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BUAD 310 hw 6

# BUAD 310 hw 6 - Ryan Sanders 7164539701 BUAD 310 Fall 2009...

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Ryan Sanders 7164539701 BUAD 310 – Fall 2009 - Dr. Arif Ansari Topics Covered – Regression Homework # 6 - 100 points (Due date 11/30/09) – Note: Time Extension For Home Work 3, Turn in Question 1(30 points), Parts (a)-(e), Question 2 (40 points turn in all parts), Question 3 ( 20 points) and Question 4 (10 points) Question 1 (30 points) Power Companies must be able to predict the peak power load at their various stations in summer months to operate efficiently. The peak power load is the maximum amount of power that must be generated each day to meet demand. Trojan Electric Power wants to predict the peak power load during summer; the peak power load is nonlinear with respect to temperature in summer months. Trojan power collected the data for a random sample of 25 summer days and built 2 polynomial models to predict the peak power load. The descriptive statistics and “2” Models are given below, analyze and help select the best model. The Y variable is peak power load in Megawatts. The X variable is Temperature in Fahrenheit °F Descriptive Statistics: Peak Power, Temperature Variable N Mean SE Mean StDev Min Q1 Median Q3 Peak Power 25 _____ 5.11 _____ 92.50 104.50 116.50 142.15 Temperature 25 87.44 2.37 11.86 67.00 77.50 89.00 96.50 Variable Maximum Peak Power 189.30 Temperature 108.00 Model 1 - THE FIRST ORDER MODEL Y = Peak Power, X = Temperature 1

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Graph 1 Temperature Peak Power 110 100 90 80 70 200 180 160 140 120 100 Scatterplot of Peak Power vs Temperature Regression Analysis: Peak Power versus Temperature The regression equation is Peak Power = - 47.4 + 1.98 Temperature Predictor Coef SE Coef T P Constant -47.39 15.67 -3.02 0.006 Temperature 1.9765 0.1776 11.13 0.000 S = 10.3236 R-Sq = 84.3% R-Sq(adj) = 83.7% Analysis of Variance Source DF SS MS F P Regression 1 13196 13196 123.82 0.000 Residual Error 23 2451 107 Total 24 15648 Unusual Observations Obs Temperature Peak Power Fit SE Fit Residual St Resid 4 108 189.30 166.06 4.20 23.24 2.46R R denotes an observation with a large standardized residual. 2 This is the Scatter plot of Peak Power Vs Temperature Graph 1
Graph 2 Temperature Standardized Residual 110 100 90 80 70 3 2 1 0 -1 -2 Residuals Versus Temperature (response is Peak Power) THE SECOND MODEL Second order model Y = Peak Power, X1 = Temperature, X2 = Temperature-Squared The regression equation is Peak Power = 385 - 8.29 Temperature + 0.0598 Temperature-Sq Predictor Coef SE Coef T P Constant 385.05 55.17 6.98 0.000 Temperature -8.293 1.299 -6.38 0.000 Temperature-Sq 0.059823 0.007549 7.93 0.000 S = 5.37620 R-Sq = 95.9% R-Sq(adj) = 95.6% Analysis of Variance Source DF SS MS F P Regression 2 15011.8 7505.9 259.69 0.000 Residual Error 22 635.9 28.9 Total 24 15647.7 Source DF Seq SS Temperature 1 13196.4 Temperature-Sq 1 1815.4 Unusual Observations Obs Temperature Peak Power Fit SE Fit Residual St Resid 4 108 189.30 187.23 3.45 2.07 0.50 X 21 100 143.60 154.03 1.65 -10.43 -2.04R Durbin-Watson statistic = 2.20408 3 Residual Plot for Model 1 Graph 2

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Graph 3 Standardized Residual Percent 2 1 0 -1 -2 99 90 50 10 1 Fitted Value Standardized Residual 180 160 140 120 100 2 1 0 -1 -2 Standardized Residual Frequency 2 1 0 -1 -2 6.0 4.5 3.0 1.5 0.0 Observation Order 24 22 20 18 16 14 12 10 8 6 4 2 2 1 0 -1 -2 Normal Probabilit y Plot  of t he Residuals Residuals Versus t he Fit t ed Values Hist ogram of t he Residuals Residuals Versus t he Order of t he Dat a Residual Plots for Peak Power Graphs 4 and 5 Temperature
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BUAD 310 hw 6 - Ryan Sanders 7164539701 BUAD 310 Fall 2009...

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