This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Review for Final Exam Stat 205: Statistics for the Life Sciences Tim Hanson, Ph.D. University of South Carolina T. Hanson (USC) Stat 205: Statistics for the Life Sciences 1 / 20 Final Exam Overview of Final Exam Logistics... * Open book, not open notes . Bring a calculator. * You can put postit notes in your book. * Thursday, April 28, 9am–noon. Be on time . * 3 regular problems, each worth 20 points: 60 total. * Rest of today’s lecture is reviewing this material. * 1 problem is short answer spanning entire course. * JeanMarie’s office hours next week: Monday 911, Tuesday/Thursday 1112, & Wednesday 111 in LeConte 215A. Dr. Hanson’s office hours: Monday/Wednesday 1:302:30, & Tuesday 12. T. Hanson (USC) Stat 205: Statistics for the Life Sciences 2 / 20 Final Exam Linear regression 12.1, 12.2, 12.3, 12.4: Linear regression * Have scatterplot of n paired values ( x 1 , y 1 ), ( x 2 , y 2 ), ... ,( x n , y n ). * Theoretical model: Y i {z} observed = β + β 1 x i  {z } unknown trend + ² i {z} slop * We use data ( x 1 , y 1 ), ( x 2 , y 2 ), ... ,( x n , y n ) to obtain the fitted line Y = b + b 1 x , where b and b 1 are the least squares estimates of β and β 1 : b 1 = ∑ ( x i ¯ x )( y i ¯ y ) ∑ ( x i ¯ x ) 2 b = ¯ y b 1 ¯ x T. Hanson (USC) Stat 205: Statistics for the Life Sciences 3 / 20 Final Exam Linear regression Linear regression * Estimate of var( ² i ) is s y  x = r SSE ( resid ) n 2 , where SS ( resid ) = X ( y i b b 1 x i ) 2 = X ( y i ˆ y i ) 2 . * s y = q 1 n 1 ∑ ( y i ¯ y ) 2 is overall variability of y 1 ,..., y n around the mean ¯ y . s y  x = q 1 n 2 ∑ ( y i ˆ y i ) 2 is overall variability of y 1 ,..., y n around the line b + b 1 x . * s y  x < s y . How much smaller tells you how “well” the line is working to explain the data. * HW: 12.3, 12.7, 12.9. T. Hanson (USC) Stat 205: Statistics for the Life Sciences 4 / 20 Final Exam Linear regression Linear regression * If we assume slop ² 1 ,...,² n are normal then SE b 1 = s y  x p ∑ ( x i ¯ x ) 2 . * Inference for β 1 : (a) (1 α )100% confidence interval for β 1 has endpoints b 1 ± t 1 α/ 2 SE b 1 , where df = n 2. (b) To test H : β 1 = 0 at level α , see if confidence interval from (a) includes zero. If not, reject H : β 1 = 0. * If you reject H : β 1 = 0 then x and y are significantly, linearly related . * 5 statistics needed: ¯ x , ¯ y , ∑ ( x i ¯ x ) 2 , ∑ ( x i ¯ x )( y i ¯ y ), SS ( resid ) = ∑ ( y i b b 1 x i ) 2 . * HW: 12.16, 12.17, 12.19, 12.23(a). T. Hanson (USC) Stat 205: Statistics for the Life Sciences 5 / 20 Final Exam Linear regression Example A criminologist studying the relationship between level of education and crime rate in mediumsized U.S. counties collected data from a random sample of n = 84 counties. Y is the crime rate (crimes per 100 people) and X is the percentage of individuals in the county having at least a...
View
Full
Document
This note was uploaded on 12/14/2011 for the course STAT 205 taught by Professor Hendrix during the Fall '09 term at South Carolina.
 Fall '09
 Hendrix
 Statistics

Click to edit the document details