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Correlation (Covariance (if exact or inverse relation btwn x & y…
Correlation
Covariance
cov(𝑥,𝑦)= 1 ∑𝑁 (𝑥𝑖 −𝑥̅)(𝑦𝑖 −𝑦̅) 𝑁−1 𝑖=1
if exact or inverse relation btwn x & y exists
the covariance = plus or minus variance of x
(i.e. y=x or y= - x)
covariance
negative
y tends to be smaller when x larger
covariance
positive
if y tends to be larger when x is larger
why?
𝑥𝑖 − 𝑥̅ and 𝑦𝑖 − 𝑦̅ then tend to have the same sign
Dependent vs independent
Dependent variable assumed to depend upon independent variable
Independent on X axis
Dependent on Y axis
Bivariate data
two variables measured together
i.e. at different times / locations / specimens for sample
Scatter plots
useful for detecting relationships
plot variables on x and y axes to visualise data as points
Measure of association
required to quantify relationships between variables
--> where covariacne & correlation come in