An Sci 361 1st Edition Lecture 16 Outline of Last Lecture I. StatisticsII. Estimationa. Of populationb. Of IndividualIII. Normal Distributiona. Histogramsb. Quincunx (or “Galton Board”)IV. The Meana. EquationV. Variationa. MeasuresVI. Heritabilitya. EquationOutline of Current Lecture I. Covariationa. Positiveb. Negativec. MeasuresII. Covariance’s and the Genetic ModelIII. RegressionCurrent LectureCovariation: How 2 traits vary together- Positive:o Birth weight and yearling weight in beef cattle- Negative:o Disease and yield traits in dairy cattle- Measures:N1iYiXiY,X)Y)(X(N1)Y,XC ov(Genetic ModelThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- P = μ + BV + GCV + Eo P = Phenotype (random)o μ = Mean (fixed)o BV = Breeding Value (random)o GCV = Gene Combination Value (random)o E = Environment (random)- Rule: Variance of a sum of random variableso Y = X + Z Var (Y) = Var (X) + Var (Z) + 2Cov (X, Z)- In general, it is assumed that BV, GCV, and E are independent.Measure of CovariationCorrelation: Strength of the relationship between 2 random variables- Notation: Correlation between variables X and Y = px,y or rx,yRegression (Prediction EquationRegression Coefficient: Amount of change in one variable (dependent variable) that can be expected from a one-unit change in the other variable (independent variable).- Note: Strong correlation does not necessarily imply a large regression
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