# 03/19/2003 Week #4 江支弘 Chapter 4 Making Predictions: Regression Analysis.

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03/19/2003 Week #4 江支弘 Chapter 4 Making Predictions: Regression Analysis

03/19/2003 Week #4 江支弘 Causation 因果關係 Smoking and Lung cancer: f5-9f5-9 Observed association Causation Common response 共同反應 Confounding 交絡, 混淆

03/19/2003 Week #4 江支弘 Association is not causation 相聯不代表因果關係 In the absence of an experiment, even a very strong association between an explanatory variable x and a response variable y does not guarantee changes in x really cause changes in y. f5-10

03/19/2003 Week #4 江支弘 Establishing causation 建立因果關係 Criteria for establishing causation without an experiment: 不能做實驗時, 確立因果關係的標準 Strong association; Consistent; Plausible cause

03/19/2003 Week #4 江支弘 Regression and Prediction 迴歸與預測 A regression line 迴歸線 is a straight line describing how a response variable 反應變數 or 因變數 y varies as an explanatory variable 解釋變數 or 自變數 x changes. Least square 最小平方差 regression line of y on x: sum of squares is minimum, f4-2f4-2

03/19/2003 Week #4 江支弘 Measuring Variability 度量變異性 Standard error of the estimate about the regression line 估計值相對於回歸線的標準誤 差 S YX (p95) Sample standard deviation of the individual Y observations 觀察值的樣本標準差 S Y (p96)

03/19/2003 Week #4 江支弘 Figure 4-3

03/19/2003 Week #4 江支弘 Correlation and Regression Analysis 相關係數與迴歸分析 Correlation coefficient r (p105) F4-6

03/19/2003 Week #4 江支弘 Figure 4-6

03/19/2003 Week #4 江支弘 Figure 4-6f

03/19/2003 Week #4 江支弘 r 2 in regression Square of the correlation, r 2, is the fraction of the variation in the values of y, which is explained by L.S. regression of y on x 可以用 y 對 x 的最小平方回歸解釋一部份 “ y 值的 變異性 ” [Lapin] sample coefficient of determination

03/19/2003 Week #4 江支弘 Multiple Regression Analysis 多重迴歸分析 3-D scatter plot Ex. Mileage and Octane, TB4-4TB4-4 3-D surface plot #1 #2 Regression coefficients, p109 Advantages: F4-9F4-9

03/19/2003 Week #4 江支弘 3-D Scatter Plot

03/19/2003 Week #4 江支弘 3-D Surface Plot

03/19/2003 Week #4 江支弘 3-D Surface  Regression Plane

03/19/2003 Week #4 江支弘 Figure 4-9a

03/19/2003 Week #4 江支弘 Figure 4-9b

03/19/2003 Week #4 江支弘 Figure 4-9c

03/19/2003 Week #4 江支弘 Residuals and Standard Error 殘差與標準誤差 Standard error of the estimate S Y12  variability in Y about the regression plane (p113) 殘差 Residuals  Vertical Deviations Y - Standard error for the regression line S YX 1 > S Y12

03/19/2003 Week #4 江支弘 Regression with Many Variables 多變數迴歸 Load  X 3, p115

03/19/2003 Week #4 江支弘 Building Empirical Model 建立經驗模式 Montgomery, Runger, Hubele, §6-1, §6-26-2 Monte, § 6-7 (S7.ppt)S7

03/19/2003 Week #4 江支弘 圖 5-6

03/19/2003 Week #4 江支弘

03/19/2003 Week #4 江支弘

03/19/2003 Week #4 江支弘

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