Correlation Flashcards
What is correlation?
measures strength of relationships between 2 variables; is one trait associated with another?
What are examples of correlation?
-Is height at withers in beef cattle associated with
body length?
-Is weight of a dairy cow related to amount of milk
produced?
What is correlation represented by?
r
What does r measure?
- the degree of association between 2 variables (traits) in a sample from a population
- the degree of tightness of the relationship between 2 traits
What range does correlation have?
-1.0 to +1.0 (-0.99 to +0.99)
What does a correlation range tell us?
the magnitude of the relationship (high or low) and the direction (positive or negative)
What does a correlation of +1.0 indicate?
for each standard unit increase in one variable, there is a standard unit increase in the correlated trait
What does a significant correlation mean?
that there is a high probability that there is a real association between the traits
What does * next to a correlation number mean?
number has been subject to many tests to see if it is accurate and is 95% of the time (p<0.05)
What does ** next to a correlation number mean?
99% accurate
Does correlation have a unit?
no it is unitless
Can correlation be used to predict the level of one variable based on another?
no
Correlation doesn’t equal_____.
causation
Why doesn’t correlation show cause and effect?
r provides no evidence as to which variable is the cause and which is the effect
Does hip height and weight have a positive or negative correlation?
positive
Does milk yield and fat % have a positive or negative correlation?
negative
Does weight and heart girth have a positive or negative correlation?
positive
Does weaning weight and yearling weight have a positive or negative correlation?
positve
Does lean cuts and backfat have a positive or negative correlation?
negative
How do you calculate the correlation coefficient?
know formula
What does a correlation coefficient of 0.01-0.2 mean?
low correlation
What does a correlation coefficient of 0.2-0.4 mean?
moderate/medium correlation
What does a correlation coefficient of >0.4 mean?
large correlation
What are the most common correlations in animal breeding?
phenotypic, genotypic, and environmental
What is phenotypic correlation?
measures the strength of relationship between performance (phenotypic value) in one trait and performance in another trait
What is genetic correlation?
measures the strength of relationships between breeding value for one trait and breeding value for the other
Why is genetic correlation important?
because of the concept of correlated response to selection
What is the concept of correlated response to selection?
select for one trait and get response in another trait that you aren’t focusing on
What is more important than phenotypic correlation?
genotypic
What is an example of correlated response to selection?
as milk yield increases and is selected for, milk fat decreases because (?)
What are the reasons for correlated response?
gene linkage, pleiotropy
What is pleiotropy?
one gene affects more than one trait
Is negative correlation bad?
NO, it just means as one increases the other decreases. It isn’t bad just as a positive correlation isn’t always good
What is environmental correlation?
measure of strength of the relationship between environmental effects
What is environmental correlation often used for?
management purposes
What is rp (subscript)?
phenotypic correlation
What is rg (subscript)?
genotypic correlation
What is re (subscript)?
environmental correlation
What is regression coefficient?
measures the change in Y response per unit change in X (shows one is cause and one is effect variable)
What is the formula for regression?
Y=a+bx
What does Ŷ represent?
predicted value of Y
What does x represent?
independent (cause) variable; X observation
What does “a” represent?
intercept for y axis
What does b represent?
regressive coefficient (slope)
How is regression coefficient expressed?
within a given range of values, positive or negative
What can regression coefficient be used to predict?
one value based on another
What does regression coefficient have?
representative units of traits of interest
What is Ῡ?
mean of Y observations
What does Y represent?
dependent (effect) variable
What does Y represent?
dependent (effect) variable
What is X (line above)?
mean of X observations
What is the equation of a straight line?
Y=a + bx
The greater the slope…..
the closer the association between 2 traits
b=0 means?
no correlation
b=0.7 means?
relatively close association
When is correlation not applicable?
outside range of values used
How many observations are better for correlation?
more
How much degree of variation is better for correlation?
less
What is regression?
the average of expected change in variable Y per unit change in X
How are X and Y expressed for Regression?
in terms of their original units of measure
What is byx (yx are subscript)?
the regression of Y on X
What does regression assume?
an assumption of cause and effect
What does variation in trait X influence?
variation in trait Y
What is the cause and effect in weaning weight of cattle?
age is the cause of variation in weight, weight is the effect
When is regression used?
when we want to predict the numerical value of one trait from the phenotypic value of another
Is it easy to measure Y directly?
no it may be difficult or expensive
Why can selecting for Y be expensive/difficult?
slaughtering best animals to determine qualities (yield grade or cutability of pork carcasses)
