511_Chap9 - Multiple Regression an Introduction Stat 511...

Info iconThis preview shows pages 1–17. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Multiple Regression – an Introduction Stat 511 Chap 9
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 case studies meadowfoam flowers brain size of mammals
Background image of page 2
3 case study 1: meadowfoam flowering designed experiment carried out in a growth chamber general goal of research: understand the biology of meadowfoam in order to elevate production response variable: number of flowers per plant
Background image of page 3

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

View Full DocumentRight Arrow Icon
4 two explanatory variables, one numeric and one categorical: light intensity timing of light six different light intensities two different times to start the light treatments
Background image of page 4
5 Both Factors Are Statistically Significant We are actually fitting two parallel lines See next slide (and page 238)
Background image of page 5

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

View Full DocumentRight Arrow Icon
6 30 40 50 60 70 80 FLOWERS 100 200 300 400 500 600 700 800 900 INTENS
Background image of page 6
7 case study 2: brain size of mammals observational study goal of research: biologists derive evolutionary conclusions from investigating which physiological characteristics are related to brain size response variable: brain weight 3 explanatory variables: body weight, gestation period, litter size
Background image of page 7

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

View Full DocumentRight Arrow Icon
8 Brain Size is Related to ?? Body Weight Gestation Time Litter Size
Background image of page 8
9 JMP Results; R-Sq =0.81 Notice p- values Intercept BODY GESTATION LITTER Term -225.2921 0.9858781 1.8087434 27.648639 Estimate 83.05875 0.094283 0.354449 17.41429 Std Error -2.71 10.46 5.10 1.59 t Ratio 0.0080* <.0001* <.0001* 0.1158 Prob>|t| Parameter Estimates
Background image of page 9

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

View Full DocumentRight Arrow Icon
10 Results: Brain Size is Related to Body Weight – no surprise Gestation Time Litter Size – not significant
Background image of page 10
11 Interpretation of Regression Coefficients 0 1 2 BrainSize gestation body b = + +
Background image of page 11

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

View Full DocumentRight Arrow Icon
12 Interpret b 1 The relationship between gestation and mean brain size after accounting for the effects of body size
Background image of page 12
13 multiple linear regression the culmination of our discussion this semester multiple linear regression methods include as special cases 1-sample t-tools 2-sample t-tools one-way ANOVA tools (separate means model) simple linear regression methods tools for many, many more models
Background image of page 13

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

View Full DocumentRight Arrow Icon
14 multiple linear regression specifies the mean of the response variable as an equation involving several (more than one) explanatory variables (e.g. μ {Y|X 1 ,X 2 }) usually unwise to think that there is some exact, discoverable regression equation often a few approximate but adequate regression equations that can be used to answer research questions
Background image of page 14
15 multiple linear regression the adjective linear in multiple linear regression does not mean that the models are restricted to things like straight lines means that the equation for the mean involves a linear combination of unknown regression coefficients, e.g. [ ] [ ] [ ] 3 2 1 0 } | { β μ + + + = . . . Y
Background image of page 15

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

View Full DocumentRight Arrow Icon
a few examples of multiple linear regression models ) log( ) log( } , | { } , | { } | { } , | { 2 2 1 1 0 2 1 2 1 3 2 2 1 1 0 2 1 2 1 2 1 1 0 1 2 2 1 1 0 2 1 X X X X Y X X X X X X Y X X X Y X X X X Y β μ = + + + = + + = + + = tilted flat plane in 3D space parabola (special curved line) in 2D space twisted tilted plane in 3D space curved surface in 3D space
Background image of page 16
Image of page 17
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/30/2011 for the course STAT 380 taught by Professor Stevens during the Spring '11 term at Brigham Young University, Hawaii.

Page1 / 47

511_Chap9 - Multiple Regression an Introduction Stat 511...

This preview shows document pages 1 - 17. Sign up to view the full document.

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