Scatterplots
Correlation
explanatory variable - may help explain or predict changes in a response variable ( x )
response variable - measures outcome ( y )
Describing Scatterplots
scatterplot - shows the relationship between two quantitative variables
needs titles
(X-planatory, response)
direction: positive or negative
form: linear
strength: (moderately) weak or strong
e.g. There is a weak, negative linear association between the percent of students taking the SAT and the mean math SAT scores in each state.
Computing Correlation
the correlation coefficient 'r' measures the direction and strength of a linear relationship
r is in the range [-1,1 ]
-1 and 1 are perfect lines, and 0 is a horizontal best fit
work must be written out when asked to calculate r
r does not change when we change units
r has no units
correlation does not imply causation
both variables must be quantitative
correlation does not describe curved relationships, only linear
a value of r close to -1 or 1 does not guarantee a linear relationship
correlation is not resistant
correlation is not a complete summary of data
Formula
where z is z-score