Lec07.Bootstrap

# Lec07.Bootstrap - Bootstrap Resampling RegressionData...

This preview shows pages 1–11. Sign up to view the full content.

Bootstrap Resampling Applied to Normal and Non-normal  Regression Data KNNL 11.5

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

View Full Document
20 40 60 80 100 0 10 20 30 leaves Leaf Length
The Mean (Average Leaf Length) = = N i i X N 1 1 μ = = n i i x n x 1 1 Sample Sample Population Population

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

View Full Document
Measures of Variation for Two Different, but Related, Populations x n s s x x x n s x n i i of Variation of Variation ) ( 1 1 2 2 1 2 2 = - - = =
) 2 / ( 1 ) 2 / ( 1 ) ( ˆ α - - ± t x E S t x t-Distribution Confidence Intervals qt(.975,30)    2.042272 qt(.025,30)   -2.042272

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

View Full Document
To determine 95% confidence intervals from repeated sampling sample.means=rep(0,1000) for(i in seq(1000)) { sample.means[i]=            mean(sample(leaves,25)) } hist(sample.means)
60 65 70 75 80 0 50 100 150 200 250 sample.means Distribution of Sample Means

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

View Full Document
97.5 th quantile, 2.5 th quantile sorted.means=sort(sample.means) sorted.means[25]    63.2 sorted.means[975]    73.2 So, 95% CI is (63.2,73.2) The population mean will fall within a CI 95% of the time  under repeated sampling.
Using single sample calculations my.sample=sample(leaves,25) mean(my.sample)      66.8 sqrt(var(my.sample)/length(my.sample))       3.109126 qt(.975,25)       2.059539 66.8-2.06*3.1    # Lower bound      60.414 66.8+2.06*3.1    # Upper bound      73.186 Compare  (63.2, 73.2)  with  (60.4, 73.2)  from above. Both are estimates of what we would expect under  repeated sampling.

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

View Full Document
Resampling Confidence intervals, hypothesis testing  and many other types of inferences make  use of the idea of the probability under
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 36

Lec07.Bootstrap - Bootstrap Resampling RegressionData...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online