in the scatter plot come to lying on the fitted line or curve
x
y
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x
y
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DEPARTMENT OF STATISTICSR 2 – big R 2 – when can it be used?
When the scatter plot of y versus x is
linear or non-linear
x
y
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x
y
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DEPARTMENT OF STATISTICSR
2 – what does it tell you?
x
x
Dotplot of the y ’s
Shows the variation in the y ’s
y
y
Dotplot of the y ’s Shows the variation in the y ’s
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DEPARTMENT OF STATISTICSR
2 – what does it tell you?
x
We see some additional variation in the y ’s. The excess is not explained by the model.
y y
2 Variation in y 'sˆVariation in fitted valuesVariation in y values Variation in y 'sR = =
Variation in the y ’s This amount of variation can be explained by the model
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DEPARTMENT OF STATISTICSR 2 – what does it tell you?
When expressed as a percentage, R 2 is
the percentage of the variation in Y that
our regression model can explain
R 2 near 100% model fits well
R 2 near 0% model doesn’t fit well
DEPARTMENT OF STATISTICSR 2 – what does it tell you?
90% of the variation in Y is explained by
our regression model.
x
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R 2 = 90%
DEPARTMENT OF STATISTICSR 2 – pearls of wisdom!
R 2 and r 2 have the same value ONLY
when using a linear model
DON’T use R 2 to pick your model
Use your eyes!
DEPARTMENT OF STATISTICSDamaged for life by too much TV
DEPARTMENT OF STATISTICSDamaged for life by too much TV
TV watching
Hea
lth S
core
r = - 0.93
Causal relationship?
DEPARTMENT OF STATISTICSCausal relationships
Two general types of studies: experiments and observational studies
In an experiment, the experimenter determines which experimental units receive which treatments.
DEPARTMENT OF STATISTICSDamaged for life by too much TV
TV watching
Hea
lth S
core
r = - 0.93
Causal relationship?
DEPARTMENT OF STATISTICSCausal relationships
Two general types of studies: experiments and observational studies
In an experiment, the experimenter determines which experimental units receive which treatments.
In an observational study, we simply compare units that happen to have received different levels of the factor of interest.
DEPARTMENT OF STATISTICSCausal relationships
Only well designed and carefully executed experiments can reliably demonstrate causation.
An observational study is often useful for identifying possible causes of effects, but it cannot reliably establish causation
DEPARTMENT OF STATISTICSCausal relationships - Summary
In observational studies, strong relationships are not necessarily causal relationships.
Correlation does not imply causation.
Be aware of the possibility of lurking variables.