10: Statistical Characterization of a Population 3 Flashcards
Covariance, correlation and regression are ________________ _____________ and these measures are _________________ ______________
mathematically related
population parameters
Covariance tells us the… And does not inform whether the outcome of the relationship will be…
The direction of the relationship btw two variables/values
Beneficial
Covariance can range from…
-inf to inf
Correlation is…
Equation?
A function of covariance between two traits and their standard deviations
r(x,y)= cov(X,Y)/sdX*sdY
Values for correlation coefficient range from
-1 to +1
r(x,y) = +1 tells us… 0 tells us… -1 tells us…
+1 = very strong and positive correlation (+ covariation)
0 = no correlation (no covariation)
-1 = very strong and negative correlation (negative covariation)
Number for correlation that is weak, moderate or large
Weak = 0.10 to 0.30
Moderate = 0.30 to 0.50
Strong = 0.50 to 1
(or opposite for neg)
What is a correlation heatmap
Shows the pattern of correlation between many traits
e.g. slide 15
Notation for correlation of breeding value for trait X and BV for trait Y
r BVx, BVy
(BVx, BVy) is lowered
Three types of correlation in animal breeding
Phenotypic, genetic and environment
Regression measures…
the amount of change in one variable that can be expected for a given amount of change in another
When is order of variables important in notation
Regression (there is dependent and independent variable)
Equation for regression
b(y*x) = cov(X,Y)/ o^2x
slide 18
The regression of variable Y on variable X is a simple function of the…
covariance between the variables and the variance of X
Independent variable is… Dependent is..
in = X
dep = Y
In the regression linear relationship of y = a + bx, what is b? a?
b = regression coefficient, aka the slope of the best line that indicates a linear relationship btw X and Y
a = the intercept of the linear regression line (b=0)
Positive regression indicates… Negative regression indicates…
Pos indicates an increase in one variable as the other increases
Neg indicates a decrease in one variable as the other increases
Another way to write the regression euqation
Y = uY + byx * (X - ux)
slide 22
Slide 23**
Using regression to predict traits e.g.
Example of regression notation for BV of trait X and BV of trait Y
b BVy*BVx
Slide 25-36
Example of evaluation of birth and weaning wight in angus calves (practice example)
