Exam3ReviewSp2011 - Review for Final Exam Stat 205...

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

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

View Full Document Right Arrow Icon
Final Exam Overview of Final Exam Logistics... * Open book, not open notes . Bring a calculator. * You can put post-it 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 9-11, Tuesday/Thursday 11-12, & Wednesday 11-1 in LeConte 215A. Dr. Hanson’s office hours: Monday/Wednesday 1:30-2:30, & Tuesday 1-2. T. Hanson (USC) Stat 205: Statistics for the Life Sciences 2 / 20
Image of page 2
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 0 + 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 0 + b 1 x , where b 0 and b 1 are the least squares estimates of β 0 and β 1 : b 1 = ( x i - ¯ x )( y i - ¯ y ) ( x i - ¯ x ) 2 b 0 = ¯ y - b 1 ¯ x T. Hanson (USC) Stat 205: Statistics for the Life Sciences 3 / 20
Image of page 3

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

View Full Document Right Arrow Icon
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 0 - 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 0 + 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
Image of page 4
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 0 : β 1 = 0 at level α , see if confidence interval from (a) includes zero. If not, reject H 0 : β 1 = 0. * If you reject H 0 : 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 0 - 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
Image of page 5

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

View Full Document Right Arrow Icon
Final Exam Linear regression Example A criminologist studying the relationship between level of education and crime rate in medium-sized 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 high-school diploma. Here’s a scatterplot: 60 65 70 75 80 85 90 2 4 6 8 10 14 highschool crimes T. Hanson (USC) Stat 205: Statistics for the Life Sciences 6 / 20
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern