1_Correlation and Regression

1_Correlation and Regression - Outline Advanced Topics in...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Fal 2007, C. Staudhammer Advanced Topics in Forest Biometrics - FOR6934 Review of correlation and Regression Fal 2007, C. Staudhammer Outline ± Correlation ± Simple Linear Regression (SLR) ² Formulae and degrees of freedom ² Hypothesis tests ² Assumptions ± Multiple Linear Regression ² Formulae and df ² Hypothesis tests ² Evaluating model fit ² Influence diagnostics ² Multicollinearity ² Model selection Fal 2007, C. Staudhammer Uses ± Often used to evaluate associations ± Continuous X and Y ± Common in mensurative (empirical observation) studies ± Used to characterize relationships between variables ± Used for parameter estimation for rates such as growth, survival Fal 2007, C. Staudhammer Correlation ± Used to evaluate the degree of association between two continuous variables x, y Birdwatcher Participation Shorebird Density Fal 2007, C. Staudhammer Causation? Fal 2007, C. Staudhammer Causation? Birdwatcher Participation
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Fal 2007, C. Staudhammer Correlation ∑∑ = 2 2 y x xy r ± r represents the linear association between x and y ± s r is the standard error of the correlation ± Usually used to imply associations rather than cause/effect 2 1 2 = n r s r Fal 2007, C. Staudhammer Correlation ± r can range from: ² -1 (complete negative relation between x, y) ² 0 (no relation) ² 1 (complete positive relation between x, y) ² Hypothesis test required to test whether r is significantly different from zero Fal 2007, C. Staudhammer Hypotheses and Testing r s r t = H o : ρ =0 H a : ρ≠ 0 Reject if: v t t ), 2 ( α = Where v = n-2 Fal 2007, C. Staudhammer Simple Linear Regression ± Attempt to find the linear relationship between x and y Model: y i = β 0 + 1 x i + ε i (population) y i = b 0 + b 1 x i + e i (sample) Predictions: ŷ i = b 0 + b 1 x i Errors: i i i y y e ˆ = * To find estimates of b o and b 1 , solve using least squares Fal 2007, C. Staudhammer Least Squares Fit Properties: 1. Always passes through ) , ( y x 2. Sum of residuals is zero, i.e., Σ e i =0 3. Sum of squared residuals is minimized in fit (least squares estimate) Fal 2007, C. Staudhammer 0.0 4.0 8.0 12.0 16.0 20.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 dbh h e i g h t i i y y ˆ i i y y ˆ i i y y ˆ i i y y ˆ
Background image of page 2
Fal 2007, C. Staudhammer Partitioning Variance Residual Regression 1 2 1 2 1 2 ) ˆ ( ) ˆ ( ) ( SS SS SS y y y y y y Total n i i i n i i n i i + = + = = = = Degrees of freedom?!?!?!
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/23/2011 for the course FOR 6934 taught by Professor Staff during the Spring '08 term at University of Florida.

Page1 / 9

1_Correlation and Regression - Outline Advanced Topics in...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online