Multiple%20Regression%20I - PowerPoint PPT Presentation

About This Presentation
Title:

Multiple%20Regression%20I

Description:

Multiple Regression I KNNL Chapter 6 Models with Multiple Predictors Most Practical Problems have more than one potential predictor variable Goal is to determine ... – PowerPoint PPT presentation

Number of Views:194
Avg rating:3.0/5.0
Slides: 16
Provided by: Larry381
Category:

less

Transcript and Presenter's Notes

Title: Multiple%20Regression%20I


1
Multiple Regression I
  • KNNL Chapter 6

2
Models with Multiple Predictors
  • Most Practical Problems have more than one
    potential predictor variable
  • Goal is to determine effects (if any) of each
    predictor, controlling for others
  • Can include polynomial terms to allow for
    nonlinear relations
  • Can include product terms to allow for
    interactions when effect of one variable depends
    on level of another variable
  • Can include dummy variables for categorical
    predictors

3
First-Order Model with 2 Numeric Predictors
4
Interpretation of Regression Coefficients
  • Additive EY b0 b1X1 b2X2 Mean of Y _at_
    X1, X2
  • b0 Intercept, Mean of Y when X1X20
  • b1 Slope with Respect to X1 (effect of
    increasing X1 by 1 unit, while holding X2
    constant)
  • b2 Slope with Respect to X2 (effect of
    increasing X2 by 1 unit, while holding X1
    constant)
  • These can also be obtained by taking the partial
    derivatives of EY with respect to X1 and X2,
    respectively
  • Interaction Model EY b0 b1X1 b2X2
    b3X1X2
  • When X2 0 Effect of increasing X1 by 1
    b1(1)b3(1)(0) b1
  • When X2 1 Effect of increasing X1 by 1
    b1(1)b3(1)(1) b1b3
  • The effect of increasing X1 depends on level of
    X2, and vice versa

5
General Linear Regression Model
6
Special Types of Variables/Models - I
  • p-1 distinct numeric predictors (attributes)
  • Y Sales, X1Advertising, X2Price
  • Categorical Predictors Indicator (Dummy)
    variables, representing m-1 levels of a m level
    categorical variable
  • Y Salary, X1Experience, X21 if College Grad,
    0 if Not
  • Polynomial Terms Allow for bends in the
    Regression
  • YMPG, X1Speed, X2Speed2
  • Transformed Variables Transformed Y variable to
    achieve linearity Yln(Y) Y1/Y

7
Special Types of Variables/Models - II
  • Interaction Effects Effect of one predictor
    depends on levels of other predictors
  • Y Salary, X1Experience, X21 if Coll Grad, 0
    if Not, X3X1X2
  • E(Y) b0 b1X1 b2X2 b3X1X2
  • Non-College Grads (X2 0)
  • E(Y) b0 b1X1 b2(0) b3X1(0) b0 b1X1
  • College Grads (X2 1)
  • E(Y) b0 b1X1 b2(1) b3X1(1) (b0
    b2)(b1 b3) X1
  • Response Surface Models
  • E(Y) b0 b1X1 b2X12 b3X2 b4X22 b5X1X2
  • Note Although the Response Surface Model has
    polynomial terms, it is linear wrt Regression
    parameters

8
Matrix Form of Regression Model
9
Least Squares Estimation of Regression
Coefficients
10
Fitted Values and Residuals
11
Analysis of Variance Sums of Squares
12
ANOVA Table, F-test, and R2
13
Inferences Regarding Regression Parameters
14
Estimating Mean Response at Specific X-levels
15
Predicting New Response(s) at Specific X-levels
Write a Comment
User Comments (0)
About PowerShow.com