10: Statistical Characterization of a Population 3

Question 1

Covariance, correlation and regression are ________________ _____________ and these measures are _________________ ______________

Answer 1

mathematically related
population parameters

Question 2

Covariance tells us the… And does not inform whether the outcome of the relationship will be…

Answer 2

The direction of the relationship btw two variables/values
Beneficial

Question 3

Covariance can range from…

Answer 3

-inf to inf

Question 4

Correlation is…
Equation?

Answer 4

A function of covariance between two traits and their standard deviations

r(x,y)= cov(X,Y)/sdX*sdY

Question 5

Values for correlation coefficient range from

Answer 5

-1 to +1

Question 6

r(x,y) = +1 tells us… 0 tells us… -1 tells us…

Answer 6

+1 = very strong and positive correlation (+ covariation)

0 = no correlation (no covariation)

-1 = very strong and negative correlation (negative covariation)

Question 7

Number for correlation that is weak, moderate or large

Answer 7

Weak = 0.10 to 0.30
Moderate = 0.30 to 0.50
Strong = 0.50 to 1

(or opposite for neg)

Question 8

What is a correlation heatmap

Answer 8

Shows the pattern of correlation between many traits
e.g. slide 15

Question 9

Notation for correlation of breeding value for trait X and BV for trait Y

Answer 9

r BVx, BVy

(BVx, BVy) is lowered

Question 10

Three types of correlation in animal breeding

Answer 10

Phenotypic, genetic and environment

Question 11

Regression measures…

Answer 11

the amount of change in one variable that can be expected for a given amount of change in another

Question 12

When is order of variables important in notation

Answer 12

Regression (there is dependent and independent variable)

Question 13

Equation for regression

Answer 13

b(y*x) = cov(X,Y)/ o^2x
slide 18

Question 14

The regression of variable Y on variable X is a simple function of the…

Answer 14

covariance between the variables and the variance of X

Question 15

Independent variable is… Dependent is..

Answer 15

in = X
dep = Y

Question 16

In the regression linear relationship of y = a + bx, what is b? a?

Answer 16

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)

Question 17

Positive regression indicates… Negative regression indicates…

Answer 17

Pos indicates an increase in one variable as the other increases

Neg indicates a decrease in one variable as the other increases

Question 18

Another way to write the regression euqation

Answer 18

Y = uY + byx * (X - ux)

slide 22

Question 19

Slide 23**

Answer 19

Using regression to predict traits e.g.

Question 20

Example of regression notation for BV of trait X and BV of trait Y

Answer 20

b BVy*BVx

Question 21

Slide 25-36

Answer 21

Example of evaluation of birth and weaning wight in angus calves (practice example)