2 df se b b t 005 2 18 se b 10139 2100041

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: df SE b b ! "0 t= SEb Example: 95% confidence interval for slope of smoking / excise tax relationship b ± t! [ 2 ],df SE b = b ± t 0.05[ 2 ],18 SE b = 1.0139 ± 2.10(0.041) = 1.0139 ± 0.0866 Hypothesis tests can use t: Confidence bands: confidence intervals for predictions of mean Y Prediction intervals: confidence intervals for predictions of individual Y Hypothesis tests on slopes H 0: HA: =0 !0 t= Non-linear relationships Transformations Quadratic regression Splines t= b ! "0 SEb 1.0139 ! 0 = 24.58 0.041 t0.05(2),18= ±2.10 So we can reject H0 Transformations If Y = aX b then ln Y = ln a + b ln X . If Y = ab X then ln Y = ln a + X ln b . If Y = a + Non-linear relationship: Number of fish species vs. Size of desert pool b 1 then set X ! = , and calculate Y = a + bX ! . X X All of the equations on the right have the form Y=a+bX. Residual plots help assess assumptions Original: Residual plot Transformed data Logs: Residual plot Polynomial regression Do not fit a polynomial with too many terms (the sample size should be at least 7 times the number of terms) Number of species = 0.046 + 0.185 Biomass - 0.00044 Biomass2 Comparing two slopes Example: Comparing species-area curves for islands to those of mainland populations L og10(Number o f s pecies) B y L og 1 0(Area o f " island") 2.5 Hypotheses H 0: HA: M = # I. I. M Log10(Number of species) 2.0 1.5 1.0 0.5 -1 0 1 2 3 4 5 Log 10(Area of "island") Linear Fit Type of island=I Linear Fit Type of island=M 6 7 Linear F it T ype o f i sland=I Log10(Number of species) = 0.24537 + 0.27554 Log 10(Area of "island") Summary o f F it RSquare RSquare Adj Root Mean Square Error Mean of Response Obs...
View Full Document

Ask a homework question - tutors are online