Session10

Session10 - EMSE 171/271: DATA ANALYSIS For Engineers and...

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EMSE 171/271: DATA ANALYSIS For Engineers and Scientists Session 10: Multiple Regression, Residual Diagnostics, Outlier Detection, Comparing Imbedded Models, Forecasting Lecture Notes by: J. René van Dorp 1 www.seas.gwu.edu/~dorpjr 1 Department of Engineering Management and Systems Egineering, School of Engineering and Applied Science, The George Washington University, 1776 G Street, N.W. Suite 110, Washington ß D.C. 20052. E-mail: dorpjr@gwu.edu.
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EMSE 171/271 - FALL 2006 J.R. van Dorp - 11/24/05; ; Page 201 dorpjr@gwu.edu REGRESSION-CASE STUDY Data Exploration ID NAME DESCRIPTION Y PRICE Sale price in $000 per acre X 1 COUNTY Santa Mateo = 0, Santa Clara = 1 X 2 SIZE Size of the property in Acres X 3 ELEVATION Average elevation in feet above sea level X 4 SEWER Distance (in feet) to nearest sewer connection X 5 DATE Date of sale counting backward from current time (in months) X 6 FLOOD Subject to flooding by tidal action = 1; otherwise = 0 X 7 DISTANCE Distance in miles from Leslie property (in almost all case, this toward San Francisco Leslie Salt Property (1968): 246.8 Acres, right on San Francisco Bay, Exactly at sea level (but diked in). Mountan View, CA, began legal proceedings to acquire this land.
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EMSE 171/271 - FALL 2006 J.R. van Dorp - 11/24/05; ; Page 202 dorpjr@gwu.edu REGRESSION-CASE STUDY Data Exploration It was upto the courts to determine a fair market value. Hence, it was decided to build a regression model. Data collection: 31 bayland properties, that were sold during the previous 10 years. Y X 1 X 2 X 3 X 4 X 5 X 6 X 7 Data Price County Size Elevation Sewer Date Flood Distance 3 1.70 0 16.10 0 2640 -98 1 10.30 4 5.00 0 1695.20 1 3500 -93 0 14.00 6 3.30 1 6.90 2 10000 -86 0 0.00 26 37.20 0 15.00 5 0 -39 0 7.20 Observe great variability in the data. Sizes vary widely. One could expect that variability increases with the size of the property. Hence it was decided to focus on the price per acre Y. FIRST STEP: PLOT A HISTOGRAM OF THE DEPENDENT VARIABE.
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EMSE 171/271 - FALL 2006 J.R. van Dorp - 11/24/05; ; Page 203 dorpjr@gwu.edu REGRESSION-CASE STUDY Data Exploration MINITAB HISTOGRAM WITH NORMAL DISTRIBUTION FIT Price 30 20 10 0 12 10 8 6 4 2 0 Mean 11.95 StDev 7.715 N3 1 Histogram of Price Normal Observation: Histogram is skewed towards the left which could be problematic in the regression analysis.
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EMSE 171/271 - FALL 2006 J.R. van Dorp - 11/24/05; ; Page 204 dorpjr@gwu.edu REGRESSION-CASE STUDY Data Exploration Recall, the dependent variable is a linear sum and the error term is ] a resultant of measurement error due to multiple independent variables \ßáß\Þ ": Hence one could expect something more "bell-shaped". Price Percent 40 30 20 10 0 -10 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean 0.069 11.95 StDev 7.715 N3 1 AD 0.677 P-Value Probability Plot of Price Normal - 95% CI Normal Probability Plots indicates non-normality of the dependent variable . ]
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EMSE 171/271 - FALL 2006 J.R. van Dorp - 11/24/05; ; Page 205 dorpjr@gwu.edu REGRESSION-CASE STUDY Data Exploration In the case of asymmetry in the variable of interest, one attempts to transform this variable (a trial and error exercise) until one achieves symmetry.
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Session10 - EMSE 171/271: DATA ANALYSIS For Engineers and...

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