Why Design? (why not just observe and model?) CopyrightCopyright © Time and Date AS / Steffen Thorsen 1995-2006. All rights reserved. About us | Disclaimer.

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

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

Data Sales; input store TV radio sales; (more code) cards; (more data) proc g3d data=sales; scatter radio*TV=sales/shape=sval color=cval zmin=8000; run; TV Sales Radio

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 <.0001  (Can’t omit both) Error Corrected Total Root MSE R-Square  Explaining 95% of variation in sales Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept TV  (can omit TV) radio  (can omit radio) Estimated Sales = TV radio with error variance (standard deviation 213). TV approximately equal to radio so, approximately Estimated Sales = TV or Estimated Sales = radio

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 <.0001 Error Corrected Total Root MSE R-Square Dependent Mean 9955 Adj R-Sq Coeff Var Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept TV radio

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 <.0001 Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept TV <.0001 Radio <.0001

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