1. Why Design? (why not just observe and model?) CopyrightCopyright © Time and Date AS / Steffen Thorsen 1995-2006. All rights reserved. About us | Disclaimer | Privacy Create short URL to this page | Linking | Feedback: webmaster@timeanddate.com Home page | Site Map | Site Search | Date Menu | The World Clock | Calendar | CountdownAbout usDisclaimerPrivacy Create short URL to this pageLinkingwebmaster@timeanddate.com Home pageSite MapSite SearchDate MenuThe World ClockCalendar Countdown

2. Q: Why Experimental Design A: To avoid multicollinearity Issues: (1) Testing joint importance versus individual significance (2) Prediction versus modeling individual effects (3) Collinearity (correlation among inputs) Example: Hypothetical company’s sales Y depend on TV advertising X 1 and Radio Advertising X 2. Y =  0 +  1 X 1 +  2 X 2 +e Jointly critical (can’t omit both!!) Two engine plane can still fly if engine #1 fails Two engine plane can still fly if engine #2 fails Neither is critical individually

3. Data Sales; input store TV radio sales; (more code) cards; 1 869 868 9089 2 836 820 8290 (more data) 40 969 961 10130 proc g3d data=sales; scatter radio*TV=sales/shape=sval color=cval zmin=8000; run; TV Sales Radio

7. Conclusion: Can predict well with just TV, just radio, or both! SAS code: proc reg data=next; model sales = TV radio; Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 32660996 16330498 358.84 <.0001  (Can’t omit both) Error 37 1683844 45509 Corrected Total 39 34344840 Root MSE 213.32908 R-Square 0.9510  Explaining 95% of variation in sales Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 531.11390 359.90429 1.48 0.1485 TV 1 5.00435 5.01845 1.00 0.3251  (can omit TV) radio 1 4.66752 4.94312 0.94 0.3512  (can omit radio) Estimated Sales = 531 + 5.0 TV + 4.7 radio with error variance 45509 (standard deviation 213). TV approximately equal to radio so, approximately Estimated Sales = 531 + 9.7 TV or Estimated Sales = 531 + 9.7 radio

9. Regression The REG Procedure Model: MODEL1 Dependent Variable: sales Number of Observations Read 40 Number of Observations Used 40 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 32660996 16330498 358.84 <.0001 Error 37 1683844 45509 Corrected Total 39 34344840 Root MSE 213.32908 R-Square 0.9510 Dependent Mean 9955 Adj R-Sq 0.9483 Coeff Var 2.14291 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 531.11390 359.90429 1.48 0.1485 TV 1 5.00435 5.01845 1.00 0.3251 radio 1 4.66752 4.94312 0.94 0.3512

10. Design The REG Procedure Model: MODEL1 Dependent Variable: SALES Number of Observations Read 40 Number of Observations Used 40 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 32641505 16320753 358.66 <.0001 Error 37 1683699 45505 Corrected Total 39 34325204 Root MSE 213.31990 R-Square 0.9509 Dependent Mean 10300 Adj R-Sq 0.9483 Coeff Var 2.07111 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 530.72803 366.53079 1.45 0.1560 TV 1 5.00492 0.25552 19.59 <.0001 Radio 1 4.66742 0.25552 18.27 <.0001

11. Design matrix -1 for low level +1 for high 12 obs. HighLow High51 Low15 HighLow High33 Low33 X 1 X 2