Mba512 Multiple Regression Notes
Upcoming SlideShare
Loading in...5
×
 

Like this? Share it with your network

Share

Mba512 Multiple Regression Notes

on

  • 4,089 views

'Enhanced' Textbook Lecture Notes

'Enhanced' Textbook Lecture Notes

Statistics

Views

Total Views
4,089
Views on SlideShare
4,089
Embed Views
0

Actions

Likes
2
Downloads
75
Comments
0

0 Embeds 0

No embeds

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

Mba512 Multiple Regression Notes Document Transcript

  • 1. Learning Objectives Statistics for Managers In this chapter, you learn: Using Microsoft® Excel  How to develop a multiple regression model  How to interpret the regression coefficients 5th Edition  How to determine which independent variables to include in the regression model  How to determine which independent variables are most important in predicting a dependent variable Chapter 14  How to use categorical variables in a regression model Introduction to Multiple Regression Some revisions made by Jennifer J. Edmonds, PhD @ Wilkes University Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-1 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-2 The Estimated The Multiple Regression Model Multiple Regression Equation The coefficients of the multiple regression model are estimated using sample data Examine the linear relationship between 1 dependent (Y) & 2 or more independent variables (Xi). Multiple regression equation with k independent variables: Multiple Regression Model with k Independent Variables: Estimated Estimated (or predicted) Estimated slope coefficients intercept value of Y Y-intercept Population slopes Random Error ˆ Yi b0 b1X1i b2 X2i  bk Xki Yi β 0 β1X1i β 2 X 2i  β k X ki εi Still only For every independent variable (xi), there is a For every independent variable (xi), we estimate a one corresponding slope (bi) Some revisions made by Jennifer J. Edmonds, PhD @ Wilkes University corresponding slope (bi) Some revisions made by Jennifer J. Edmonds, PhD @ Wilkes University intercept Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-3 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-4 1
  • 2. Coefficient of Regression Analysis Multiple Determination When performing a regression analysis, use this list as a guide…  Reports the proportion of total variation in Y Define the variables Describe the relationship explained by all X variables taken together Calculate the regression coefficients How good is the model? SSR regressionsum of squares Is the model significant? r2 Is each x variable significant? SST total sum of squares Some revisions made by Jennifer J. Edmonds, PhD @ Wilkes University Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-6 Test Adjusted r2 for Overall Significance  r2 never decreases when a new X variable is Is there a linear relationship between all of the X added to the model variables considered together and Y?  This can be a disadvantage when comparing models…  Examines the effect of using regression analysis to  What is the net effect of adding a new variable? describe the relationship between X(‘s) and Y  We lose a degree of freedom when a new X variable is  To examine this effect, we compare the variability (in Y) added explained by the regressionFanalysis to the variability due to 0  Did the new X variable add enough independent power randomness (noise) to offset the loss of one degree of freedom?  Variability comparisons require a different test than mean comparisons Some revisions made by Jennifer J. Edmonds, PhD @ Wilkes University Some revisions made by Jennifer J. Edmonds, PhD @ Wilkes University Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-7 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-8 2
  • 3. F-Test F-Test for Overall Significance for Overall Significance  H0: β1 = β2 = 0 Test Statistic: Is there a linear relationship between all of the X  H1: β1 and β2 not both zero variables considered together and Y? MSR  = .05 F  Use F test statistic (to test the variance) MSE  df1= 2 df2 = 12 Decision: NULL H0: β1 = β2 = … = βk = 0 no linear relationship with any of Since F test statistic is in the rejection the variables region (p-value < .05), reject H0 Critical Value ALT H1: at least one βi ≠ 0 at least one independent variable = .05 has a relationship with Y Conclusion: 0 F There is evidence that at least one Do not Reject H0 Some revisions made by Jennifer J. Edmonds, PhD @ Wilkes University reject H0 F.05 = 3.89 independent variable affects Y Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-9 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-10 Individual Variables Multiple Regression Assumptions Tests of Hypothesis Is there a linear relationship between the variable Xi Errors (residuals) from the regression model: and Y? <  Use t-tests of individual variable slopes ei = (Yi – Yi)  Hypotheses: NULL H0: βi = 0 no linear relationship Assumptions: ALT H1: βi ≠ 0 linear relationship does exist  The errors are independent between Xi and Y  The errors are normally distributed  Errors have an equal variance Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-11 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-13 3
  • 4. Multiple Regression Assumptions Using Dummy Variables  These residual plots are used in multiple regression:  A dummy variable is a categorical <  Residuals vs. Yi independent variable with two levels:  Residuals vs. X1i  yes or no, on or off, male or female  Residuals vs. X2i  coded as 0 or 1  Residuals vs. time (if time series data)  Assumes equal slopes for other variables  If more than two levels, the number of dummy Use the residual plots to check for variables needed is violations of regression assumptions (number of levels) - 1 Some revisions made by Jennifer J. Edmonds, PhD @ Wilkes University Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-14 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-15 Dummy Variable Example Dummy Variable Example ˆ Y b0 b1X1 b2 (1) (b0 b2 ) b1X1 Holiday ˆ Y b0 b1X1 b 2 X 2 ˆ Y b0 b1X1 b2 (0) b0 b1X1 No Holiday Let: Y (sales) Different Same intercept slope Y = pie sales b0 + b2 If H0: β2 = 0 is X1 = price b0 rejected, then “Holiday” has a X2 = holiday (X2 = 1 if a holiday occurred during the week) significant effect (X2 = 0 if there was no holiday that week) on pie sales Some revisions made by Jennifer J. Edmonds, PhD @ Wilkes University X1 (Price) Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-16 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-17 4
  • 5. Chapter Summary In this chapter, we have  Tested individual regression coefficients  Tested portions of the regression model  Used dummy variables Some revisions made by Jennifer J. Edmonds, PhD @ Wilkes University Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 14-18 5